pedro_jurado_ygt_finalreport

___________________________________

FINAL REPORT

OF THE

YOUNG GRADUATE TRAINEESHIP (YGT)

MTG IMAGE NAVIGATION & REGISTRATION PERFORMANCE SIMULATION

IN THE OPTICAL INSTRUMENT SECTION

INSTRUMENT PRE-DEVELOPMENT DIVISION EARTH OBSERVATION PROJECTS DEPARTMENT

EARTH OBSERVATION DIRECTORATE

___________________________________

Author: Pedro José Jurado Lozano

Traineeship Duration: May 2008 – May 2009

Address Code: EOP-PIO

Supervisor: Donny Aminou

Final Report – Pedro José Jurado Lozano May 2009

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Preface

This Young Graduate Trainee (YGT) Position was created not only to provide some training to the selected YGT, but also to allow me as a supervisor to have a different view of the problematics of MTG Image Navigation and Registration (INR).

Going from a Spinning satellite with super stable spin rate giving stability to the satellite (MSG) to a three-axis stabilised satellite (MTG) for imaging mission in geostationary orbit is the first time for ESA. After trade-off between radiometry, image repeat cycle and image geometric performance, the choice was clear to go for the three-axis stabilised satellite.

Now, the INR is one of the key elements to get the satellite to work at the performance required by the end users. For that, Pedro José Jurado Lozano was selected as an YGT for his skills in maths, attitude control simulations …

His work focused in - understanding the software and algorithms delivered by MTG primes on MTG image quality assessment tools (MTG phase A), - producing concurrent tools capable of performing satellite INR using the observables from the satellite (star trackers, gyroscope, scanning law, orbit knowledge, ADCS, etc…) and using ground landmarks and horizon etc.... My goodness, this was a very difficult task. For that, Pedro has managed to sample Earth images as could be seen by MTG imaging satellite, including image deformations induced by the scan law, thermo-elastic deformations assumptions are taken and other perturbations coming from the satellite considered; He used image analysis (image processing, thus state vectors, landmarks, observables and other appropriate algorithms); He performed covariance analysis and Kalman filtering using Matlab. He has been able to address problems relevant to the various aspects of MTG satellite navigation and image navigation, thus providing us some hints on the problems we will have to face in putting in place the overall MTG INR.

In addition, Pedro José was always available for help on other fields. For instance, he was able to compute under request, the sun glint behaviour of MTG imager. This part of his work is also included in this final report.

It was very nice working with you Pedro.

Donny Aminou

MTG Phase A Technical Officer

MTG Payload Manager


of 97 INTRODUCTION

Table of Contents

1 Introduction.......................................................................................................................................9

1.1 Scope of the Document .............................................................................................................9

1.2 Applicable Documents ..............................................................................................................9

1.3 Reference Documents................................................................................................................9

1.4 Bibliography............................................................................................................................10

1.5 List of Abbreviations...............................................................................................................10

2 Traineeship in the “Instrument Predevelopment Division”........................................................12

2.1 Organization and Duties ..........................................................................................................12

2.2 The Living Planet Programme.................................................................................................14

2.2.1 Earth Explorer Missions .....................................................................................................14

2.2.2 Earth Watch Missions.........................................................................................................14

3 Meteosat Third Generation Mission .............................................................................................15

3.1 Introduction .............................................................................................................................15

3.2 MTG mission definition ..........................................................................................................15

3.3 MTG space segment configuration .........................................................................................16

3.4 MTG system driver .................................................................................................................17

4 Image Navigation and Registration Overview..............................................................................18

4.1 Introduction .............................................................................................................................18

4.2 Definitions...............................................................................................................................18

4.2.1 Image Navigation ...............................................................................................................18

4.2.2 Image Registration..............................................................................................................18

4.3 INR performance requirements ...............................................................................................19

4.4 Evaluating INR performance requirements .............................................................................19

4.5 INR types of correction ...........................................................................................................20

5 Image Navigation and Registration For Geostationary Weather Satellites...............................21

5.1 Introduction .............................................................................................................................21

5.2 Geostationary weather missions ..............................................................................................21

5.3 Satellites designs and their impact on the INR system............................................................23

5.3.1 Meteosat and spinners ........................................................................................................23

5.3.2 GOES-I-M and three-axis stabilized platforms with momentum bias................................24

5.3.3 MTSat-2 and three-axis stabilized platforms without momentum bias ..............................24

5.3.4 GOES NO/P/Q and three-axis stabilized platforms with Stellar Inertial Navigation .........25

5.4 Error Sources and Compensation on the INR system .............................................................26

5.4.1 Attitude Errors ....................................................................................................................26

5.4.2 Orbit Errors.........................................................................................................................27

5.4.3 Thermal Distortions............................................................................................................28


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5.4.4 Instrument Pointing Control Errors ....................................................................................29

5.4.5 Uncompensated Disturbance Torques ................................................................................29

5.4.6 Dynamic Interactions..........................................................................................................29

5.4.7 Station Keeping ..................................................................................................................29

6 MTG Image Navigation and Registration Performance Simulator ...........................................30

6.1 Introduction .............................................................................................................................30

6.2 Objectives of the simulator......................................................................................................30

6.3 General principles of the simulator .........................................................................................30

6.3.1 The image simulation mode................................................................................................31

6.3.2 The landmarks simulation mode.........................................................................................31

6.4 General architecture of the simulator ......................................................................................31

7 Scanning Concept ...........................................................................................................................34

7.1 Introduction .............................................................................................................................34

7.2 Assumptions & Constraints.....................................................................................................34

7.3 Scanning Concepts Identification............................................................................................34

7.4 Candidate Scanning Concepts .................................................................................................35

7.5 Brief Overview and Baseline of the Scanning Concepts Impact.............................................36

7.5.1 Accommodation aspects .....................................................................................................36

7.5.1.1 Telescope ..................................................................................................................36

7.5.1.2 Scan assembly ...........................................................................................................36

7.5.1.3 Calibration.................................................................................................................37

7.5.2 Thermal aspects ..................................................................................................................37

7.5.3 Structural aspects................................................................................................................37

7.5.4 Scanning concept baseline..................................................................................................37

7.6 Scanning Mirror Law Calculation ...........................................................................................37

7.7 Scanning Mirror Torques ........................................................................................................39

8 Attitude & Orbit Control Subsystem simulation .........................................................................40

8.1 Introduction .............................................................................................................................40

8.2 MTG INR-PS and AOCS simulator interface .........................................................................40

8.3 External AOCS simulation files ..............................................................................................41

8.4 Internal ACS simulator for Attitude data ................................................................................41

9 Line Of Sight simulation ................................................................................................................42

9.1 Introduction .............................................................................................................................42

9.2 General Direct Navigation Equation .......................................................................................42

9.3 Focal plane and Telescope geometry.......................................................................................43

9.3.1 Telescope Reference Frame................................................................................................43

9.3.2 General Model ....................................................................................................................43

9.3.3 Simplified Model................................................................................................................43


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9.4 Scanning geometry ..................................................................................................................45

9.4.1 Scanning assembly frame (SAF) ........................................................................................45

9.4.2 Instrument frame (IF) .........................................................................................................45

9.4.3 Mathematical model ...........................................................................................................46

9.5 Optical Site and Elevation angles calculation .........................................................................47

9.6 Focal Plane Mapping...............................................................................................................48

9.7 Satellite Attitude......................................................................................................................48

9.8 Satellite Orbit ..........................................................................................................................49

9.9 Intersection on the Earth..........................................................................................................50

9.10 Projection and Scaling.............................................................................................................51

9.10.1 Projection function.........................................................................................................51

9.10.2 Scaling function .............................................................................................................53

9.11 Time interpolation ...................................................................................................................53

10 Observables Selector.......................................................................................................................54

10.1 Introduction .............................................................................................................................54

10.2 State vector..............................................................................................................................54

10.3 Observables types....................................................................................................................54

10.4 Landmarks residuals calculation .............................................................................................55

10.4.1 Definition.......................................................................................................................55

10.4.2 Landmark Database .......................................................................................................55

10.4.3 Landmarks Position Determination ...............................................................................58

10.4.4 Landmarks in image overlapping zone ..........................................................................59

10.4.5 Landmarks residual calculation .....................................................................................59

10.5 Ranging stations residual calculation ......................................................................................60

10.6 Horizons residuals calculation.................................................................................................61

10.7 Stars residuals calculation .......................................................................................................61

10.7.1 Measuring the angle between the Earth and a Star ........................................................61

10.7.2 Star elevation measurement ...........................................................................................62

10.7.3 Star occultation measurement ........................................................................................63

10.7.4 Measuring the angle between two known directions .....................................................64

11 Navigation Filter .............................................................................................................................65

11.1 Introduction .............................................................................................................................65

11.2 System state model..................................................................................................................65

11.3 System state evolution.............................................................................................................66

11.4 System observables or input to the filter .................................................................................66

11.5 Filtering ...................................................................................................................................67

11.6 Outputs ....................................................................................................................................68

12 Performance Extractor...................................................................................................................69


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12.1 Introduction .............................................................................................................................69

12.2 General definition of the problem ...........................................................................................69

12.3 Statement of meaning of the problem......................................................................................70

12.4 Navigation residuals obtainment plan .....................................................................................71

13 Simulation Results ..........................................................................................................................72

13.1 Introduction .............................................................................................................................72

13.2 Landmarks residuals................................................................................................................72

13.3 Azimuth and Elevation Navigation errors ...............................................................................73

13.4 State parameters ......................................................................................................................74

13.5 Covariance analysis.................................................................................................................74

14 Possible Solution .............................................................................................................................76

14.1 Introduction .............................................................................................................................76

14.2 Attitude determination.............................................................................................................76

14.3 Attitude modelling...................................................................................................................76

14.4 Observation modelling ............................................................................................................77

14.4.1 The landmark observable...............................................................................................78

14.4.2 The Earth Edge observable ............................................................................................80

14.4.2.1 Spherical Earth Model ..............................................................................................80

14.4.2.2 Non-Spherical Earth Model ......................................................................................82

14.5 The sequential batch estimator ................................................................................................82

14.5.1 Summary of the sequential batch estimation algorithm is as follows ............................83

14.5.2 Calculation of the sensitivity matrix ..............................................................................84

14.5.2.1 Landmark observation partials ..................................................................................85

14.5.2.2 Earth Edge observations partials with spherical Earth model ...................................86

14.5.2.3 State partials..............................................................................................................87

15 MTG Sun-Glint Study ....................................................................................................................88

15.1 Introduction .............................................................................................................................88

15.2 Sun-glint definition .................................................................................................................88

15.3 Sun-glint algorithms ................................................................................................................89

15.3.1 General Algorithm .........................................................................................................89

15.3.1.1 Algorithm definition .................................................................................................89

15.3.1.2 Limitations ................................................................................................................91

15.3.2 Complete two dimensional algorithms ..........................................................................91


15.3.2.2 Limitations ................................................................................................................92

15.3.3 Two dimensional first-order algorithm..........................................................................93


15.3.3.2 Limitations ................................................................................................................93


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15.3.4 Simplified algorithm......................................................................................................93


15.3.4.2 Limitations ................................................................................................................94

15.4 MTG sun-glint simulation .......................................................................................................94

15.4.1 Input parameters ............................................................................................................94

15.4.2 Output ............................................................................................................................96

List of Tables

Table 1-1: List of Applicable Documents ................................................................................................... 9

Table 1-2: List of Reference Documents................................................................................................... 10

Table 1-3: List of Abbreviations ............................................................................................................... 11

Table 3-1: MTG mission reference planning............................................................................................. 15

Table 3-2: Summary of MTG Observation Missions ................................................................................ 16

Table 3-3: MTG payloads complement (reference within the MTG Space Segment Phase A) ............... 17

Table 5-1: ACS pointing errors for different attitude sensor configurations ............................................. 25

Table 7-1: Scanning pattern definition parameters.................................................................................... 38

Table 7-2: Parameters to define dynamically the scanning mirror ............................................................ 39

Table 8-1: Parameters contained on the AOCS file................................................................................... 40

Table 10-1: Landmark database ................................................................................................................ 56

Table 15-1: Grid over the Earth definition parameters.............................................................................. 94

List of Figures

Figure 2-1: Organization of the Earth Observation Directorate (state: May 2009) .................................. 13

Figure 3-1: MTG deployment in the two satellites type implementation (MTG-I and MTG-S) .............. 17

Figure 5-1: Meteosat ................................................................................................................................. 23

Figure 5-2: Image Rotation ....................................................................................................................... 23

Figure 5-3: GOES-I picture ....................................................................................................................... 24

Figure 5-4: GOES-13 picture .................................................................................................................... 25

Figure 5-5: attitude errors.......................................................................................................................... 27

Figure 5-6: orbit errors .............................................................................................................................. 27

Figure 5-7: optical bed misalignments ...................................................................................................... 28

Figure 5-8: scanning mirror misalignments............................................................................................... 28

Figure 6-1: MTG INR-PS general architecture by functionalities............................................................. 32

Figure 6-2: MTG INR-PS landmarks simulation mode architecture block diagram ................................. 32

Figure 6-3: MTG INR-PS image simulation mode architecture block diagram........................................ 33

Figure 7-1: scanning concept identification .............................................................................................. 35

Figure 7-2: candidate scanning concepts................................................................................................... 36

Figure 7-3: Scanning pattern used on MTG INR-PS................................................................................. 38

Figure 7-4: NS and EW mirror angles....................................................................................................... 39


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Figure 7-5: scanning mirror torques .......................................................................................................... 39

Figure 8-1: AOCS simulator overview...................................................................................................... 41

Figure 9-1: General Direct Navigation Equation....................................................................................... 42

Figure 9-2: Focal plane and telescope geometry definition....................................................................... 44

Figure 9-3: Scanning geometry definition................................................................................................. 45

Figure 9-4: Scanning mirror reflection...................................................................................................... 47

Figure 9-5: Optical Site and Elevation angles calculation from (ULOS)IF .................................................. 48

Figure 9-6: Generic geolocation algorithm representation ........................................................................ 49

Figure 9-7: projection and scaling functions ............................................................................................. 51

Figure 9-8: Coordinate frames for GEOS projection................................................................................. 52

Figure 9-9: Projection and scaling process................................................................................................ 53

Figure 10-1: Bias (left) and measurement error (right) distribution for landmarks ................................... 57

Figure 10-2: Details and differences over Europe between the landmarks database files available.......... 57

Figure 10-3: Landmarks database files available on this MTG INR-PS ................................................... 58

Figure 10-4: Landmarks Position Determination process ......................................................................... 59

Figure 10-5: Landmark overlapping possibilities...................................................................................... 59

Figure 10-6: Landmark residual calculation.............................................................................................. 60

Figure 10-7: Ranging station residual calculation for a GEO orbit ........................................................... 60

Figure 10-8: Apparent angular radius of a planet ...................................................................................... 61

Figure 10-9: Measurement of star elevation angle .................................................................................... 63

Figure 12-1: Landmark residual files in a case directory .......................................................................... 71

Figure 13-1: Landmark residuals over the simulation ............................................................................... 72

Figure 13-2: Landmark residuals over the first image divided by scanning lines ..................................... 73

Figure 13-3: Azimuth and Elevation Navigation errors over the simulation............................................. 73

Figure 13-4: Azimuth and Elevation Navigation errors over one scanning line........................................ 73

Figure 13-5: State parameter evolution: Azimuth and Elevation state vectors.......................................... 74

Figure 13-5: covariance matrix diagonal elements on the simulation ....................................................... 75

Figure 14-1: Instrument filed of view with no attitude errors ................................................................... 77

Figure 14-2: Instrument filed of view with attitude errors ........................................................................ 78

Figure 15-1: Sun-glint process .................................................................................................................. 89

Figure 15-2: Observation zenith angle and sun zenith angle definition .................................................... 90

Figure 15-3: Sun-glint geometry ............................................................................................................... 90

Figure 15-4: MTG-SG tool video file........................................................................................................ 96


of 97 INTRODUCTION

1 INTRODUCTION

1.1 Scope of the Document This report, including the linked reference documents, aims at presenting the contributions of Pedro José Jurado Lozano during his Young Graduate traineeship from May 2008 till May 2009 to activities in the Optical Instrument Section, Instrument Pre-Development Division, EO Projects Department, Directorate of Earth Observation Programmes (EOP-PIO).

1.2 Applicable Documents The applicable documents are introduced in the next table:

Ref.-No. Title, Reference, Date Organisation

AD1 MTG Space System Requirement Document revision 2B

AD2 ESA Pointing Error Handbook

AD3 Proposed pointing summation rules for MTG

ESA

AD4 INR Prototype Simulator Algorithms and Models MTG-ASG-TN-014

AD5 INR Simulator Prototype and User Manual MTG-ASG-ML-003

AD6 Refined Analysis of INR MTG-ASG-RP-017

AD7 AOCS Performance Simulator MTG-ASG-TN-024

AD8 MTG: Scanning concept trade-off MTG-ASF-IN-005

AD9 Preliminary Definition of INR approach

EADS Astrium

AD10 MTG INR Simulator Models and algorithms description MTG-AAF-SA-TN-23

AD11 MTG INR simulator user manual MTG-AAF-SA-MA-1

AD12 Refined Analysis of INR MTG-TAF-SA-RP-0076

AD13 Methodology for the establishment of pointing, geolocation and co-registration budgets MTG-TAF-SA-TN-6

TAS

Table 1-1: List of Applicable Documents

1.3 Reference Documents The documents listed in Table 1-2 were studied and used to contribute to the final understanding and simulation by the trainee during the traineeship at ESA.

Ref.-No. Title, Reference, Date Organisation

RD1 Simulation Studies of the GOES-I INR System

RD2 GOES INR On-orbit Performance

NASA


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RD3 Attitude Determination Improvements for GOES

RD4 Study on INR for Imagery & sounding observations Makalumedia

RD5 Geolocation VIS/IR Imager/Radiometer Suite Algorithm Raytheon

RD6 LRIT/HRIT Global Specification EUMETSAT

RD7 High Representativity Image Quality Simulator for MTG TAS

RD8 Attitude and Orbit Estimation Using Stars and Landmarks Charles Starks Draper laboratory

Table 1-2: List of Reference Documents

1.4 Bibliography Next books were consulted during the traineeship:

• Optimal Estimation of Dynamic Systems. John L. Crassidis and John L. Junkins • An engineering approach to Optimal Control and Estimation Theory. Georges M.

Siouris • MIT opencourse on estimation and control of aerospace systems (link below) • An Introduction to Mission Design for Geostationary Satellites. J.J. Pocha • Handbook of Geostationary Orbits. Space Technology Library. EM Soop • Analysis of variance. Guenther • Kalman filtering: theory and practice using Matlab. Third edition. Mohinder S. Grewal

1.5 List of Abbreviations Abbreviation Description ADM-Aeolus Atmospheric Dynamic Mission AOCS Attitude & Orbit Control Subsystem ATS IS Application Technology Satellite BRC Basic Repeat Cycle BRF Body Reference Frame Cryosat Cryogenic Satellite DCS Data Collection Subsystem DE Detection Efficency DMC Dynamic Motion Compensation EarthCARE Earth Clouds Aerosols and Radiation Explorer ECEF Earth Centered Earth Fixed ECLF Earth Centered Local Frame EO Earth Observation EOP Earth Observation Project department EPS EUMETSAT Polar System ESA European Space Agency EUMETSAT EUropean organization for the exploitation of METeorological SATellites EV Elevation EW East-West FDC Full Disk Coverage FCI Flexible Combine Imager FDHSI Full-Disk High-Spectral-Resolution Imagery FY Feng Yin GEO Geostationary Orbit


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GEOS Normalized Geostationary Projection GERB Geostationary Earth Radiation Budget GMES Global Monitoring for Environment and Security GMS Japanese Geostationary Meteorological Satellite GOCE Gravity field and steady-state Ocean Circulation Explorer GOES Geostationary Operational Environmental Satellite GOMS Russian Geostationary Operational Meteorological Satellite HRFI High-Resolution Fast Imagery IF Instrument Frame IMC Image Motion Compensation INR Image Navigation and Registration INSAT Indian Satellite IQT Image Quality Tool IR Infrared IRS Infrared Sounder ISCCP International Satellite Cloud Climatology Project ISRO Indian Space Research Organization LAC Local Area Coverage LI Lightning Imagery, Lightning Imager LORF Local Orbital Reference Frame LOS Line Of Sight Meteosat Meteorological Satellite MetSat Meteorological Satellite MMC Mirror Motion Compensation MSG Meteosat Second Generation MTG Meteosat Third Generation MTG-I MTG Imaging satellite MTG INR-PS MTG INR Performance Simulator MTG-S MTG Sounding satellite MTSat Japanese Multi-function Transport Satellite NASA National Aeronautics and Space Administration NASDA National Space Development Agency of Japan NIR Near Infrared NS North-South OA Optical Axis ODHS Onboard Subsystem Data Handling PDF Probability Density Function PDM Pre-Development Model PIO Instrument Pre-development division, Optical instrument section rms Root mean square SAF Scanning Assembly Frame SC Optical Site SEVIRI Spinning Enhanced Visible and Infrared Imager SIAD Stellar Inertial Attitude Determination SMOS Soil Moisture and Ocean Salinity SMS US Synchronous Meteorological Satellite SSD Spatial Sampling Distance STR Star TRacker S&R Search & Rescue TF Telescope Frame TIR Thermal Infrared TMTC Telemetry Telecommand UV Ultraviolet VHRR Very High Resolution Radiometer VIS Visible VISSR Visible and Infrared Spin Scan Radiometer

Table 1-3: List of Abbreviations


of 97 TRAINEESHIP IN THE “INSTRUMENT PREDEVELOPMENT DIVISION”

2 TRAINEESHIP IN THE “INSTRUMENT PREDEVELOPMENT DIVISION”

2.1 Organization and Duties The Optical Instrument Section (EOP-PIO) forms part of the Instrument Pre-Development Division within the Projects Department of the Earth Observation Directorate. The whole organization of the Earth Observation Directorate is illustrated in Figure 2-1.

The general task of the Instrument Pre-Development Division and its sections is the end-to-end definition of the Earth Explorer and Earth Watch missions’ instruments from concept to implementation. This task is carried out aiming at the objective of risk reduction before committing to full development of instruments approved for flight or of specific strategic interest. As there is a strong interaction between the sections and their responsibilities, the overall duties of this division can be summarized as follows:

• Contribution to the preparation of technical and scientific dossiers on Earth Explorer and Earth Watch missions;

• Definition and management of industrial technology development activities for the preparation of future Earth Explorer and Earth Watch missions;

• Contribution to the evaluation of industrial and scientific proposals;

• Definition of future observation techniques and sensor concepts for Earth Observation (EO) satellites;

• Contribution to proposals for mission implementation and instrument pre-development activities;

• Demonstration of instrument performances versus defined requirements;

• Design, manufacturing and tests of critical subsystems, possibly up to full or partial instrument model (PDM: Pre-Development Model);

• Space-representative build standards;

• Realisation of ground/airborne instruments, to measure science data in order to validate new mission concepts;

ESA’s future EO programme is called “The Living Planet Programme”, which, as already mentioned before, consists of two different mission types: the Earth Explorer and Earth Watch missions. Due to the fact that almost all activities in the division contribute to them, both are shortly introduced hereafter.



Figure 2-1: Organization of the Earth Observation Directorate (state: May 2009)



2.2 The Living Planet Programme ESA's Living Planet Programme is comprised of two main components: a science and research element in the form of the Earth Explorer missions, and an element designed to facilitate the delivery of EO data for the eventual use in operational services called Earth Watch missions. This includes the well-established meteorological missions with EUMETSAT and also new missions focusing on the environment and civil security. This latter element, which is a joint initiative between the European Commission and ESA, is called GMES.

2.2.1 Earth Explorer Missions Earth Explorer missions are divided into two categories – Core and Opportunity. Core missions respond directly to specific areas of public concern and are selected through widespread consultation with the science community. Opportunity missions are smaller, low-cost satellites that are relatively quick to implement so that they are to address areas of immediate environmental concern.

• Core Missions

− GOCE

− ADM-Aeolus

− EarthCARE

• Opportunity Missions

− CryoSat

− SMOS

− Swarm

2.2.2 Earth Watch Missions

• Meteorological Missions

− Meteosat Third Generation (MTG) The MTG will take the relay in 2015+ from Meteosat 11, the last of a series of four satellites of the MSG. This is a joint project between ESA and EUMETSAT that followed the success of the first generation Meteosat satellites. The first of four MSG satellites was launched in 2002. The Young Graduate Traineeship opportunity was based on this project.

− Future EUMETSAT Polar System (EPS)

• GMES The overall aim of the GMES initiative is to support Europe’s goals regarding sustainable development and global governance of the environment by providing timely and quality data, information, services and knowledge.


of 97 METEOSAT THIRD GENERATION MISSION

3 METEOSAT THIRD GENERATION MISSION

3.1 Introduction Today, the Meteosat geostationary meteorological satellites play a key role in providing continuous atmospheric observations both for weather forecasting and for monitoring a wide variety of environmental phenomena. The Meteosat Second Generation (MSG) system is the primary European source of geostationary observations over Europe and Africa.

As a worse case, the second generation of Meteosat satellites is expected to provide operational services at least until 2015. According to that, following the successful commissioning of the first satellite in the MSG series, EUMETSAT and ESA were already actively planning the next European operational geostationary meteorological satellite system in the form of the Meteosat Third Generation (MTG).

MTG preparatory activities started end of 2000 in cooperation with ESA, following the decision of the EUMETSAT Council to proceed. Since September 2004 up to now, the MTG mission has been the subject of two parallel ESA system studies led by Alcatel Space and EADS Astrium GmbH, respectively. A first pre-phase A was dedicated to the mission architecture and system drivers to give the final concepts which needed to be studied further. After pre-phase A, a phase A study on MTG was launched at the beginning of February 2007 for the space segment system feasibility and programmatic aspects to be accomplished during 2007-2008 time frame and covering all elements to the level of details allowing to conclude on the feasibility of the system and to produce cost estimates with a good level of confidence.

Further activities toward the definition, development and implementation of the MTG system are planned according to the MTG Reference Planning. This planning is consistent with the 2015+ need date for the first MTG satellite. A brief can be seen on Table 3-1.

Phase Event Period/Date

MTG date need 2015

Development and test of the MTG system 2009-2015

Coordinated EUMETSAT and ESA Preparatory Programmes (Phase B) and Programme approval process 2008-2009

Parallel EUMETSAT and ESA Phase A studies 2007-2008

Pre-phase A studies 2002-2006

• Pre-phase A Mission Architecture and System Concepts 2004-2005

• User consultation – Workshop 2 April 2005

• Observation Techniques and Sensor Concept Studies 2003-2004

Table 3-1: MTG mission reference planning

3.2 MTG mission definition Five candidate observation missions were assessed during phase A studies:

• Three distinct imaging missions dedicated to operational meteorology, with emphasis on nowcasting and very-short-term forecasting:

o FDHSI mission, as the successor to the MSG SEVIRI instrument. 16 spectral channels, delivering high radiometric resolution performance and geometric



performances of 1 Km for solar channels and 2 Km for IR channels in terms of Spatial Sampling Distance (SSD), with a BRC of 10 minutes for a full Earth disc coverage.

o HRFI mission, based on enhancement of the MSG High-Resolution Imagery mission. This mission aims at BRC/n minutes (with n being equal to 1,2,3 or 4) revisit time with 0.5 Km SSD for solar channels and 1 Km SSD for TIR channels.

o LI mission, capable of detecting very low energy flash events with high Detection Efficiency (DE>90%).

• Two atmospheric-sounding missions:

o IRS mission focusing on operational meteorology, with potential relevance to atmospheric chemistry applications. It supports NWP through the provision of atmospheric motion vectors, temperature and water vapour profiles.

o UV/VIS/NIR sounding (UVS or Sentinel 4) mission dedicated to atmospheric chemistry and Air Quality (as part of GMES payload to be flown as a MTG payload complement).

Table 3-2: Summary of MTG Observation Missions

3.3 MTG space segment configuration To meet the user needs, minimise the risks inherent in the development of the payload complement, and also to allow flexible approach to the MTG system’s operational deployment, the MTG space segment configuration will consist of the so called “twin” configuration, i.e. the MTG imaging satellite, called MTG-I, and the MTG sounding satellite, called MTG-S. The dramatic improvement in performance compared with the previous generations of Meteosat is made possible by the use of a three-axis-stabilised rather than a spin-stabilised platform, allowing a much higher duty cycle for observing the Earth. According to this fact, both series of satellites will be based on a three axis stabilised platform, supported by trade-off performed during requirement analyses. Moreover, the high availability required for the provision of operational meteorological satellite services implies the need for backup satellites in orbit. The MTG mission lifetime of 15 years with extension to 20 year will therefore require up to 6 satellites (4 MTG-I and 2 MTG-S), each with a lifetime of 8.5 years. For programmatic reasons, it is envisaged to apply and adapt a commercial telecommunication platform as basis for the MTG platform. Several platform concepts have been analysed. The mass for both spacecrafts is kept to the launch capabilities of Soyuz in Kourou to allow later flexibility in the potential selection of the European launcher, Ariane 5 or Soyuz. It is also planned to use the same bus for



both satellites with minimum adaptations as required per mission (structure, thermal, AOCS, propulsion, power, OSDH, TMTC subsystems are in common for both satellites).

Figure 3-1: MTG deployment in the two satellites type implementation (MTG-I and MTG-S)

As depicted in Table 3-3, the payload complement of both MTG-I and MTG-S are presented:

Space Segment Composition FCI LI IRS DCS+S&R UVN (option)

Imaging Satellite (MTG-I)

Sounding Satellite (MTG-S)

Sum of Payload Complement 4 x FCI 4 x LI 2 x IRS 4 x DCS 2 x UVN

Table 3-3: MTG payloads complement (reference within the MTG Space Segment Phase A)

The Imagery Mission spacecraft will embark the FCI and the LI. The FCI meets the first two imagery mission requirements. In such a way, the FCI will be operated in an exclusive way to satisfy FDHSI or HRFI missions at a time. With 2 satellites in hot redundancy, both the LAC of HRFI mission and the FDC of FDHSI mission should be met. The Sounding Mission spacecraft will embark the DCS and S&R.

3.4 MTG system driver Since MTG satellites are going to be located in the geostationary orbit, and it is envisaged to adapt a commercial telecommunication platform as a basis for the MTG platform, all the subsystem have a wide heritage and are flight-proof. On the other hands, and due to the stringent pointing and stability requirements, accurate and automatic INR of remotely sensed data will be an essential element of the MTG system, especially if we take into account the main change from spin stabilized solution to a three-axis stabilized satellite. INR describes the process by which geographic locations of the image pixels are computed and successive images form the same sensor are aligned to each other over time. That is the reason why the INR subsystem considered as a whole becomes the main driver for MTG mission and its performance requirements have to be evaluated.

Owing to this fact, extensive discussions have been carried out with the aim at achieving the user needs without leading the space system into an over-design impacting risks and therefore cost impacts, and rightly so. The discussions are always focused on the geometric performances bearing in mind image deformations induced by the satellite and instruments pointing, thermo-elastic deformations and micro-vibrations. And all of this leads to extensive INR simulations in order to be capable of providing preliminary analyses that allow consolidating the imagery requirements. At this point, MTG system studies bring about the necessity of INR performance simulations and it is within this framework where the INR performance studies and simulations executed by Pedro José Jurado Lozano during his Young Graduate traineeship are included.


of 97 IMAGE NAVIGATION AND REGISTRATION OVERVIEW

4 IMAGE NAVIGATION AND REGISTRATION OVERVIEW

4.1 Introduction Although image navigation and geometric correction were already well established practices (as in Landsat-4), the GOES I-M system was the first space imaging system in which the term Image Navigation and Registration was utilized.

Ideally, if the spacecraft were perfectly located on the geostationary orbit in space with an unchangeable attitude, which means without any dynamic perturbations, carrying an instrument with an accurate repetitive scanning mechanism and without any misalignment or internal errors due to internal vibrations or thermal deformations, just then the optical axes of the imaging system were held perfectly known and fixed relative to a geocentric coordinate frame, and just then the corresponding pixels of successive images would have the same earth location. Nevertheless, coming back to the real world, the orbital motion due to perturbing forces and the changing attitude evolution of the optical axes due to several sources such as external and internal disrupting torques, optical bench thermal distortions or internal micro vibrations and miscalibrations, cause a state of uncertainty and varying image motion over time. The purpose of the Image Navigation and Registration system is to correct for such motions and estimate this uncertainty so that the apparent pixel shift due to these effects is compensated for and the resulting earth projection remains fixed and with a limited known uncertainty.

4.2 Definitions Before introducing the usual performance requirements it is necessary to provide some definitions. Bearing in mind the previous paragraph, it can be said that the Image Navigation and Registration system comprises all aspects of the system contributing to high pointing and high stability. Both of them, pointing and stability, lead to a high geometric image quality of the products since Image Navigation and Registration system aims at controlling and monitoring the geometric performances of the image processing. This task is a two-part process:

4.2.1 Image Navigation Image Navigation is the knowledge of the relationship between a pixel in instrument coordinates and the corresponding point on the Earth, given by latitude and longitude coordinates. The image navigation accuracy is a measure of how well that relationship is known. In general, it refers to the methods employed to obtain that knowledge.

4.2.2 Image Registration Image registration refers to maintaining the spatial relationship between samples / pixels within an image, between images or between channels. Therefore, it is an indication as to how well that navigation knowledge is maintained and controlled over time. It is related to the Line Of Sight stability requirements and it is applied to every sample couple on the same or different images or channels. Therefore, it gives us relative information about the evolution of the navigation knowledge over time. From a ground processing’s point of view, it can be defined as the process of spatially aligning two or more images of a scene.



4.3 INR performance requirements Image Navigation is related to the pointing requirements and it is applied to every sample on a single image. Therefore, it gives us absolute information about the image location. The navigation performance requirement is the absolute error defined in NS and EW angles inside a region 3σ. The registration performance requirements are usually broken into several categories (in descending order of challenge):

Within Frame Registration (WIF), refers to the relative error between two samples that are acquired within the same image and channel or the relative error between two landmark sites that are acquired within the same image and channel.

Frame to Frame Registration (FTF), refers to the relative error between the same two samples on the same channel acquired in different time or the relative error between the same two landmark sites on the same channel acquired in different images. The period of time between both acquisition must be integer multiple of the full-disk scanning duration and must be specified. Since there are usually an integer number of full-disk scannings in a day period, one of the specified period of time between images is usually 24 hours. Of course, the longer the period of time, the more relaxed the requirement.

Inter-channel Co-registration (ICR), refers to the relative error between the same two samples acquired at the same time within the same image but in different channel on the same focal plane assembly or the relative error between the same landmark sites acquired at the same time in the same image but in different channel on the same focal plane assembly.

Inter-focal plane assembly Co-registration (IFPAR), refers to the relative error between the same two samples acquired at the same time within the same image but in different focal plane assembly or the relative error between the same landmark sites acquired at the same time in the same image but in different focal plane assembly.

Inter-instrument Co-registration (IIR), refers to the relative error between the same two samples acquired at the same time within different instruments on the same satellite or the relative error between the same landmark sites acquired at the same time within different instruments on the same satellite.

These are in the general sense the requirements used, although for each project some specification to tightly define these requirements have to be done. For a more specific INR requirements applied to MTG, the reader can go to Annex A of AD1.

4.4 Evaluating INR performance requirements The evaluation of the INR performance is often a controversial topic. In general, there are two approaches that are useful in evaluating: simulation results and in-flight data.

In-flight performance evaluation is obviously more difficult to assess than through simulation. During post-launch testing, INR performance is inferred by a specific test directed at verification of error budget line items and flight hardware characterization. Operational performance is evaluated by gathering statistical information on pre and post a priori measurements residuals. This approach in essence is the characterization of all unmodelled errors in the estimation process and may only provide performance at specific landmark sites.

In the case of simulation, a true state vector must be generated so an explicit relation can be written for the navigation error. Mathematically, the navigation error can be defined with the following relation:



trueestimatedresidual angEWangNS

angEWangNS

angEWangNS

⎟⎟⎠

⎞⎜⎜⎝

⎛−⎟⎟

⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛ΔΔ

__

__

)_()_(

Where both NS and EW scanning angles are given by:

( )ϕλχχθφψθφψθφ ,,,,,,,,,,,,__ EW

INSI

maI

maIIIIACSACSACSrf

angEWangNS

=⎟⎟⎠

⎞⎜⎜⎝

⎛, where

f is the functional relationship between state vector and instrument scanning angles.

r is the spacecraft position vector in true of date TOD coordinates ( )ACSACSACS ψθφ ,, are the roll, pitch and yaw attitude angles pointing errors

( )III ψθφ ,, are the roll, pitch and yaw instrument attitude angles

( )maI

maI θφ , are the instrument roll and pitch misalignments

( )EWI

NSI χχ , are the instrument scan mechanism errors in NS and EW

( )ϕλ, are the longitude and geodetic latitude of Earth point.

4.5 INR types of correction As we already know, Image Navigation refers to knowledge of the geographic locations of pixels within an image, while Image Registration refers to alignments of pixels relative to each other. With future satellite observation systems which will generate enormous amounts of data representing multiple observations of the same features at different times and/or by different sensors, automatic and accurate image navigations and registration is becoming the first essential step for such tasks as weather predictions, building assimilation models, data fusion or formation flying. Most image distortions are combined effects of sensor operation, satellite orbit and attitude, and atmospheric and terrain effects. Two different types of correction are usually applied to minimize these distortions.

The first one, called systematic correction, relies on image acquisition models taking into account satellite orbit and attitude, sensor characteristics, platform/sensor relationship, and terrain models. But it is very difficult to determine exact location within an image using only ancillary data. The second type of correction, also called precision correction, is feature-based, starting from the results of the systematic correction (usually accurate within a few pixels), and refining the geolocation or relative registration to subpixel precision. Two approaches can be taken for combining systematic and precision correction:

• Precision correction (or image registration) is performed after systematic correction. • Systematic and precision corrections are integrated in a feedback loop to iteratively

refine the navigation model. Within the task objective of this traineeship, the first approach has been chosen; the navigation model will be constantly updated using different telemetry (AOCS provided knowledge) and therefore the estimated attitude information is used to calculate the residuals over the landmark. An iterative optimization method, such as Kalman filter, is applied to the task of continually refining the knowledge of all the parameters required to accurately navigate and register images at the sub pixel level. For the sake of simplicity on the filtering, it must be emphasized that two different filters have been used for each, EW angle and NS angle, although we are dealing with a cross-coupled problem in the yaw angle.


of 97 IMAGE NAVIGATION AND REGISTRATION FOR GEOSTATIONARY WEATHER SATELLITES

5 IMAGE NAVIGATION AND REGISTRATION FOR GEOSTATIONARY WEATHER SATELLITES

5.1 Introduction Remote sensing from geostationary altitude poses some unique challenges for image navigation, especially for three-axis stabilized platforms which experience a stressing thermal environment. The great distance requires that the remote sensing platform possess extraordinary pointing accuracy and stability since one kilometre at the satellite nadir subtends only 28 mrad. Absolute navigational accuracy is important to the consumer of weather satellite imagery but perhaps more important is the image to image registration, errors in which degrade the observation of winds. Ideally all images should appear in the same reference though they have been obtained from a geostationary satellite at different times. That is the reason why the overall mission will try to achieve this goal through its INR system.

This section reviews the image navigation problems for spinners and three-axis stabilized systems. The general features of each type of design are discussed along with error sources and compensation.

5.2 Geostationary weather missions Several geostationary meteorological spacecraft are in operation and some other non operative programs were intended to the weather forecast from geostationary altitude. The United States has two in operation; GOES-11 and GOES-12. GOES-12 is designated GOES-East, over the Amazon River and provides most of the U.S. weather information. GOES-11 is GOES-West over the eastern Pacific Ocean. The Japanese have one in operation; MTSAT-1R over the mid Pacific at 140°E. The Europeans have Meteosat-8 (3.5°W) and Meteosat-9 (0°) over the Atlantic Ocean and have Meteosat-6 (63°E) and Meteosat-7 (57.5°E) over the Indian Ocean. The Russians operate the GOMS over the equator south of Moscow. India also operates geostationary satellites which carry instruments for meteorological purposes. China operates the Feng-Yun （風雲) geostationary satellites, FY-2C at 105°E, FY-2D at 86.5°E and FY-2E at 123.5°E. The main geostationary meteorological series on the history are:

• US Application Technology Satellites (ATS) series:

ATS series was a set of 6 NASA spacecraft intended as test beds. They also collected and transmitted meteorological data. Different attitude stabilization methods were proved: spinning stabilization, gravity gradient stabilization, etc…

• US Synchronous Meteorological Satellite (SMS) / Geostationary Operational Environmental Satellite (GOES) series:

The SMS/GOES program was initiated after the successes achieved by ATS I and ATS III. The ATS research satellites demonstrated the operational feasibility and capability of placing a satellite in geostationary orbit. This craft could then be instrumented with meteorological sensors to observe the Earth's cloud cover and weather patterns from space twenty-four hours per day.

• European METEOrological SATellite (Meteosat) series:

Operational geostationary Meteosat satellites followed 3 pre-operational versions (Meteosat-1,-2,-3/P2). Meteosats had a 2.1 m diameter, 3.195 m high stepped cylindrical body with solar cells on six main body panels. The spacecraft was spin-stabilized at 100 rpm around the main

http://en.wikipedia.org/wiki/United_States

http://en.wikipedia.org/wiki/GOES

http://en.wikipedia.org/wiki/Amazon_River

http://en.wikipedia.org/wiki/Pacific_Ocean

http://en.wikipedia.org/wiki/Japan

http://en.wikipedia.org/wiki/MTSAT

http://en.wikipedia.org/wiki/Europe

http://en.wikipedia.org/wiki/Meteosat

http://en.wikipedia.org/wiki/Atlantic_Ocean

http://en.wikipedia.org/wiki/Indian_Ocean

http://en.wikipedia.org/wiki/Russia

http://en.wikipedia.org/wiki/GOMS

http://en.wikipedia.org/wiki/Moscow

http://en.wikipedia.org/wiki/India

http://en.wikipedia.org/wiki/China

http://en.wikipedia.org/wiki/Feng-Yun



axis aligned almost parallel to the Earth's axis. Attitude information was provided by Earth horizon and Sun-lit sensors.

• European Meteosat Second Generation Satellite (MSG) series:

MSG 1 was a European (EUMETSAT consortium) geostationary weather satellite. Spin stabilized 3.2m diameter cylindrical satellite had a dry mass of about 1000 kg and carried about 1010 kg of propellant. MSG was to allow quicker and more accurate weather forecasts in Europe than in the past. It carried two major instruments: SEVIRI and GERB.

• Japanese Geostationary Meteorological Satellite (GMS) / Himawary series:

The GMS series were spin-stabilized satellites. They were developed to contribute to the improvement of Japan's meteorological services and the development of weather satellite technology. The satellites consisted of a despun section which held the earth-oriented antennas and a 100-rpm rotating spin section which contained the VISSR, electronic devices, etc.

• Japanese Multi-functional Transport Satellite (MTSat) / Himawary (continued) series:

The MTSat series fulfils a meteorological function for the Japan Meteorological Agency. The MTSAT series succeeds the GMS series as the next generation of satellites covering East Asia and the Western Pacific. Three-axis stabilization with a system to control roll, pitch and yaw using thrusters and momentum wheels.

• Indian National Satellite (INSAT) series:

INSAT is a series of multipurpose geostationary satellites launched by ISRO to satisfy the telecommunications, broadcasting, meteorology, and "search and rescue" needs of India. Some of the satellites have the VHRR. The satellites also incorporate transponder(s) for receiving distress alert signals for search and rescue missions in the South Asian and Indian Ocean Region.

• Indian Meteorological Satellite (MetSat) / Kalpana series:

METSAT is the first exclusive meteorological satellite built by ISRO. Three axis stabilized satellite, so far, meteorological services had been combined with telecommunication and television services in the INSAT system. For meteorological observation, METSAT carries a VHRR capable of imaging the Earth in the visible, thermal infrared and water vapour bands. At the time of its launch, METSAT weighed 1055 kg including about 560 kg of propellant.

• Russian Geostationary Operational Meteorological Satellite (GOMS) / Elektro series:

Elektro or GOMS is a three-axis stabilized satellite with a payload that includes a three-channel, earth-imaging radiometer together with a capability to measure space radiation spectra and densities. Only a single Elektro spacecraft was launched in 1994. The troubled spacecraft could not be put into use. The whole project was finally cancelled.

• Chinese Feng Yun (FY-2 and FY-4) geostationary satellites series:

The FY-2 spin-stabilized geosynchronous meteorological spacecraft bus diameter was 2.1 m, and total height on-station was about 4.5 m. The major payload was a scanning radiometer with S-band and UHF data distribution. The two principal sensors were visible and infrared imaging instruments. The first FY-2 satellite was undergoing final checkout on 2 April 1994 before being mated to its launch vehicle when a fire and explosion erupted, destroying the vehicle. The operational satellite finally launched was stationed over 104.6E.

http://en.wikipedia.org/wiki/Indian_Space_Research_Organisation

http://en.wikipedia.org/wiki/India

http://en.wikipedia.org/w/index.php?title=VHRR&action=edit&redlink=1



5.3 Satellites designs and their impact on the INR system Geostationary weather satellites may be classified as either spinners (e.g. , Meteosat, MSG, GOES-7, and GMS), or three-axis stabilized limited to spinners with the notable exception of INSAT. This changed with the launch of GOES-I. Nevertheless, in Europe, present GEO weather satellite on-orbit experience is limited to spinners. This will change with the launch of MTG which is based on GEO telecommunication platform heritage but with vastly more capability in terms of pointing and stability. The large angular momentum of a spinner provides an inherently stable platform for an imaging bus with low imaging duty cycle because during 95% of the spin cycle the instruments view environment. For these reasons the image navigation problem for the spinner is simpler but the potential for data collection is less.

5.3.1 Meteosat and spinners Figure 5-1 is a diagram of the Meteosat satellite. The Earth is scanned by a combination of the elevation of the radiometer telescope and the spin of the satellite. The telescope tertiary mirror folds the line-of-sight into the aft optics which is fixed in the satellite body. Because the Meteosat focal plane is fixed in the body while the telescope is elevated the image on the focal plane will appear to rotate directly in proportion to the NS elevation angle. Figure 5-2 illustrates this rotation by plotting the vertical orientation of the focal plane as it is mapped onto a 20ºx20º field in object space. The Meteosat sun sensor detects the position of the sun and is used to synchronize line starts.

Figure 5-1: Meteosat

This Meteosat design differs from the US GOES-7 where the telescope optical axis is oriented along the spin axis and scanned by means of an object plane scan mirror. Since the GOES-7 focal plane rotates about the spin axis with the body of the spacecraft there is no image rotation as a function of scan NS elevation.

Figure 5-2: Image Rotation



5.3.2 GOES-I-M and three-axis stabilized platforms with momentum bias Three axis stabilized configurations can be categorized by their mode of attitude control and the means by which their imaging instruments scan the earth. Attitude control for INSAT and GOES-I (shown in Figure 2.3) is provided by a set of V-momentum wheels and a scanning IR earth sensor. The V-wheel configuration controls the roll and pitch of the satellite but has no authority to control yaw, similarly, the earth sensor senses roll and pitch but not yaw. Yaw is effectively controlled by the quarter-orbit coupling of roll and yaw due to the precession of the bias momentum in an earth-fixed frame.

Figure 5-3: GOES-I picture

The GOES-I satellite is configured with an imager and a sounder. They will execute raster scans of the earth by means of a double gimballed object plane scan mirror. The scan mirrors are under closed loop control using inductosyns for angular encoders. The double gimbal configuration induces an image rotation like with Meteosat when the line-of-sight is elevated NS. This is compensated for by staggering the sampling of detectors during the East-to-West and West-to-East scanning of the imager to electronically erect the detectors.

5.3.3 MTSat-2 and three-axis stabilized platforms without momentum bias The alternative attitude control concept is the three-axis stabilized system using a zero-momentum bias array of reaction wheels. This system requires sensing of all three attitude angles. The DS-2000 standard satellite platform based on a design for NASDA is on this direction. Its Attitude Control can be switched to control bias momentum or zero momentum with satellite controller and four skew reaction wheels. This is used on the three-axis stabilized MTSat-2 concept. This system utilizes an earth sensor for the observation of roll and pitch, and a polaris star sensor for the observation of roll and yaw. To achieve high stability in the control of pitch it is necessary to apply a very low bandwidth filter to the relatively noisy earth sensor output. A low disturbance environment is, therefore, required. This is achieved by utilizing a fixed set of solar arrays (with obvious mass penalty) and instruments with low inertia scan mirrors. Another advantage of the MTSat-2 solar array lay-out is that there is no requirement for a solar sail to balance solar torques and hence the instruments passive radiative coolers have unobstructed views of space. In a principal it is also possible to delete the solar sail from a solar array and sail configuration like GOES-I and unload momentum by frequent thrusters firings. It may also be possible to combine these momentum dumps with nearly continuous station keeping.



5.3.4 GOES NO/P/Q and three-axis stabilized platforms with Stellar Inertial Navigation

A final possible configuration for a three-axis stabilized system is a system based on star tracker and gyroscope attitude determination (SIAD). This configuration was the one chosen for the next generation beyond GOES-I in the US. Table 5-1 shows an idea of the improvement in pointing performance between SIAD and Earth Sensor control systems [RD3]. The comparison is actually quite conservative since the Earth Sensor errors do not account for eclipse season, where the sun intrusion inhibits the northern or southern roll/pitch measurement.

ACS Pointing Errors (μrads, 3σ) Attitude sensor

configuration Roll Pitch Yaw

Earth Sensor with gyros and sun sensor for yaw 200 200 300

1 Star Tracker with gyros 7 30 12

2 Star Tracker with gyros and Kalman filtering 5 9 7

Table 5-1: ACS pointing errors for different attitude sensor configurations

Figure 5-4: GOES-13 picture

GOES-13 is the first in the GOES N-P series. The GOES NO/P/Q INR system design represents an evolution of the GOES INR architecture and an infusion of advanced spacecraft pointing technologies. Improvements for the NO/P/Q series support tighter navigation and frame-frame registration requirements. The important innovations include:

• Stellar Inertial Attitude Determination (SIAD) for fine attitude determination • Optical Bench accommodations for the Imager and Sounder instruments • Image Motion Compensation (IMC) implementation improvements • Closed-Loop Dynamic Motion Compensation (DMC) that is added to the IMC to

compensate for residual attitude control error • INR operations to accommodate thrusters manoeuvres for momentum management SK • INR operations for continuous operation across eclipses • INR operations following yaw flips



5.4 Error Sources and Compensation on the INR system Three types of errors enter into the navigation problem for all satellite configurations: orbital, attitude, and instrumental errors. Various strategies for minimization, calibration, and compensation have been adopted. For the GOES-7 system the orbit and attitude of the satellite are measured and the navigation is adjusted accordingly, there is no compensation applied. The Meteosat ground system observes the effects corrupting the current imagery and applies a resampling process to compensate. In GOES-I, a predictive model is developed and a compensation signal is applied the instrument pointing during imaging and sounding. But although the INR concept was demonstrated on GOES I with GOES-8 as the pathfinder, there were many problems encountered. A major concern was the frequent updates to instrument attitude to compensate for the non-repeatable errors. The most advanced compensation concepts are found in GOES-NO/P/Q with a completely redesigned bus with state of art ACS (SIAD system) and asymmetrical configuration. The solar sail to balance the solar radiation pressure torque is not included on GOES NO/P/Q since it was thought to reduce radiometric performance of the instrument. Moreover, the imager and sounder are able to operate through eclipses on the new GOES concept with a redesigned Dynamic Motion Compensation for the scan mirrors.

5.4.1 Attitude Errors The attitude of systems utilizing an earth sensor (GOES-I) is most naturally described by roll, pitch, and yaw angles referenced to the orbital plane. The attitude of spinners (angular momentum vector right ascension and declination) and systems with stellar inertial navigation is more naturally described with respect to the equatorial plane of the earth.

The angular momentum vector of a spinner will precess very slowly (on the order of 0.01º per day for Meteosat) due to the very small environmental torques. It is also the case that the spin axis may migrate during NS scanning due to inertia tensor changes. This induces wobble which is repeatable from disk to disk.

This situation with respect to three-axis stabilized platforms is more complex where attitude errors may occur on several time scales with various levels of predictability. At the highest frequency is the jitter due to the filtered white noise from the earth sensor. This is totally unpredictable and must be minimized by design. Advanced earth sensors such as those used in the GOES-I program will also produce a non-white component of noise similar to 1/f-noise. This sort of noise is especially bothersome to a low bandwidth control system and must also be minimized by design. At an intermediate scale are long-term yaw errors are diurnally repeatable to within about 50 radians but are influenced by geomagnetic storms. At the longest time scale are slow drifts in the earth sensor bore sight reading due to meteorological effects on the earth. IR earth sensors are susceptible to small changes in IR radiance to the presence of high clouds or stratospheric waves which cause local cool spots and radiance gradients across an earth chord. These effects have been greatly reduced by the design of the lockheed earth sensor used for GOES-I but they remain a significant source of error.



Figure 5-5: attitude errors

5.4.2 Orbit Errors Orbital position must be controlled by periodic station keeping operations or the longitude drift, eccentricity and inclination will become unacceptably large. Between station keeping events the orbit is readily modelled and compensations may be developed and applied, leaving residual errors which reflect the error in the orbit determination process. Orbital effects will be slowly varying and approximately diurnally repeatable.

Orbital effects are more important for spinners than for three-axis stabilized platforms controlled by earth sensors. This is illustrated by the example of an inclination error. With a spinner the spin angular momentum vector will remain invariant during an orbit.

When the satellite is at the top of its figure-”8” ground track the image of the earth will be translated in the opposite direction by an amount equal to the inclination error. With an earth sensor, however, such a translation would be sensed as a roll error and removed by the attitude control system, leaving the earth nominally centred within the imaging frame. In both cases there is also the smaller effect of the changing perspective of the satellite and orbit plane yaw. These effects are about 1/6 of the associated maximum roll error.

Orbit errors are also critically important for inertial navigated systems. This is because inertial attitude must continually be transformed into earth referenced attitude to keep the instruments accurately pointed at the earth. Errors in longitude for example will translate one-for-one into equivalent pitch errors.

Figure 5-6: orbit errors



5.4.3 Thermal Distortions Except for during eclipse the thermal environment of a spinner is quite benign and thermal effects are not very important. This is not the case for a three-axis stabilized platform. During the course of a day the sun will appear to orbit the spacecraft exposing different faces of the satellite to heating. Deformations of the satellite body, instruments, and attitude control sensors will occur. To the extent that the thermal inputs repeat diurnally (and there are no “thermal snapping” events) these deformations should also repeat. No selection of materials will allow their elimination by design and so it is desirable to develop compensation for their effects. In the GOES-I program space systems/loral devised a compensation which specifically exploits the diurnal repeatability of the thermal distortions and other errors. This compensation is called Image Motion Compensation (IMC). Every day an IMC model will be up-loaded to the satellite based on the previous day’s observations of the positions of stars and landmarks as seen to compute corrections to the instrument pointing to be applied during imaging and sounding as compensation for these errors.

The IMC also applies an orbital compensation so that the satellite precisely on station. A complete characterization of the distortions as a function of pointing gimbal angles is required.

Figure 5-7: optical bed misalignments

Figure 5-8: scanning mirror misalignments



5.4.4 Instrument Pointing Control Errors The pointing of the instrument lines-of-sight will be subject to both random and systematic errors (Fixed Pattern Error which is a function of gimbal angles). In principal, the systematic errors may be measured and compensated.

5.4.5 Uncompensated Disturbance Torques The motion of mechanisms (scan mirrors, solar arrays, filter wheels) without mechanical momentum compensation can induce attitude errors. Of most importance are the errors induced by large inertia objects such as scan mirror. Three-axis stabilized systems are especially sensitive to such disturbances. For INSAT, such disturbances have been minimized by a low inertia scan mirror design. For GOES-I, the disturbances are of greater significance since the double gimbal scan mirror has a greater rotating inertia. The solution selected was an open-loop compensation using a dynamic model of the spacecraft. This is designated as Mirror Motion Compensation (MMC) and is applied during instrument imaging and sounding along with the IMC.

The MMC implementation preserves maximum operational flexibility in that both instruments may be operated independently.

5.4.6 Dynamic Interactions High frequency (near 100 Hz) excitations may occur due to static and dynamic imbalance of momentum wheels. These must be minimized by design and great care should be taken to avoid resonances (with the earth sensor mirrors for example) within the operating range of the wheels.

5.4.7 Station Keeping Station keeping events represent a major perturbation in the operation of a weather satellite. This is a particular problem for the GOES-I configuration because of the lack of direct yaw control. Immediately after a NS station keeping event there exists a yaw error equal to the inclination change. A yaw reset thrusters firing will remove most of the error except for a residual amount which must be determined along with updated orbital parameters through the image navigation process and compensated with IMC.


of 97 MTG IMAGE NAVIGATION AND REGISTRATION PERFORMANCE SIMULATOR

6 MTG IMAGE NAVIGATION AND REGISTRATION PERFORMANCE SIMULATOR

6.1 Introduction During the traineeship, various tasks had to be accomplished. The trainee was focused on the development of an INR performance simulator (INR-PS since now) applied to MTG phase A projects. To do that, the first step was the reading of all the documentation available from the two consortiums set up: EADS Astrium and TAS. On the other hand, the trainee had at his disposal two different pre-executable codes (*.p code) from both consortiums with relative different results. Both codes are unworkable since no source code is available and a lot of functionalities are accessible just from the Graphical User Interface. Users manuals and algorithm descriptions were provided but with some limitations.

The trainee work was based on the EADS Astrium simulator apart from the Scanning pattern which can be defined as a mixture between both Astrium and TAS solutions.

6.2 Objectives of the simulator MTG INR-PS stands for Meteosat Third Generation Image Navigation and Registration Performance Simulator. The main objectives of this tool are:

• Estimation of the INR performances.

• INR algorithmic design and assessment of filter parameters.

• INR algorithmic verification.

In order to fulfil those objectives, the INR-PS will:

• See how on-board observables (orbit & attitude estimation) allow geometrical restoration.

• See how on-ground observables (ranging and landmarks) allow geometrical restoration.

• Quantify the performance of this restoration depending on the Scanning geometry, AOCS configuration and accuracy, distribution and reliability of landmarks, number and configuration of ranging stations, …

• Quantify the preliminary geometrical image quality of the whole MTG satellite system.

• Allow detailed algorithmic studies in the frame of MTG project.

6.3 General principles of the simulator The general principles for an INR image simulator are based on:

• The capacity to model and simulate the “geometry” of an image including a certain number of deformations

• With “assumptions on how representative” the simulation is with respect to MTG system characteristics.

The geometrical modelling function can be used considering two different modes as discussed in the following paragraphs:



6.3.1 The image simulation mode The principle for image simulation is to start from images issued from existing Earth observation systems (MSG, MTSAT, GOES, Landsat...). Such images are re-sampled and filtered with respect to the geometrical modelling of the MTG system. In the same time, is consistency with the image data, auxiliary data and external data are also simulated (gyro and star tracker models, instrument model, ranging, science data...). The complete output data set (image and auxiliary) can then be used by INR processing prototype for image restoration. It is then possible to perform the whole simulation chain on different configurations and to compare results for performances estimation.

6.3.2 The landmarks simulation mode The estimation of performances generally implies statistical computations (covariance analysis, temporal statistics, sensitivity analysis...). That requires running a great number of image cases. The use of end-to-end simulation including pixel image data may be very heavy, and even impossible to manage due to the lack of source image data, the precise knowledge of the source image geometry, the volume of generated data, and most of all, the necessary computation time.

The way to bypass the difficulty is agree on some assumptions, for instance by inserting a landmark model that can represent landmarks performances in terms of availability, accuracy, and false detection. Instead of simulating pixel image data, it is then possible to generate directly landmarks positions as being at the output of the landmark matching processing. The navigation filtering and the overall performance estimation can then be performed nominally.

As stated before, this landmark simulation mode was chosen to develop the MTG INR-PS due to computation time saving. The previous image simulation mode can be considered as the natural extension of the landmarks simulation mode.

6.4 General architecture of the simulator The INR Performance Simulator is composed of three main modules:

• The INR On-board simulation module: It is the forward modelling part of the simulator and it is in charge of image observation, AOCS estimation with the on-board measurements, image restoration with this AOCS information.

• The INR On-ground simulation module: It is the inverse modelling part of the simulator and it is in charge of observables selection, on-ground estimation, image restoration with the accurate estimation.

• The INR Performance Extraction module: It’s the output result modelling part of the simulator and it is in charge of the performance analysis, calculating different figures of merit.



Figure 6-1: MTG INR-PS general architecture by functionalities

The simulator developed during the traineeship just includes the first mode or landmarks simulation mode. Figure 6-2 represents an architecture block diagram for this mode:

Figure 6-2: MTG INR-PS landmarks simulation mode architecture block diagram

Although next step and natural extension of landmarks simulation mode, the image simulation mode, was not accomplished during the traineeship, some time was spent to think and design an architecture taking profit of the previous architecture already done for landmarks simulation



mode. This mode makes up a real Image Quality Tool (IQT) which is the end-to-end tool for on-ground and in-flight characterization and performance demonstration. Figure 6-3 represents an architecture block diagram for the image simulation mode. It can be seen that the architecture is really similar to the previous mode, where some other blocks covering new functionalities have been added up.

Figure 6-3: MTG INR-PS image simulation mode architecture block diagram

From this point further, this document is going to focus on each block and explain the mathematical concepts and models used.


of 97 SCANNING CONCEPT

7 SCANNING CONCEPT

7.1 Introduction This chapter presents a trade-off on the possible scanning concepts that can be considered.

7.2 Assumptions & Constraints A large number of scanning concepts can be envisaged. On the simulator, this analysis is limited to the 2-axes gimballed systems, since spinning or librating platforms are not planned for MTG and the corresponding single axis scanner will not be utilized.

2 mirror systems are considered too much bulky, especially in view of the implementation of several instruments on the same platform. In addition, such concepts feature a very large instrument aperture, which is a significant drawback in view of the thermal control aspects and solar impacts around the midnight period.

The geometry of the gimballed system is fully determined by the definition of 3 vectors: the two scan axis directions and the telescope optical axis direction. The number of possibilities is reduced considering the following assumptions and constraints:

• The fast scan direction is set along EW. This assumption ensures continuity with the former Meteosat imager series, and ensures better temporal coherence for each Earth hemisphere.

• The scan mirror is fixed on the fast scan mechanism. This is the configuration minimizing the requested torque and consequently providing the minimum perturbations to the spacecraft.

• The South-North scan axis shall be perpendicular to the EW scan axis for the Nadir pointing direction. This condition is obvious to obtain a regular image grid.

• In order to minimize polarization effect, the incidence angle on the scan mirror shall be minimized. Two cases will be considered:

o A first case with an incidence angle of 45º for Nadir pointing corresponding to the usual GEO image configuration (GOES, SEVIRI)

o A second case with an incidence angle reduced to 22.5 º. It must be noted that a lower incidence angle is deemed not feasible for telescope accommodation constraints.

• In terms of instrument accommodation on the spacecraft, two basic configurations can be envisaged:

o Either the telescope axis or the scan assembly is set in an horizontal plane (the YZ plane for example)

o Either the telescope axis or the scan assembly is set in a vertical plane (the XZ plane for example)

7.3 Scanning Concepts Identification The Scanning concept can be easily identified by a code of alphanumeric digits. See Figure 7-1.

This code is divided into three groups separated by a slash:



• The first group is used to define the telescope axis as follows:

o First digit is always either an H to indicate the telescope axis is on the horizontal plane, or a V to indicate the telescope axis in on the vertical plane.

o The rest of the digits of the group are the angle between telescope axis and Nadir (Z axis).

• The second group is used to define the fast scan axis as follows:

o First digits can be one or two letter among X,Y and Z. If there is one letter, it means the fast scan axis in on the axis with the same denomination. If there are two letters, it means the fast scan axis in on the plane defined by the two axes with the two letters denomination.

o Just in the case there is two letters, the second group is compound by more digits which indicate the angle between the fast scan axis and the telescope axis known since it is defined on the first group.

• The third group is used to define the slow scan axis as follows:

o First digits can be one or two letter among X,Y and Z. If there is one letter, it means the slow scan axis in on the axis with the same denomination. If there are two letters, it means the slow scan axis in on the plane defined by the two axes with the two letters denomination.

o Just in the case there is two letters, the third group is compound by more digits which indicate the angle between the slow scan axis and the telescope axis known since it is defined on the first group.

In the next Figure 7-1, an example can be seen:

Figure 7-1: scanning concept identification

7.4 Candidate Scanning Concepts Consideration of the above constraints leads to the definition of 12 possible scanning configurations which can be tested on the MTG INR-PS. They are illustrated on Figure 7-2 together with their denomination.



Figure 7-2: candidate scanning concepts

7.5 Brief Overview and Baseline of the Scanning Concepts Impact

7.5.1 Accommodation aspects

7.5.1.1 Telescope

The low incidence angle 45º provides a more compact assembly, but might be more difficult for the support structure to interface with the spacecraft; this however depends on the position of the spacecraft interface plane.

The large incidence angle 90º allows a priori more flexibility for the telescope focal plane accommodation. The focal optics can be placed either on south or north side of the instrument.

Moreover, low incidence angle geometry imposes a longer entrance baffle, which is favourable on the thermal point of view, but actually provides less protection against direct sun illumination.

These consideration lead to select H90 and V90 configurations as the preferred ones for the optics accommodation aspects, but this selection shall not be considered as a strong driver.

7.5.1.2 Scan assembly

The mechanical accommodation of the mechanisms is certainly an important constraint for the scanning concept selection.

The fast scan drive shall be directly connected to the scanning mirror to minimize the moving inertia, hence the motor torque requirements. So, the horizontal telescope configuration with the motor and encoder connected to the smallest side of the scanning mirror provides the easiest configuration from the mechanical point of view. However, this configuration is not the best one in terms of dynamic perturbations since the rotating inertia is not minimized.



For the vertical telescope configurations, the mechanical connection of the scan mirror to the drive unit is less evident, especially when the scan axis corresponds to the largest mirror side (V90-XZ45-Y and V45-XZ67.5-Y). Configurations with the drive unit in the back of the scan mirror (V90-XZ0-Y and V90-XZ90-Y) are certainly the most simple in terms of accommodation and connection to the slow scan device

7.5.1.3 Calibration

Calibration can be achieved by inserting a calibration source in the field of view or by the possibility of scanning mirror viewing a full aperture calibration source placed in the scanning assembly cavity (GOES imager). The first option is preferred, especially in the infrared spectral range.

7.5.2 Thermal aspects The most critical orbital configuration is when the Sun is entering the instrument cavity around the midnight period. The thermal inputs are determined by the size of the entrance baffle which depends just on the instrument angular field of view. This field of view is the same for all the configurations, so all of them are equivalent on the thermal aspects.

The small difference may come from the entrance baffle length. Long baffle are preferred to limit the thermal inputs, so configurations H45 and V45 will be better in these terms. On the other hand, for thermal control of the instrument cavity, one side of the instrument shall have connection to space for evacuating solar thermal loads and also the number and positions of the instruments on-board are important. The accommodation constraints at spacecraft level drives all the previous ideas and therefore no better configurations can be obtained taking into account just thermal aspects.

7.5.3 Structural aspects The instrument structure can be designed to support any instrument configuration. Nevertheless, some configurations will lead to more complex structures, with a potential impact on the mass budget. Configurations H90 and V90 will lead to simpler structural design and are preferred to the H45 and V45 layouts.

7.5.4 Scanning concept baseline From all the possibilities, the baseline concept is the one represents in Figure 7-1 and highlighted in Figure 7-2. This configuration is the one used in all the simulation results.

7.6 Scanning Mirror Law Calculation Next step, once the scanning concept is defined, is the calculation of the scanning mirror law or the movement needed on the mirror to describe a specific scanning pattern. This calculation is based on three assumptions:

• Spacecraft position conforms to a perfect geostationary orbit

• Instrument attitude is perfectly aligned to the orbit

• Instrument scanning mirror control is perfect

The scanning pattern used on the MTG INR-PS is the one represented in Figure 7-3. This pattern is defined with a bunch of parameters whose value used in the simulation results is



indicated in Table 7-1. The difficulty appears on how accurate the East/West scan speed can be controlled to better than 0.05% scan rate (producing an error of about 140 m in the sampling distance). In this simulation case, the scanning is assumed perfect, with the exception of the deformations induced naturally by the scan law.

Figure 7-3: Scanning pattern used on MTG INR-PS

Parameter Value used in simulations

Total acquisition time 600 seconds

Swath change duration 0.5 seconds

Retrace duration 60 seconds

Percentage overseen 19%

Initial NS Line of Sight angle 10.2º

Integration time 155 microseconds

Table 7-1: Scanning pattern definition parameters

With all the assumptions introduced in the previous paragraphs, the results for the scanning angles are displayed in Figure 7-4:



Figure 7-4: NS and EW mirror angles

7.7 Scanning Mirror Torques Once the scanning mirror movement is perfectly defined kinematically, it must be characterized dynamically with the help of the inertia matrix. The values used on the simulations are in Table 7-2:

Parameter Value used in simulations

Total mass 4.5 Kg

Radius 0.6 m

Width 0.2 m

Table 7-2: Parameters to define dynamically the scanning mirror

Then, the internal scanning mirror torque in Instrument Reference Frame can be calculated. This torque is one of the perturbing torques to take into account on the AOCS simulation. The result with the previous data is shown in Figure 7-5:

Figure 7-5: scanning mirror torques


of 97 ATTITUDE & ORBIT CONTROL SUBSYSTEM SIMULATION

8 ATTITUDE & ORBIT CONTROL SUBSYSTEM SIMULATION

8.1 Introduction MTG INR-PS is able to work with different attitude files that come from AOCS simulators. The scope of this project also includes an AOCS simulator which has been developed by Igone Urdampilleta Aldama during her Spanish Traineeship, so it is going to be briefly described since it is not the purpose of this document. According to that, there are two possibilities at this point: some AOCS files used by the industrial INR simulators and files generated with this internal ACS simulator.

8.2 MTG INR-PS and AOCS simulator interface AOCS simulators generate files that are used as input files on the MTG INR-PS. These files include all the parameters needed by MTG INR-PS in order to reconstruct the knowledge of the attitude on-board and calculate the landmark residual to introduce on the post-processing filtering.

The AOCS file has to contain 13 parameters which can be seen in Table 8-1:

Parameter Description

UTC time UTC time since 1/1/2000 0:00h in seconds

Real_r True orbit radius in ECEF in meters

Real_lon True orbit longitude in ECEF in degrees

Real_lat True orbit latitude in ECEF in degrees

Real_roll True roll attitude in ECEF in degrees

Real_pitch True pitch attitude in ECEF in degrees

Real_yaw True yaw attitude in ECEF in degrees

Measured_r Estimated orbit radius in ECEF in meters

Measured _lon Estimated orbit longitude in ECEF in degrees

Measured _lat Estimated orbit latitude in ECEF in degrees

Measured _roll Estimated roll attitude in ECEF in degrees

Measured _pitch Estimated pitch attitude in ECEF in degrees

Measured _yaw Estimated yaw attitude in ECEF in degrees

Table 8-1: Parameters contained on the AOCS file


of 97 ATTITUDE & ORBIT CONTROL SUBSYSTEM SIMULATION

8.3 External AOCS simulation files Some AOCS files with all the information needed are available as input files on the INR simulators developed by the two consortiums. These files have being used to obtain the simulation results.

8.4 Internal ACS simulator for Attitude data The detailed specifications of the ACS simulator developed can be found in [AD7]. As stated in chapter 4.5 page 20, precision correction is performed after systematic correction. So the ACS simulator is in charge of the first on-board processing and later on a systematic on-ground processing is simulated.

It must be noticed that just the attitude data is simulated and not the orbit data. There is just an orbit propagator, so in this case the true and estimated orbit data are identical.

The main objective of this simulator would allow to analyze different sensors (STR, sun sensor, earth sensor,…), actuators (momentum wheel, reaction wheel, chemical propulsion thrusters, ion propulsion thrusters, etc..) and control laws combination, for the stabilization of a geostationary satellite itemized for MTG.

The simulator is divided in three main modules External Environment and Disturbances, Internal Disturbances, Spacecraft Dynamics and AOCS, as Figure 8-1 shows. External Environment and Disturbances module contains calculation of external disturbances forces and torques applied in a geostationary orbit and environment data needed for their assessment. AOCS module obtains corrections should be applied on spacecraft taking account external disturbances and satellite dynamics. Finally, Spacecraft module calculates new position, velocity and attitude after AOCS control.

Figure 8-1: AOCS simulator overview

The AOCS simulator is based on the MTG-I dual wind concept from EADS Astrium.


of 97 LINE OF SIGHT SIMULATION

9 LINE OF SIGHT SIMULATION

9.1 Introduction The navigation model is based on the simulation of the Line Of Sight taking into account all the possible disturbances that can affect it. It consists in the method that relates any pixel within raw images to, the coordinates of the corresponding point on Earth, either in terms of longitude and latitude, in terms of Cartesian coordinates, or in terms of projection coordinates.

It can be noted this relationship can be establish directly or the other way around defining what it is called Direct and Inverse Navigation. The Direct Navigation is the one that for any pixel within the raw image allows computing the coordinates of the corresponding point on Earth. The Inverse Navigation calculates the pixel within the raw image when the point on Earth is known.

Moreover, this study is focus on the sensor module of the FCI which is supposed to be mounted on the North side of the platform. It is composed of two main assemblies: the scanning mirror assembly and the telescope assembly made up of primary and secondary mirrors plus a focal plane detector array. To each assembly is associated a reference frame.

In the current chapter, the mathematical model of the LOS selecting the direct way: it is described from the detector definition on the focal plane until the intersection of this LOS with the Earth and final projection and scaling to transform in row and column of the pixel within an image.

9.2 General Direct Navigation Equation This general navigation equation is shown in detail in the next Figure 9-1, with a synthesis on the origin of parameters. This equation relates the location of a pixel i of the band j in the focal plane, at a certain time t to a corresponding sighted Earth point.

Figure 9-1: General Direct Navigation Equation



A correction rotation is applied to the LOS in Instrument Reference Frame to transform to Body Reference Frame. On top of that, we can see the temporal dependency due to thermo-elastical deformations.

Next step, the direction seen from the AOCS Local Orbital Frame may be rotated by non-zero attitude perturbations, represented by the angle vector, and provided by on-board attitude estimation.

Later on, a pure mathematical transformation is done to calculate the LOS in Earth Centered Local Frame, so the angles are constants and a final transformation, where the angles from the orbit information are used, is carried out to calculate the LOS in Earth Centered Earth Fixed reference frame.

The last part, just define the intersection over the Earth surface of this LOS in ECEF.

Now, the algorithm is going to be explained step by step.

9.3 Focal plane and Telescope geometry Each detector's i position can be characterised in the telescope reference frame (see Figure 9-2) by the vector (Xi(t),Yi(t),Zi(t)). Two different approaches can be followed from this point: the general model or the simplified one

9.3.1 Telescope Reference Frame A “virtual” focal plane is defined by superimposing all focal planes even though some of them are physically located in different planes. The telescope reference plane definition is as follows:

• Origin: intersection of the telescope optical axis with the focal plane.

• X axis: optical axis.

• Y axis: in the focal plane aligned with the line of detector.

• Z axis: perpendicular to X and Y axes such that the frame is a right handed triad.

9.3.2 General Model The LOS simulator is ready to receive a file with the position of each detector in telescope axis for each time (X(i,t), Y(i,t), Z(i,t)) which accounts thermo-elastical deformations. This approach means less computation but these kinds of files are really difficult to obtain and assess. So, a simplified model is used.

9.3.3 Simplified Model If we consider a line of n_det equidistant detectors with a distance between one and the next of d_pix and they are indexed by value N (between 0 and n_det-1), and if we assume it as perfectly linear and regular, as in Figure 9-2, we can have the following relationship:

( )( )00

00

_sin_cos

0

NNpixdZZNNpixdYY

X

−⋅⋅−=−⋅⋅+=

=

θθ

Where is the orientation of the line with respect to the Y axis and (Y0 Z0) is a reference position corresponding to the pixel N0



This approach is considering the detectors are rigidly connected and a rotation around telescope axis. On the other hand, two focal tilts are considered second order effects and they are taken into account with a little movement of the optical axis intersecting the focal plane in OOA=(0,YOA,ZOA). We take:

⎟⎟⎠

⎞⎜⎜⎝

⎛ −=

+=⇒

−=−=

real

real

realrealreal

OAreal

OAreal

YZ

ZY

ZZZYYY

arctan

22

θ

ρ

The optical distortion has been later modelled at third order by:

( )21 realrealthe ρξρρ ⋅−⋅=

And with this distortion, where ξ is the distortion parameter in m-2, the new positions can be calculated:

OAthe

OAthe

realthethe

realthethe

ZZZYYY

ZY

+=+=

⇒⋅−=

⋅=''

sincos

θρθρ

Where (0,Y’,Z’) are the virtual position of the pixel. Finally, the direction unitary vector expressed within the telescope frame (U0)TF for each pixel is computed within the focal plane through the telescope by:

( )⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−−⋅

++=

''

''1

2220

ZYf

ZYfU TF

Figure 9-2: Focal plane and telescope geometry definition

The inter-channel co-registration is not modelled, but it can be inserted, in the future, through any relative positioning of the different detectors within the focal plane geometry.



9.4 Scanning geometry The description of the scanning assembly is given in chapter 7 on page 34. The objective here is to compute the direction of the LOS in the Instrument reference frame (ULOS)IF after reflection onto the scanning mirror. But some reference frames must be defined first.

9.4.1 Scanning assembly frame (SAF) An intermediate frame, see Figure 9-3, is defined, by convenience, based upon the NS scanning axis. The scanning assembly frame definition is as follows:

• Origin: intersection of the telescope optical axis with the scanning mirror plane when the scanning mirror is in Nadir pointing position.

• X axis: NS scanning axis (positive direction from South to North).

• Y axis: EW scanning axis when the Nadir is pointed (NS scanning angle = 0º).

• Z axis: perpendicular to X and Y axes such that the frame is a right handed triad.

Note that when both axes are not perfectly perpendicular (in case of some misalignments), the projection of the EW scanning axis within the plane perpendicular to the NS scanning axis is considered. The scanning assembly frame is fixed and does not move with the scanning mirror. This means the EW scanning axis is not aligned with the YSAF axis when the NS scanning angle is not zero.

9.4.2 Instrument frame (IF) This reference frame, see Figure 9-3, can be deduced from the scanning assembly frame through a rotation of an angle α/2 (with α equal to the angle between the optical axis and the perfect nadir) around the NS scanning axis.

Figure 9-3: Scanning geometry definition



9.4.3 Mathematical model The scanning mirror position is defined by the scanning angles around the EW axis and NS axis, respectively site mirror angle and elevation mirror angle. By convention, The Nadir direction is pointed when both of these mirror angles are null.

First step is to obtain the direction unitary vector expressed within the instrument frame (U0)IF. Nominally, the telescope axis is perpendicular to the NS scanning axis and:

( ) ( )TFIF UU 00

0sincos0cossin100

⋅⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−=

αααα

The misalignments associated with the NS and EW scanning axes can exist during the integration of the scan mirror assembly. In order to compute (U0)IF more precisely, these terms are considered in the equation of the geometric model and it is assumed that their exact values will be provided before launch. The misalignments associated with the NS and EW scanning axes do not change the definition of the scan assembly frame (SAF). The small angle assumption for roll, pitch and yaw misalignment angles and the first order approximation for the expansion of trigonometric equations are applied to save space on this report but in the code the complete rotation matrix is calculated. The transformation is now:

( ) ( )TFIF Upq

prqr

U 00

11

1

0sincos0cossin100

⋅⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−−

−⋅

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

−=

αααα

Second step is to compute the direction of the mirror with respect to the scanning angles, corresponding to the mechanical motor angular position given by site SC and elevation EV angles. In other words, express the perpendicular vector (Nmirror)IF to the mirror plane taking into account that the normal vector is defined by the unit vector normal to the mirror plane from the centre of the scan mirror reference frame when the mirror plane is assumed to be perfectly flat.

By construction of the SAF, the NS scanning axis is aligned to the X axis and bearing in mind the telescope axis in on the vertical plane YZ with an angle α from Nadir, it is known:

( ) [ ]

( ) ⎥⎦⎤

⎢⎣⎡ −=

=

2cos

2sin0

001

ααIFnadir

IFNS

N

R

The EW fast scanning axis is on the YZ plane when the Nadir is pointed. The positive direction corresponds to scan from West to East. A misalignment β corresponding to a non perpendicularity between both axes is also considered, so:

( ) [ ] ( )⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛⋅

⎟⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜⎜

⎝

⎛

−

=⇒=0

cossin

2cos

2sin0

2sin

2cos0

0010cossin β

β

αα

ααββ IFEWSAFEW RR



It must be remembered that to know the orientation (Nmirror)IF, EW scanning axis rotates around

the NS scanning axis. Using the quaternion notation defined as ⎥⎦⎤

⎢⎣⎡ ⋅=

2sin

2cos),( θθθ vvQ rr

with the rotation angle θ and the axis defined with the unitary vector vr , the two rotation can be notated as ( )NSREVQ , and ( )EWRSCQ , .

Figure 9-4: Scanning mirror reflection

According to the previous paragraph, the (Nmirror)IF can be calculated from: ( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( ) ( )( )IFNSIFEWIFnadirIFEWIFNSIFmirrorIFmirror REVQRSCQNQRSCQREVQNQN ,,,,,, −⋅−⋅⋅⋅=⇒ ππ

The third and last step is to compute the effect of the mirror reflection, see Figure 9-4,which can be expressed through the following relationship:

( ) ( ) ( ) ( )( ) ( )IFmirrorIFIFmirrorIFIFLOS NUNUU ∧∧⋅−= 00 2

9.5 Optical Site and Elevation angles calculation As it can be seen from the geometry on Figure 9-5, the optical site SC and elevation EV angles with refers to EW and NS respectively, can be calculated through the following formulations:

( )( )( )( ) ( )( )

( )( )( )( ) ⎟

⎟⎠

⎞⎜⎜⎝

⎛=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

+=

ZIFLOS

YIFLOS

ZIFLOSYIFLOS

XIFLOS

UU

arctgEV

UU

UarctgSC

22



Figure 9-5: Optical Site and Elevation angles calculation from (ULOS)IF

9.6 Focal Plane Mapping Once the Line of Sight vector is known on the Instrument reference frame, some kind of calculations have to be done in order to introduce the focal plane misalignment due to some integration malformations and thermo elastical deformations to obtain the Line of Sight vector on the body reference frame BRF which is defined as follows:

• Origin: satellite centre of mass, as a rigid body.

• X axis: specified direction fixed to the satellite and near to the velocity vector in operational mode.

• Y axis: specified direction fixed to the satellite and near to the south direction in operational mode.

• Z axis: perpendicular to X and Y axes such that the frame is a right handed triad, fixed also to the satellite and near to the nadir in operational mode.

These deformations [ ])()()( 321 ttt ϕϕϕ are provided by a file based on previous geostationary missions.

See Figure 9-6 a graphical representation.

9.7 Satellite Attitude Next step is to transform from the Body reference frame to the Local Orbital reference frame LORF which is defined as follows:

• Origin: satellite centre of mass.

• X axis: spacecraft velocity direction from West to East.

• Y axis: South-North direction from North to South.

• Z axis: perpendicular to X and Y axes such that the frame is a right handed triad, on the nadir direction.



The transformation between both frames is defined by three Euler angles [ ])()()( tRtPtY which are simulated on the ACS simulation. This step can be seen in Figure 9-6.

9.8 Satellite Orbit Last step to calculate the Line of Sight unit vector in Earth Centered Earth Fixed frame is introduce the satellite orbit information. This transformation is divided into two different transformation:

The first one transforms from LORF to the ECLF. It is a mathematical constant transformation

computed as a rotation matrix with this angles [ ]2,2,0 ππZYXR .The ECLF is defined as

follows:

• Origin: Earth centre.

• X axis: pointing to the satellite.

• Z axis: pointing to the mean rotational terrestrial axis, so near polar.

• Y axis: perpendicular to X and Z axes such that the frame is a right handed triad.

The second one transforms from ECLF to the final ECEF. It is a transformation computed thanks to the satellite latitude and longitude information. The ECEF is defined as follows:

• Origin: Earth centre.

• X axis: it is on the plane of terrestrial equator crossing the 0º longitude meridian.

• Z axis: pointing to the mean rotational terrestrial axis, so near polar.

• Y axis: perpendicular to X and Z axes such that the frame is a right handed triad. It is on the plane of terrestrial equator crossing the 90º longitude meridian.

Both transformations can be seen in Figure 9-6.

Figure 9-6: Generic geolocation algorithm representation

At this point, we have a LOS simulator taking into account



• Focal plane definition errors (with tilts considered as distortion on the optical axis)

• Misalignment between the telescope and the scan assembly

• Misalignment corresponding to non perpendicularity between rotation axes

• Misalignment between satellite and optical bed

• AOCS data from simulation with all the onboard hardware and software.

9.9 Intersection on the Earth A given pixel within an image has been acquired at a time t by the pixel i. The general process consists first in computing the line of sight orientation of this pixel with respect to an Earth reference frame and that has been explained above. The corresponding vector (ULOS)ECEF is the output of a processing that models the geometry of the satellite, including the instrument geometry, bus geometry, (orientation of the instrument with respect to the satellite mechanical frame), the attitude restitution, the frame transform between satellite frame, local orbital frame and Earth reference frame.

As can be seen in Figure 9-6, if we defined:

• (ULOS)ECEF = [XE YE ZE] the unit vector direction in ECEF coordinates

• OT = [XT YT ZT] as the intersection point in ECEF coordinates

• OS = [XS YS ZS] as the spacecraft position in ECEF coordinates

• A as the equatorial Earth radius

• B as the polar Earth radius

• [XC YC ZC] as the Earth centre in ECEF coordinates which by definition are going to be null.

• The altitude of the point which is considered null is h.

Then, the equation to obtain the Earth intersection point is given by these two equations:

[ ] [ ] [ ]( )

( )( )( )

( )( )

12

2

2

2

2

2

=+

−+

+

−+

+

−

⋅+=

hBZZ

hAYY

hAXX

ZYXdistZYXZYX

CTCTCT

EEESSSTTT

Solving for these two equations for dist gives:

( )( )

( )( )

( )( )

1222

222

222

2

−⎟⎠⎞

⎜⎝⎛

+−

+⎟⎠⎞

⎜⎝⎛

+−

+⎟⎠⎞

⎜⎝⎛

+−

=

+

⋅−+

+

⋅−+

+

⋅−=

⎟⎠⎞

⎜⎝⎛

++⎟

⎠⎞

⎜⎝⎛

++⎟

⎠⎞

⎜⎝⎛

+=

⋅−−−=

hBZZ

hAYY

hAXX

termC

hBZZZ

hAYYY

hAXXX

termB

hBZ

hAY

hAX

termA

termAtermCtermAtermBtermBdist

CSCSCS

ECSECSECS

EEE

Last but not least, from these data in Cartesian coordinates, the geodetic latitude and longitude of the intersection point can be derived by the next equations:



9.10 Projection and Scaling Each pixel on an image is addressed by a pair of coordinates: the column number c and the line number l. The relation between image coordinates and geographical coordinates is determined by the concatenation of two functions in each direction, see Figure 9-7:

Figure 9-7: projection and scaling functions

Note that the geographical coordinates (lon and lat) and the intermediate coordinates (x and y) are real numbers while the image coordinates (l and c) are integer numbers.

The projection functions:

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛⇔⎟⎟

⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛ −

yx

flatlon

latlon

fyx 1

are nonlinear functions specified by the projection name.

The scaling functions:

⎟⎟⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛⇔⎟⎟

⎠

⎞⎜⎜⎝

⎛=⎟⎟

⎠

⎞⎜⎜⎝

⎛ −

lc

gyx

yx

glc 1

are linear functions specified by the scaling factors.

9.10.1 Projection function The projection used is GEOS where the sub-longitude has to be specified, in this case 0º. The normalized geostationary projection describes the view from a virtual satellite to an idealized earth. Herein, the virtual satellite is in a geostationary orbit, perfectly located in the equator plane exactly at longitude λD. The idealized Earth is a perfect ellipsoid with an equator radius of A and a polar radius of B.

In the following a short description of the theoretical background is provided:

Two Cartesian coordinate frames are introduced. (e1,e2,e3) has its origin in the centre of the earth. (e3) points in northern direction, (e1) points towards the Greenwich meridian. (s1,s2,s3) has its origin at the satellite position. Again (s3) points northwards, and (s1) directs to the centre of the earth. Figure 9-8 visualizes this situation and identifies several angles and lengths used in the following.

The earth is described as an oblate rotational ellipsoid:

12

23

2

22

21 =+

+Be

Aee



The vector re points from the centre of the earth to a point P on the earth’s surface. Thus, le is the longitude and fe is the geocentric latitude describing the point P. The transformation from geographic coordinates (lon, lat) is as follows:

( )⎟⎟⎠

⎞⎜⎜⎝

⎛⋅⎟

⎠⎞

⎜⎝⎛=

=

lattgABarctg

lon

e

e

2

φ

λ

The length of re is:

e

e

ABABr

φ22

22

cos1 ⋅−

−

=

The Cartesian components of the vector rs (in the satellite coordinate frame) result as follows:

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⋅−⋅⋅−

−⋅⋅−=

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛=

ee

Deee

Deee

s

rr

rdistGEO

rrr

rφ

λλφλλφ

sin)sin(cos

)cos(cos_

3

2

1

Figure 9-8: Coordinate frames for GEOS projection

The forward projection function is as follows:

⎟⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜⎜

⎝

⎛

⎟⎟

⎠

⎞

⎜⎜

⎝

⎛

++

⎟⎟⎠

⎞⎜⎜⎝

⎛

=⎟⎟⎠

⎞⎜⎜⎝

⎛

23

22

21

3

1

2

rrr

rarctg

rr

arctg

yx

Which if everything is perfect coincide with the optical site SC and elevation EV scanning angles.



9.10.2 Scaling function The scaling function provides a linear relation between the intermediate coordinates (x,y) and the image coordinates (l,c). Supposing the number of lines and columns are known, the process consist on making integer the scanning angles by rounding.

In Figure 9-9, the complete projection and scaling process can be seen.

Figure 9-9: Projection and scaling process

9.11 Time interpolation In the case a variable is expressed directly in a temporal series, its value at any requested time is defined by time interpolation between the two surrounding closest-in-time values. If time is after the time stamp of the last value in the series, the value of this last point is used. Respectively, if time is before the time stamp of the first value in the series, the value of this first point is used.

Supposing )(tVariable is known for Nttt ≤≤0

( )⎪⎪⎩

⎪⎪⎨

⎧

⇒≥

+−⋅−−

⇒≤≤

⇒≤

= −−−

−−

)(

)()()(

)(

)( 111

11

00

NN

iiii

iiii

tVariablett

tVariabletttt

tVariabletVariablettt

tVariablett

tVariable


of 97 OBSERVABLES SELECTOR

10 OBSERVABLES SELECTOR

10.1 Introduction Observables have always played an important role in verifying the accuracy of a system and even to improve it. Observability is a measure for how well internal states of a system can be inferred by knowledge of its external outputs.

Formally, a system is said to be observable if, for any possible sequence of state vectors, the current state can be determined in finite time using only the outputs (this definition is slanted towards the state space representation). Less formally, this means that from the system outputs it is possible to determine the behaviour of the entire system. If a system is not observable, this means the current values of some of its states cannot be determined through system outputs: this implies that their value is unknown.

For an imaging spacecraft system, several observables can be used. As will be shown, each measurement establishes a set of components of spacecraft state vector. If q is the quantity to be measured and q∂ is the difference between the true and estimated values, then it will be seen

that the relation between q∂ and the deviation in spacecraft state vector r∂ from the estimated state vector is, to first order:

rhrhqT

∂⋅=∂⋅=∂

Regardless of the type of measurement. Thus, the h vector alone will characterize the measurement.

10.2 State vector The implementation on the MTG INR-PS subject of this traineeship is done separately in both EW and NS directions. That is not the most accurate way to approach the problem but on the other hand is the most intuitive and the simplest. This way does not allow to estimate yaw angles, as well as to account for coupling between axes.

Bearing in mind the previous paragraph, for each dimension EW and NS a serie of parameters are defined as the state vector:

• The pointing state including attitude and thermal distortions θ

• The scanning misalignment error κ

• The scanning misalignment error drift κ&

• The orbital position error λ

• The pointing state including attitude and thermal distortion drift δ

10.3 Observables types Four types of on-ground observables can be simulated:

• Landmarks: They provide two-dimensional information in EW and NS directions. A good landmark catalogue with well defined information is needed.

http://en.wikipedia.org/wiki/Measure

http://en.wikipedia.org/wiki/System

http://en.wikipedia.org/wiki/State_space_(controls)



• Ground Stations ranging: They provide three-dimensional information in range, elevation and azimuth. A ranging stations database including the location of Darmstadt, Kourou, Maspalomas, etc… for MTG is needed.

• Stars: They provide two-dimensional information in EW and NS directions. A star database built from Hipparcos catalogue filtered with declination between ±10º and SNR higher than 3 can be used for MTG.

• Horizons: They provide one-dimensional information along Earth radii. The Earth can be modelled as the WGS84 ellipsoid and the Greenwich hour angle can be assumed to be zero at the beginning of the simulation for MTG.

On the MTG INR-PS just the landmarks residuals have been simulated, due to the fact that they are the observables providing better information just on the parameters that defined the state vector, there are plenty of them and they are better known.

A more detailed explanation about the landmarks residuals used in the simulation is going to be presented and finally the other kinds of observables are going to be briefly analysed since they can be introduced in future updates of this software.

10.4 Landmarks residuals calculation

10.4.1 Definition Landmark can be defined as the position of a prominent or well-know object used as a point of origin in locating other objects or structures or as a point from which measurements can be taken.

As stated before, the INR ground processing can employ all available geo-location knowledge and the most important one is the landmark.

10.4.2 Landmark Database Operational landmark database (MSG, MTSAT, etc…) consist mainly on coastlines. But, the landmark database can be compound by not only coastal landmark but also inland landmarks such as lakes, rivers, geological features, infrastructural buildings and even forest. All the last ones might serve as landmarks in addition to coastlines but their stability in time has to be carefully investigated. The characterization of landmarks is therefore an essential part in achieving high knowledge measurement accuracy: landmarks’ reference coordinates are generally biased within certain accuracy. Time of date, season of year o tidal conditions might affect landmark position significantly. It is the so called geo-physical error.

The landmark database as been built by Logica CMG with the intention to meet the following goals:

• Good spatial distribution in order to have landmarks across the whole globe with precise information in EW and NS. On the simulation can be seen more landmarks are available around Europe and less of them on the Atlantic Ocean.

• Good temporal visibility. It means landmarks remain visible for as much of each time-of-day and each day-of-year as possible. To do that, regions with low probability of cloud cover are preferable, and regions which are not ice-covered in winter.

• Good temporal stability. Landmarks which do not change shape as a function of time-of-day or day-of-year are preferred. So landmarks are usually cliffs and not beaches.



In the second part of the study, the landmark characteristics and detection probabilities have been modelled, based on the experience gained from MTSAT. Information derived from the ISCCP was used to help determine appropriate detection probabilities, along with experience gained from actual operational landmarks used for the MSTAT missions. The landmarks database for MTG contains the following entries:

Field Description

Landmark ID Unique identifier for each landmark

Latitude Latitude of mi-point of landmark

Longitude Longitude of mid-point of landmark

BiasX (per band) Simulated non-zero value assigned, based on expected distribution of bias values (derived from MTSAT experience)

BiasY (per band) Simulated non-zero value assigned, based on expected distribution of bias values (derived from MTSAT experience)

Simulation-specific fields

MeasErrX (per band) Simulated Measurement Error. Non-zero value assigned, based on expected distribution of measurement errors (derived from MTSAT experience)

MeasErrY (per band) Simulated Measurement Error. Non-zero value assigned, based on expected distribution of measurement errors (derived from MTSAT experience)

Cloudiness A structure comprising various models of expected cloud cover for each landmark, as a function of time-of-day and month/season: - Average annual % cloud over (*1) - Average seasonal % cloud over (*4: winter, spring, summer, autumn) - Average diurnal % cloud cover (*8*12=96: Three-hourly averages for each month)

Table 10-1: Landmark database

Concerning the way this landmark database was built, it must be said that (Figure 10-1): • For the bias in the East/West (X) position and/or North/South (Y) position of each

landmark, the individual landmark bias is calculated as the mean of (Measured - Predicted) position for each landmark measured over multiple observations (several days of data). Where the measured landmark position is where it is located within the current image, and the predicted landmark position is based on least-square fit of all landmark positions to the orbit/attitude calculated from landmarks observed in multiple previous observations.

• For the measurement Error of each landmark. After removing the per-landmark bias from each landmark measured position, the remaining error in the difference between the measured landmark location and the expected landmark location (derived from "Goodness of Fit" calculations), gives an estimate of the landmark measurement error, for each landmark. This is derived from the standard deviation of the distribution of measured landmark locations around the mean (Bias) landmark location.



Figure 10-1: Bias (left) and measurement error (right) distribution for landmarks

Moreover, four landmarks database file are available with a different number of records. A first file of 442 landmarks, a second one with 868 landmarks, a third one with 2232 and a final one with 3097 landmarks. All of them can be seen on the next figures.

Figure 10-2: Details and differences over Europe between the landmarks database files available



Figure 10-3: Landmarks database files available on this MTG INR-PS

10.4.3 Landmarks Position Determination The overall process is decomposed as can be seen in Figure 10-4:

• The inverse navigation function, called with the real state vector (real attitude profile, real orbit profile, real thermo-elastic profile, etc) provide the ideal coordinates in the image.

• A Gaussian white noise is applied on those positions, in both EW and NS directions, to be representative of the performance of the landmark determination algorithm, corresponding to the image correlation error: This gives the real perturbed coordinate. The error also takes into account the fact that visible image is available or not for landmark determination: during daytime, the standard deviation of the error is reduced.

• A given ratio of these landmarks is simulated as wrong landmarks: for these randomly selected wrong landmarks, a higher noise is applied.



Figure 10-4: Landmarks Position Determination process

10.4.4 Landmarks in image overlapping zone For MTG it is foreseen that the image swath will be overlapping. As a consequence, the problem is not unique defined and some landmarks will appear twice in the image.

In general, there are three cases to be considered (see Figure 10-5):

• Case 1 applies when the landmark centre is located in the overlap zone.

• Case 2 presents the cases when the landmark is located in the upper half of the image swath and extends into the overlapping zone but the centre remains outside. The landmarks might then be also visible in the previous image trip.

• Case 3 applies for landmarks located in the lower half of the image swath and extend into the overlapping zone.

Figure 10-5: Landmark overlapping possibilities

Just on the first case, the landmark is going to be considered in both swaths as independent observables. On case 2, only one observable on the bottom swath is considered and respectively, only one observable on the top swath is considered on case 3.

10.4.5 Landmarks residual calculation For each landmark, a viewing direction residual is computed as it is shown in Figure 10-6. The residual, at the date of the observation, is the angle between:

• The estimated line of sight from attitude, orbit and focal plane geometry “raw” knowledge as given by the on-board AOCS and on-ground calibration, at the observed landmark matched position in the image, and

• The objective line of sight given by direction from S/C orbital position, as given by the AOCS data, to the landmark ground location (or tie point intersection with Earth ellipsoid).



Figure 10-6: Landmark residual calculation

At each landmark, the residual angle is decomposed in term of azimuth (EW or equivalent pitch angle) and elevation (NS or equivalent roll angle). Those values are given as input of the navigation filter.

10.5 Ranging stations residual calculation They are based on radar range, azimuth and elevation measurements. Assuming a radar site on the surface of the Earth to be the origin of the coordinate system and letting a Cartesian coordinate system be chosen such that the Z axis is radially out from the centre of the Earth through the radar site, the X axis is positive in the direction from which radar azimuths are to be measured, and the Y axis completes the coordinate system. Then, it may be written:

Figure 10-7: Ranging station residual calculation for a GEO orbit

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛⋅⋅

⋅=ε

αεαε

sinsincoscoscos

rr

Where αε ,,r are, respectively, the range, elevation and azimuth of the vehicle as observed from the radar site. Hence:



rr

rr

rrI

rr

∂∂

⋅⋅⋅⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛−+

∂∂

⋅⋅⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛⋅−⋅−

+∂∂

⋅⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛⋅⋅

==∂∂ αεα

αε

εαεαε

εαεαε

cos0

cossin

cossinsincossin

sinsincoscoscos

The vector coefficients in these equations are recognized as orthogonal unit vectors in the directions of increasing αε ,,r respectively. Thus, it may be solve for the partial derivatives by successively multiplying this last equation by the transpose of these unit vector to obtain:

[ ]

[ ]

[ ]0cossincos1

cossinsincossin1

sinsincoscoscos

ααε

α

εαεαεε

εαεαε

−⋅⋅

=∂∂

⋅−⋅−⋅=∂∂

⋅⋅=∂∂

rr

rr

rr

10.6 Horizons residuals calculation Referring to Figure 10-8, if R is the actual radius of a planet, the apparent angular radius A is found from:

RAr =⋅ sin

Again assuming that the state vector of the spacecraft is measured relative to the planet:

rr iAr

RiAr

ArAr

Arr

rA

rAArA

rr

⋅⋅

−=⋅⋅⋅

−=⋅

⋅∂∂

−=∂∂

⇒=∂∂

⋅⋅+⋅∂∂

coscossin

cos

sin0cossin 22

Figure 10-8: Apparent angular radius of a planet

10.7 Stars residuals calculation Bearing in mind the stars as possible observables, a lot of measurements can be taken:

10.7.1 Measuring the angle between the Earth and a Star The first type of measurement to be considered is that of the angle between the lines of sight to the Earth and a star. The angle A will be a function of the state vector r of the vehicle. Then, A may be expanded in a Taylor series about the reference state vector 0r at which point the

angle to be measured is 0A .



rhArrArArA T δδ ⋅+≅+⋅

∂∂

+= 00 ...)()(

Where the derivative is understood to be evaluated at the reference point. To calculate the coefficient of rδ , we differentiate the measurement equation

riArTS ⋅−=⋅ cos

Where is Si the unit vector in the direction of the star, to obtain:

rri

rAArA

rr T

S∂∂

⋅−=∂∂

⋅⋅−⋅∂∂ sincos

Or, equivalently,

TS

Tr i

rAArAi −=

∂∂

⋅⋅−⋅ sincos

Solving for the derivative of A with respect to the components of r gives

( ) Tn

TSr i

riiA

ArrA

⋅=+⋅⋅⋅

=∂∂ 1cos

sin1

The vector Tni is readily seen to be a unit vector which is in the plane of the measurement and is

normal to the line of sight.

( )SrTn iiA

Ai +⋅⋅= cos

sin1

10.7.2 Star elevation measurement Considering next the measurement of the angle between the lines of sight to a star and the Earth limb. From XXX

( ) riArTS ⋅−=+⋅ γcos and Rr =⋅ γsin

Where A is the angle to be measured and γ is the angle between the lines of sight to the center of the planet and to the planet edge. Therefore,

( ) ( ) TS

Tr i

rrAAriA −=⎟

⎠⎞

⎜⎝⎛

∂∂

+∂∂

⋅+⋅−⋅+γγγ sincos

And

0cossin =∂∂

⋅⋅+⋅r

riTr

γγγ

So that

( )Tnr ii

rrA

⋅+⋅⋅⋅

=∂∂ γγ

γcossin

cos1

Where is ni a vector in the plane of the measurement and perpendicular to the line of sight to the Earth.



( ) ( )[ ]Srn iiAA

i +⋅+⋅+

= γγ

cossin

1

It is easy to see that rn ii ⋅−⋅ γγ cossin is a unit vector in the direction from the spacecraft to the planet edge and that is the corresponding distance to that edge. Thus, the measurement geometry vector is simply

ργ

ir

h ⋅⋅

=cos1

where rn iii ⋅+⋅= γγρ sincos

The unit vector ρi lies in the plane of the measurement and perpendicular to the line of sight to the Earth limb.

Figure 10-9: Measurement of star elevation angle

10.7.3 Star occultation measurement The next time of measurement to be considered is that of noting the time at which a star is occulted by the Earth. The analysis depends directly on the star-elevation measurement just considered.

Let earthv and v be the respective velocity vectors of the Earth and the spacecraft so that:

earthr vvv −=

rv is the velocity of the spacecraft relative to the Earth. Clearly, the rate of change of the star-elevation angle A is

ργ ivdtdAr

Tr ⋅−=⋅⋅ cos or dArdtiv

Tr ⋅⋅=⋅⋅− γρ cos

Hence,

TTr i

dtdAr

rtiv ρρ γ −=⋅⋅=

∂∂

⋅⋅− cos

So that

ρρ

iiv

hr

⋅⋅

−=1



Where ρi the unit vector is defined as in the previously in 10.7.2 page 62.

10.7.4 Measuring the angle between two known directions For specificity, consider the two known directions to be two different stars S1 and S2. Let S be the reference position of the spacecraft at the time of measurement as shown in . Further, let r be the vector form S1 to the spacecraft and z the vector form the spacecraft to S2. With A denoting the angle from S1-spacecraft line to the spacecraft-S2 line.

rzzrzrAzrTT

⋅−=⋅−=⋅−=⋅⋅ cos and 21SSrzr =+

Hence,

rrz

rzr

rAAzr

rzAr

rrAz

TT

∂∂

⋅−∂∂

⋅−=∂∂

⋅⋅⋅−∂∂

⋅⋅+∂∂

⋅⋅ sincoscos

To dispose of the various partial derivatives in this equation, the next scalar relation must be differentiated

TTr

TSSSSSS zirr

rzzrrrrz ⋅−=⋅⋅+⋅−=

∂∂

⋅⋅⇒+⋅⋅−= 22222 212

212

212 so that

Tzi

rz

−=∂∂

Then, from the vector relation between r and z

0=∂∂

+∂∂

rz

rr

so that Irz

−=∂∂

As a consequence, the measurement geometry vector T

rAh ⎥⎦

⎤⎢⎣⎡

∂∂

= for this measurement is:

mn iz

ir

h ⋅+⋅=11

Where ni and mi are unit vectors, each lying in the plane of the measurement, the plane determined by the spacecraft and the two near bodies. The vector ni is normal to the line of sight to the S1 whereas mi is normal to the line of sight to S2.

( )rzn iAiA

i ⋅+⋅= cossin

1 and ( )zrm iAi

Ai ⋅+⋅−= cos

sin1

The measurement of the angle between the lines of sight to Earth and star (section 10.7.1 page 61) may be regarded as a special case of this measurement.


of 97 NAVIGATION FILTER

11 NAVIGATION FILTER

11.1 Introduction In 1960, R.E. Kalman published his famous paper describing a recursive solution to the discrete-data linear filtering problem. Since that time, due in large part to advances in digital computing; the Kalman filter has been the subject of extensive research and application, particularly in the area of autonomous or assisted navigation. This kind of filtering is used on this work to provide performance from a GEO imaging system landmark navigational model.

The Kalman filter is a set of mathematical equations that provides an efficient computational (recursive) means to estimate the state of a process, in a way that minimizes the mean of the squared error. The filter is very powerful in several aspects: it supports estimations of past, present, and even future states, and it can do so even when the precise nature of the modelled system is unknown.

The purpose of this document is to introduce the discrete Kalman filter mathematical model used. This chapter includes a description and some discussion of why this basic discrete Kalman filter has been used.

11.2 System state model As stated previously, the implementation on the MTG INR-PS subject of this traineeship is done separately in both EW and NS directions. That is not the most accurate way to approach the problem but on the other hand is the most intuitive and the simplest. This way does not allow to estimate yaw angles, as well as to account for coupling between axes.

Bearing in mind the previous paragraph, for each dimension EW and NS a serie of parameters are defined as the state vector:

• The pointing state including attitude and thermal distortions θ

• The scanning misalignment error κ

• The scanning misalignment error drift κ&

• The orbital position error λ

• The pointing state including attitude and thermal distortion drift δ

The pointing state θ representing attitude and thermal distortion error, evolves according to the linear drift state δ and is affected by AOCS attitude errors. The linear drift state δ representing all time-linear effects, mainly linear drift of attitude and linear evolutions of the thermal distortion error, is considered constant.

The scan mislignment error κ representing the coupling between the scan angle on one axis and the error on the other axis, is considered as a slowly drifting variable. The rate of evolution κ& of the scan misalignment error is considered constant in terms of state dynamics representation in the filter. In reality, it is subject to variations, and in order to prevent the filter from “locking” onto a given estimate, a state noise is introduced, representing a random walk effect forκ& . By changing the value for the state noise covariance, the filtering horizon for κ& can be adapted, depending on our knowledge of time characteristics of thermal effects.

Alternatively, instead of a random walk effect, an unknown linear drift effect could be modelled by adding an additional state κ&& corresponding to the second derivative of the misalignment error. The filter would not estimate this extra state (corresponding Kalman gains



are set to zero), so that the state only represents an effect of unknown drift ofκ& . This technique is called “considered parameters” and is a simple way to model linear evolutions of a Kalman filter state for which a more detailed model of evolution is not known or not needed.

The orbital position error state λ is considered a constant in terms of state dynamics representation in the filter. Similarly to scan misalignment drift, a state noise is introduced for λ therefore representing all unknown orbital evolutions and manoeuvres as random walk. The objective is to keep a very simple filter structure, as a model involving orbital effects and orbital parameters is not needed.

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

i

i

i

i

i

ix

κκλδθ

&

11.3 System state evolution The state evolution is given by:

iii

i

i

i

i

i

i

i

i

i

i

ii

ii

i

i

i

i

i

i vxF

vvvvv

tt

tt

x +⋅=

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

+

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

⋅

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

−

−

=

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

=

+

+

+

+

+

+

+

+

κ

κ

λ

δ

θ

κκλδθ

κκλδθ

&&& 100001000

00100000100001

1

1

1

1

1

1

1

1

Where iv denotes the various state propagation noise components. For instance, covariance θiQ

for noise θiv is related to the standard deviation θσ through: ( )iii ttQ −⋅= +1

2θ

θ σ .

Therefore, the estimated state is propagated according to:

iiiii xFx //1 ⋅=+

And the associated state covariance is propagated according to:

iT

iiiiii QFPFP +⋅⋅=+ //1

11.4 System observables or input to the filter The filter receives time-tagged landmark residuals, corresponding to the difference, in image frame (i.e. Angular error in the line or column direction), between the expected landmark coordinates and the observed landmark coordinates after the matching process. The expected coordinates take into account the best available knowledge of the state:

• Attitude measured by the AOCS

• Best knowledge of scan misalignments

• Best knowledge of thermal distortion



• Best knowledge of the orbital position

In addition, all landmark sightings are tagged with a landmark-matching covariance value, representing the expected validity of the landmark observation: this incorporates correlation sharpness and geographical uncertainties. The filter uses this covariance knowledge to weight observations, and to give more importance to landmarks which we know have a better “quality”. The filter also receives the list of dates for which the estimation is required. The list corresponds to the nodes of the performance grid as defined by the simulator user. Indeed, as landmark sightings are essentially asynchronous timescale has to be specified separately, to force an output at the required time steps.

In addition, the filter needs some parameters to have knowledge of the geographical location and the scan coordinates of the landmark observations in order to determinate the geometric sensitivity coefficients: sensitivity of parallax effect to orbital position error and sensitivity to scan misalignments. That is true because a new observation iy is available each time a new landmark is visible and this observable provides:

• Direct observation of the attitude state iθ .

• No observation of linear drift effects (state iδ ); those are indirectly observed via the propagation. Indirect observation of the orbital position error state iλ through a parallax sensitivity (geometric effect) ig , which depends on the latitude and relative longitude of the landmark. Landmarks just below the satellite have a maximum sensitivity ( ig = Earth radius / Orbit radius ~ 0.15), while landmarks on the horizon have null sensitivity ( ig = 0).

• Indirect observation of the scan misalignment error iκ via the sensitivity factor

iα , which is directly the value of the scan angle in radians on the other axis: NS scan angle for EW error, and vice-versa.

Therefore, the observation equation can be written as:

[ ] iiii

i

i

i

i

i

iii wxHwgy +⋅=+

⎥⎥⎥⎥⎥⎥

⎦

⎤

⎢⎢⎢⎢⎢⎢

⎣

⎡

⋅=

κκλδθ

α

&

001

Where iw is the observation noise. Its covariance iR is related to the landmark matching

accuracy yiσ for landmark i through: ( )2y

iiR σ= .

11.5 Filtering Again it is noted that the implementation on the MTG INR-PS subject of this traineeship is done separately in both EW and NS directions. So there is not only one filter but two identical ones acting on EW and NS respectively.

Each filter only estimates tiny deviations of the states with respect to this best knowledge: all macroscopic, zero-order deviations are already removed from the residuals. It is then possible to



use a linear implementation of the Kalman filter, allowing a good stability of its behaviour. It is here worth to notice that non-linear perturbations should preliminary modelled for residual compensation. So the system dynamics for this INR application is ideally linear:

• The attitude has only small angles excursions, all the more so as the filter onsly estimates deviations from the measured attitude.

• Thermal distortions are very small angles too, all the more so as the filter only estimates deviations from the “nominal” thermal distortion profile.

• Scan misalignments are small angles, and scan angles themselves remain within ± 10º.

• Orbital position errors are in the micro radian range when expressed as angular errors.

This guarantees the validity of a purely linear Kalman filter expression, without the need for extended Kalman formulations. This increases the robustness of the filter and, providing that the settings are correct, prevents from estimation divergence.

The mathematical formulation of the filter which let the propagated state and the propagated covariance be updated taking into account the optimal Kalman gains is the next:

( )( )

( ) iiiiii

iiiiiiiii

Tiiiii

Tiiii

PHKIP

xHyKxx

HPHRHPK

/1111/1

/111/11/1

1

1/111/11

+++++

++++++

−

++++++

⋅⋅−=

⋅−⋅+=

⋅⋅+⋅⋅=

Consequently, after a long period without observations, the filter covariance can reach values that result in sharp updates when a new observation is available. This may result in discontinuities in the state estimate, especially at the first few visible landmarks in a new full-disk image. To prevent these discontinuities, the best solution is not to limit update amplitudes within the Kalman filter, but to add an explicit lowpass filter as a postprocess, thus retaining the formal validity of the Kalman filter structure.

The operations of propagation and update are executed at each interruption it of the filter. Interruptions are triggered at each landmark observation (true observations) as well as at each date for which the filter output is required. In the latter case, the best way to do it is by introducing dummy observations, with infinite covariance (therefore null Kalman gains), to force a new filter step.

11.6 Outputs The filter provides the estimated states at the time steps specified, as well as the estimation covariance for each state. This covariance provides a notion of the quality of the estimation, but is only valid when the model in the filter is reasonably representative of the real physical phenomena.

The estimation error, and thus the performance, can be established by comparing the estimated state with the true state, or the estimated geolocation of pixels at the synchronous output dates with the true geolocation, which is the key indicator of performance. This last point applies to the performance estimation by simulation.

In the frame of an operational process, a covariance indicator is obtained as an output, which gives information of the accuracy of the state vector estimation. Nevertheless, it will be necessary to validate this indicator by simulation, and to verify the validity of the linearity assumption.


of 97 PERFORMANCE EXTRACTOR

12 PERFORMANCE EXTRACTOR

12.1 Introduction The final module on the MTG INR-PS is the performance extractor which computes the navigation and registration performances from the navigation errors. After de filtering, the actual performance data must be extracted from the simulation results using a set of performance extractor scripts.

12.2 General definition of the problem At this point, it could be useful to summarize and generalize the problem simulated to have a wider idea of what kind of information the performances must give.

The structure of a typical estimation problem assumes the following form:

• Given a dynamical system, a mathematical model is hypothesized or simulated based upon the experience, which is consistent with whatever physical laws known to govern the system’s behaviour, the number and nature of the available measurements, and the degree of accuracy desired. Such mathematical models almost invariably embody a number of poorly known parameters.

• Determine the best estimates of all poorly known parameters so that the mathematical model provides an optimal estimate of the system’s actual behaviour.

Any systematic method which seeks to solve a problem of the above structure is referred to as an estimation process, and for any variable or parameter in estimation, there are three quantities of interest:

• True value or truth. It is usually unknown in practice. This represents the actual value sought of the quantity being approximated by the estimator.

• Measured value. It denotes the quantity which is directly determined form a sensor. Measurements are never perfect since they will always contain errors. Thus, measurements are usually modelled using a function of the true values plus some error.

• Estimated value. It is determined from the estimation process itself and are found using a combination of a static/dynamic model and the measurements.

Other quantities used commonly in estimation are:

• Measurement error. It is equal to the measurement value minus true value. The actual measurement error, like the true value, is never known in practice. However, the errors in the mechanism that physically generate this error are usually approximated by some known process as a Gaussian noise with known variance. These assumed known statistical properties of the measurement errors are often employed to weight the relative importance of various measurements used in the estimation scheme.

• Residual error. It is equal to the measurement value minus estimated value. Unlike the measurement error, the residual error is known explicitly and is easily computed once an estimated value has been found. The residual error is often used to drive the estimator itself.

It should be evident that both measurement errors and residual errors play important roles in the theoretical and computational aspects of estimation.



12.3 Statement of meaning of the problem Moving from the general to the specific, all these kind of values can be defined for the present problem.

• The true value can be defined as the viewing direction defined by a reference grid node ground location and the spacecraft position on its orbit as measured by the onboard AOCS.

• The measured value can be defined as the line of sight as computed using the on-board AOCS measurements and the instrument on-ground geometric characterization.

• The estimated value can be defined as the line of sight as computed using the navigation estimation from Kalman filtering and the instrument on-ground geometric characterization.

Following the same approach, the error can be derived:

• The true navigation error is the angular error, in term of azimuth and elevation in the spacecraft reference frame, on the line of sight measurement. This error is, at a given time, the angular separation between measured and true values which are:

The line of sight as computed using the on-board AOCS measurements and the instrument on-ground geometric characterisation; and

The viewing direction defined by a reference grid node ground location and the spacecraft position on its orbit measured by the on-board AOCS.

• The estimated navigation error is the angular error, in term of azimuth and elevation in

the spacecraft reference frame, on the line of sight measurement. This error is, at a given time, the angular separation between estimated and true values which are:

The line of sight as computed using the navigation estimation from Kalman filtering and the instrument on-ground geometric characterisation; and

The viewing direction defined by a reference grid node ground location and the spacecraft position on its orbit as measured by the on-board AOCS.

• The navigation residual is the difference between the true navigation error and the

estimated navigation error. So it can be derived that the navigational residual is the angular serparation between measured and estimated values which are:

The line of sight as computed using the on-board AOCS measurements and the instrument on-ground geometric characterisation; and

The line of sight as computed using the navigation estimation from Kalman filtering and the instrument on-ground geometric characterisation.

The navigation performance is estimated with statistics on navigation residuals over a long period (several repeat cycles). Those navigation residuals are computed on a regular grid of pseudo-landmarks positions on Earth called “performance grid”. The navigation residual is computed on each node of the performance grid, defined at user input.



12.4 Navigation residuals obtainment plan The landmarks residual calculation function create a *.mat file every image with the residual value for each landmark watched on this image and information about the scan line where the landmark was detected. Later on, the navigational filtering can be done for all the scan lines the user wants and registration performances can be obtained.

The scan-to-scan registration performance can be calculated using the two *.mat files belonging to the scan lines to be compared.

The image-to-image registration performance can be calculated using all the *.mat files of the scan lines belonging to the images to be compared.

Even instrument-to-instrument or satellite-to-satellite registration performance could be calculated if we change the instrument definition parameters, creating a new case with a complete set of *.mat files.

As can be seen, the idea is to generate all *.mat files needed to the comparison and later on to choose the correct *.mat files to be compared.

Figure 12-1: Landmark residual files in a case directory


of 97 SIMULATION RESULTS

13 SIMULATION RESULTS

13.1 Introduction These results correspond to a detail analysis of the FCI nominal case 1Km. This case is considered the nominal case for performance evaluations and it must be recalled that this case is a simulation of a sequence of 21 FDC images.

On top of that, it must be pointed out that:

• All contributors to the navigation error were included apart from the yaw external misalignment because yaw was not estimated by the navigation filter as stated before.

• The less populated landmark database was used.

• The misalignment given by the thermal files were those corresponding to equinox (Sun eclipse around midnight)

Due to these facts, this case can be considered as a worst case for INR although no cloud coverage statistics have been considered and the 442 landmarks on the rougher database were used.

13.2 Landmarks residuals After the LOS simulation over the 442 landmarks, the residuals acting as input on the navigation filter can be seen below:

Figure 13-1: Landmark residuals over the simulation

It can be seen that the residuals on EW are higher than in NS due to the higher level of uncertainly in EW scanning. Next figure is a better view of those plots making a zoom on the 1st repeat cycle.



Figure 13-2: Landmark residuals over the first image divided by scanning lines

13.3 Azimuth and Elevation Navigation errors The navigation errors obtained as output of the Kalman navigation filter are show below:

Figure 13-3: Azimuth and Elevation Navigation errors over the simulation

Next figure is a better view of those plots making a zoom on a repeat cycle.

Figure 13-4: Azimuth and Elevation Navigation errors over one scanning line



The two figures show the estimated navigation errors follow the true navigation errors after a delay for filter convergence, despite the relatively large measurement noise.

13.4 State parameters Using the measurements, the Kalman navigation filter estimates the following state parameters:

Figure 13-5: State parameter evolution: Azimuth and Elevation state vectors

13.5 Covariance analysis The state parameters standard errors are also computed by the filter and to see the Kalman filtering convergence, the diagonal elements on the covariance matrix are plotted on the next figures.



Figure 13-6: covariance matrix diagonal elements on the simulation

It can be noted that after a long period without observations, the filter covariance can reach values that result in sharp updates when a new observation is available. This results in discontinuities in the state estimate. To prevent these discontinuities, a couple of solution can be investigated:

Not to limit update amplitudes within the Kalman filter, but to add an explicit lowpass filter as a posprocess, thus retaining the formal validity of the Kalman filter structure.

Use a fixed lag formulation, where the estimation is not required in real time, as it is not used in a feedback loop. The filter can wait for a few future observations to improve the estimation at a given epoch. This is particularly useful to improve the estimation of fast states over observation gaps.


of 97 POSSIBLE SOLUTION

14 POSSIBLE SOLUTION

14.1 Introduction The following provides the mathematical foundation of an analytical INR algorithm for MTG developed during the traineeship. No star measurements are considered on this mathematical explanation. Instead, measurements of the Earth's edges in the imagery are used to supplement images of landmarks. The Earth edge observable is a good approach to providing the attitude estimation, and a comprehensive theory of its use is described herein.

The main advantage of this method is that it can be developed analytically although as a drawback; each angle must be pre-modelled as a function of time. Due to lack of time, this algorithm could not be developed, but maybe it could in future work.

14.2 Attitude determination Because the daily attitude profiles change very slowly, it is possible to process successive frames of imagery via the technique of a priori processing, or sequential batch least squares filtering. The imagery is first reduced to yield time-tagged information of the instrument line of sight EW and NS scan angles.

The inputs to the Navigation Algorithm are the landmark and Earth edge scan angles. The desired output is the attitude of the instrument. However, the attitude angles themselves are not preferred as the solve-for parameters of the estimation process. This is because the attitude angles tend to vary extensively during the data collection and processing span. Therefore, each attitude angle is preferably modelled as a function of time with a set of constant coefficients. The constant coefficients then become the solve-for parameters of the estimation process. Once these parameters have been determined, the attitude can be re-constructed from the model time function.

14.3 Attitude modelling The combined attitude of the on-board instrument and the spacecraft is characterized by the Euler angles roll φ , pitch θ and yaw ψ . The attitude state of the on-board instrument, relative to the spacecraft body, is further described by the misalignment of its optical axis with respect to the spacecraft body axes. Hence, two additional angles, roll misalignment mφ and pitch misalignment mθ are introduced to describe this effect. The attitude state of the instrument is thus defined by five angles.

The spacecraft body and the instrument mounting structure are subject to-diurnal thermal distortion caused by the Sun. In addition, the spacecraft attitude is also subject to no repeatable effects caused by Earth sensor radiance gradient, clouds, and geomagnetic field variations. Thus, the spacecraft roll, pitch, and yaw will have both repeatable and no repeatable components and are modelled as a combination of Fourier and polynomial terms. The misalignment angles, on the other hand, are believed to be effected only by the daily thermal effect and are modelled by Fourier terms only. These five angles, collectively referred to as the attitude state vector [ ]mm θφψθφβ = can therefore be represented as a time series as follows:



( ) ( )[ ] ( )∑∑==

⋅+⋅+⋅=pf n

j

jij

n

n

in

in

i tatnstnc01

sincos ωωωβ

With the understanding that the polynominal coefficients for misalignment angles are zero. In the above equation, i = 1, ...,5 is the ith attitude angle, nf and np are the maximum orders of the Fourier and polynomial terms, i

nc and ins are the cosine and sine coefficients, i

ja are the polynomial coefficients, and ω is the daily solar rate.

The Fourier and polynomial coefficients can be used as the solve-for parameters of the attitude determination estimation process. Furthermore, because the Sun angle changes very slowly from day to day, the attitude coefficients can be treated as a priori parameters in the estimation process.

14.4 Observation modelling The Navigation Algorithm processes scan angle data available through image processing of the downlink digital signals returned by the spacecraft. Two data types are considered: Landmark Data Type and Earth Edge Data Type.

Both data types manifest themselves as EW and NS scan angles. Despite their apparent similarities, there are subtle differences between these two data types. These differences are due to the fact that landmarks can be uniquely, whereas Earth edges can be recognized only in “outline form”. Because the Earth's outline is very nearly circular, edge measurements are insensitive to rotations about the yaw axis.

Figure 14-1 shows the ideal instrument field-of-view with no attitude errors, Here, the Earth's disk is perfectly centred. Points A and B are representative landmarks. Let the scan coordinates corresponding to these landmarks be designated as (L1, P1) and (L2,P2). Let it be assumed that Earth edge measurements are carried out at line L3 with the East and West edge coordinates being (L3, PE3) and (L3, PW3), respectively and let E and W be the physical points on the Earth's surface associated with these coordinates.

Figure 14-1: Instrument filed of view with no attitude errors



Figure 14-2 is an exaggerated instrument field of view in the presence of attitude errors. It can be seen that the Earth centre has been offset and its apparent spin axis has been rotated with respect to the absolute (line, pixel) reference system. Landmarks A and B are now observed at scan coordinates (L1', P1') and (L2', P2') that are different from the ideal scan coordinates. However, there is no way to follow the movement of the original edge points E and W since they are not identifiable, or the may have disappeared to the other side of the Earth. Instead, the Earth edge observation, carried out for the same line number L3, will have different contact points. The new edge coordinates can be designated as (L3, PE3') and (L3, PW3').

Figure 14-2: Instrument filed of view with attitude errors

14.4.1 The landmark observable A data base of landmarks locations with known geographic coordinates to very high accuracy is given as stated before Table 10-1. Since the spacecraft ephemeris is also assumed to be known at any time, the nominal LOS vector from the spacecraft to the landmark can be predicted. The deviations of the observed line-of-sight scan angles from their predicted values are a sensitive function of attitude, and thus constitute the primary observables for the navigation algorithm.

Each landmark is identified by its geographic coordinates: longitude λ , geodetic latitude gφ and height H above a reference ellipsoid model (taken to be the world geodetic system-84, or WGS-84, for the Earth). Hence its position vector [ ]zyx LLLL = can be predicted accurately at any time via the following equations:



( )

( )

g

g

ex

gg

g

ey

gg

g

ex

He

RL

He

RL

He

RL

φφ

λθφφ

λθφφ

sinsin1

sincossin1

coscossin1

2

2

2

⋅⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+

⋅−=

+⋅⋅⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+

⋅−=

+⋅⋅⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛+

⋅−=

Where gθ is the Greenwich Sidereal time, eR is the Earth's equatorial radius, and e is Earth's ellipticity.

Let r be the instantaneous radius vector of the spacecraft at the time of observation. The LOS unit vector s pointing from the spacecraft to the landmark of interest is therefore given by:

rLrLs

−

−=

The mathematical model for the landmark scan angles is summarized below:

( ) mab

bmab NS

zsysNSEWxsEW δδ +⎟⎟

⎠

⎞⎜⎜⎝

⎛

⋅⋅−

=+⋅= arctan,arcsin

Where EW is the EW scan angle and NS the NS scan angle of the instrument when pointing to the landmark, s is the line-of-sight unit vector from the spacecraft to the landmark, bx , by ,

bz are the unit vectors of the Spacecraft Body Coordinate System, and, maEWδ , maNSδ are corrections to the respective scan angles due to the misalignment effect and are given by the following expressions:

EWNSNS

NSNSNSEW mamamamamama cos

sincos,cossin

⋅+⋅−=⋅−⋅−=

θφδθφδ

The components of the line-of-sight unit vector in the Body frame are related to the components

in the Orbital frame by the Euler rotation matrix EM :

sEb sMs ⋅=

Where

[ ] [ ]ssssbbbb zsysxsszsysxss ⋅⋅⋅=⋅⋅⋅= ,

The Euler matrix can be thought of as the product of three successive elementary rotations about each of the roll, pitch, and yaw axes. The order of the elementary rotation is arbitrary, it has been adopted the “1-2-3” order; first a rotation by φ about the x-direction, followed by a rotation by θ about the new (body) y-directions, and finally followed by a rotation by ψ about



the new z-direction. With this ordering of elementary rotations, the Euler Matrix takes the following form:

⎥⎥⎥

⎦

⎤

⎢⎢⎢

⎣

⎡

⋅⋅−⋅+⋅⋅⋅+⋅⋅−⋅−

⋅+⋅⋅−⋅+⋅⋅⋅=

θφθφθψφψθφψφψθφψθψφψθφψφψθφψθ

coscoscossinsincossinsinsincoscoscossinsinsinsincossinsincossincossincoscossinsincoscos

EM

The unit vectors in the Orbital frame are given in terms of the spacecraft position and velocity vector:

sssss zyzvrvryr

rz ∧=∧

∧−=−= ,,

The elements of the Euler Matrix EM are denoted by ijm , and its three row vectors by 1m ,

2m , 3m . Note that the entire spacecraft attitude dependency of the scan angle observables is

contained in the matrix elements of EM ; the components of the unit vectors im , The misalignment dependency is contained in the terms maEWδ and maNSδ .

14.4.2 The Earth Edge observable

14.4.2.1 Spherical Earth Model

The Earth edge observables are obtained by measuring the instrument line-of-sight scan angles during an EW scan when the line-of-sight enters and exits the Earth's horizon. In this section, the Earth edge observable is developed with the assumption that the Earth is a perfect sphere. Corrections to this model, due to the oblateness of the Earth, are considered in the next section.

With the spherical Earth assumption, the condition that the point (EW, NS) in scan angle space lies on the edge of the Earth is tantamount to the constancy of the instantaneous maximum central angle (the angle between the LOS and the line joining the spacecraft position and the centre of the Earth);

ms sx αcos=⋅

The quantity mα is dependent on the position of the spacecraft and is given by:

S

Em R

R=αsin

Where ER is the Earth's equatorial radius, and SR is the instantaneous radial distance from the geocentre to the spacecraft. Note that SR is dependent on the orbit of the spacecraft.

Equations on angles EW and NS , plus the fact that the sum of squares of the components of a unit vector in any reference frame should add up to 1, allows one to write the following equations:

( )( ) ( )

( ) ( )mamab

mamab

mab

NSNSEWEWsz

NSNSEWEWsy

EWEWsx

δδ

δδ

δ

−⋅−=⋅

−⋅−−=⋅

−=⋅

coscos

sincos

sin



Using the relationship between the two unit vectors ss and bs the Earth edge condition, Eq. on

mα can be rewritten as follows:

mmNSmNSm αξξξ cossin'sincos'coscos 132333 =⋅+⋅⋅−⋅⋅

Where we have defined

mama NSNSNSEWEWEW δδ −=−= ','

Third equation szb ⋅ can further be rewritten

( ) mEWmEWNSmNSm αcos'sin'cos'sin'cos 132333 =⋅+⋅⋅−⋅

We now define auxiliary quantities D , α and γ by the following equations

( )

D

mNSmNSmD

Dm

DNSmNSm

mαγ

ζ

ζ

coscos

'sin'cos

sin

'sin'coscos

213

22333

13

2333

=

+⋅−⋅=

=

⋅−⋅=

Note that ζ can be determined from the following equation:

⎟⎟⎠

⎞⎜⎜⎝

⎛⋅−⋅

='sin'cos

arctan2333

13

NSmNSmm

ζ

The above definitions, when combined with the previous equation give:

γξξ cossin'sincos'cos =⋅+⋅ EWEW or ( ) γξ cos'cos =−EW

Which leads to the solution

γξ ±=−'EW

Where the plus or minus sign corresponds to the east or west edge respectively. The east edge, eEW and west edge wEW , can now be obtained:

γξδγξδ −+=++= mawmae EWEWEWEW ,

The edge observables can be combined to form the “half-sum” sH and “half-difference” dH pseudo observables as follows:

002,2 EWEWEWEWHEWEWEWH wedma

wes −=−−=+=+= γξδ

Where ⎟⎠⎞

⎜⎝⎛=

NSEW m

coscos

arccos0α

is the ideal east edge scan angle for the given NS scan angle.

Physically, the half-sum pseudo-observable sH can be interpreted as the EW coordinate of the mid-point of the line joining the two measured Earth edges corresponding to a given NS scan



line. The half-difference pseudo-observable dH may be interpreted as the deviation of the half-chord length of the line joining the two Earth edges from the nominal value.

The significance of these pseudo observables can be made clear by expanding their mathematical model to first order in attitude angles, and the following equations can be obtained:

( )φδθδ −⋅=−= madmas NSEWNSH

NSEWH

tantan,

cos

The two pseudo-observables are simpler to use than the “raw” edge observables. The only drawback to their use is that in forming the sum and difference of the raw measurements, the error estimates must also be roost-sum-squared. However, the factor of one-half helps to bring the errors back to the same level as the raw measurements.

The half-sum pseudo-observable sH can be interpreted as the EW coordinate of the midpoint of the line joining the two measured Earth edges corresponding to a given NS scan line. sH is made up of the negative pitch angle θ− and the EW misalignment compensation term maEWδ at the corresponding NS scan angle. One conclusion that can be drawn from this observation is as follows: in the absence of optical axis misalignment, the deviation of the centre-point of the line joining the Earth edges from zero would be due entirely to pitch and independent of scan angles. Thus, a single measurement of Earth could in principle determine the pitch.

The half-difference pseudo-observable dH may be interpreted as a deviation of the half-chord-length of the line joining the two Earth edges for the same scan line from its nominal value due to attitude. It is made up mainly of roll and the NS misalignment term (which is itself a function of roll misalignment and pitch misalignment). However, unlike the half-sum pseudo-observable, it is scan angle dependent. In the absence of misalignment, a single measurement of dH could determine roll by comparing the measured value to the nominal value.

In practice, optical axis misalignment cannot be ignored. Therefore the foregoing technique for determining roll and pitch does not lead to accurate results. A simultaneous solution of roll, pitch, roll, misalignment, and pitch misalignment is preferably performed on multiple Earth edge observations at different NS scan angles in order to obtain a good fix on the instantaneous attitude.

14.4.2.2 Non-Spherical Earth Model

The equations developed for the Earth edge observables given in the previous section are based on the assumption that the Earth's surface is a perfect sphere. Since the actual shape of the Earth is more closely approximated by an oblate spheroid than a perfect sphere, the actual Earth edge outline in scan angle space is different from what the spherical Earth model predicts. It is possible to generalize the Earth edge formulation so that the Earth's nonsphericity effect can be corrected by the navigation algorithm. Review the work from Ahmed A. Kamel for more information about this subject.

14.5 The sequential batch estimator The landmark and Earth edge measurement can be fitted to the observation models developed in the previous sections to determine the attitude coefficients via a least squares procedure. The attitude Fourier coefficients can be treated as a priori parameters whereas the polynomial coefficients should be freely determined. Thus, the problem of estimating the attitude



coefficients based on landmark and Earth edge observations can be formulated as a hybrid sequential batch filter.

For each half-frame of image data, the observed EW and NS scan angles are first corrected for the non-spherical Earth effect, using the current orbit and attitude knowledge. These modified observations are then fitted to the (spherical Earth-based) mathematical model using a sequential batch filter. The solve-for parameters are the Fourier and polynomial coefficients of the five attitude angles, and the a priori knowledge of these coefficients are determined as follows.

For a “normal image”, i.e., no special events occurring immediately before this image, the a priori is the current solution and its full covariance matrix. For the images immediately following certain attitude disturbing “special events” such as momentum wheel unload, Earth sensor single-chord operation, or station keeping manoeuvres, only the Fourier coefficients are treated as a priori information whereas the constant, ramp, and quadratic terms of each attitude angle are allowed to vary with much larger a priori errors. An “a priori retention factor” can be used to tune the relative importance of the a priori information with respect to the new data.

14.5.1 Summary of the sequential batch estimation algorithm is as follows

For each iteration, we start with a nominal solution 0x . Let the attitude state be denoted by the vector of coefficients x , and that Γ denotes its covariance matrix. The algorithm is an iterative one using a “differential corrections” approach. In general, several iterations are needed before a convergent solution can be established. The nominal solution for the first iteration may conveniently be set equal to the a priori solution, but that is not necessary-any initial estimate will suffice. The nominal solution for each successive iteration is determined from the previous iteration's corrected solution, whereas the a priori solution remains unchanged throughout the differential correction process.

The differential corrections to the nominal solution for each iteration are calculated via the following formula:

( )⎥⎦⎤

⎢⎣⎡ −⋅Λ⋅+⋅⋅⋅⎟

⎠⎞

⎜⎝⎛ Λ⋅+⋅⋅=

−

0

1

xxfMWAfAWAx aaa

Taa

Tδδ

Where

• x represents the solve-for parameters vector (all attitude coefficients)

• xδ is the differential correction to the solve-for parameters

• ax is the vector of nominal solve-for parameters

• 0x is the vector of nominal solve-for parameters

• A is the partials matrix of the observation vector with respect to the solve-for parameters, evaluated at the nominal solution,

• W is the data weight matrix,

• af is an a priori tuning factor, (value 1 means a priori data receives full weight as current data)

• aΛ is the a priori information matrix (inverse of the a priori covariance matrix Γ ) and



• Mδ is the vector of observation residuals.

The A matrix can be computed analytically from the mathematical models of the respective observable developed previously, and by using the chain-rule for partial differentiation:

j

i

i i

m

j

mmj c

Mc

MA

∂∂

⋅∂

∂=

∂∂

= ∑=

ββ

5

1

Where ( )( )mm tMM β= is the mth component of the observation vector, mt is the time of this

observation, and ( )mtβ the attitude state vector evaluated at the observation time. The

calculation of elements of the A matrix is described below. The covariance matrix of the solution, for the current iteration, is given by

1−

⎟⎠⎞

⎜⎝⎛ Λ⋅+⋅⋅=Γ aa

TfAWA

The corrected solution is the used as the nominal for the next iteration. The process is continued until convergence is established, or the solution is otherwise accepted or rejected by other criteria. The solution may be deemed convergent if it meets any one of the following criteria:

• Criterion 1: The percent change from the normalized rms residual to the predicted rms residual is smaller than a data-base-specified tolerance. The predicted residual is computed from the current iteration's solution by the following formula:

( ) xxxfMWARNP aaa

T

m δδ ⋅⎥⎦⎤

⎢⎣⎡ −⋅Λ⋅+⋅⋅−⋅= 0

22

Where mN is the total number of measurements and R is the normalized rms residual based on the nominal solution.

• Criterion 2: The percent change from the normalized rms residual to the previous iteration's normalized rms residual is smaller than a data-base-specified tolerance.

• Criterion 3: All normalized rms residuals for each data type used (landmark EW and NS scan angles, Earth edge half-sum and half-difference pseudo-observables) are less than their data-base specified values.

In a manual mode of operation, and after convergence has been established, an analyst can decide whether or not to update the operational data base containing the current solution and the stored covariance matrix file. In automatic or batch mode, the update is automatic. If the maximum number of iterations has been reached without convergence, or if the analyst decides not to accept the solution, then the data base is not updated, and both the solution and the covariance matrix are written to temporary files for further analysis.

14.5.2 Calculation of the sensitivity matrix To complete the mathematical formulation of the sequential batch estimator, the partial derivatives of the observables with respect to each of the solve-for parameters are needed. These partials form the elements of the Sensitivity Matrix. Two kinds of partials are needed: the “observation partials” and the “state partials”. Observation partials are partials of the observables (scan angles and Earth edges) with respect to the (attitude) state vector, and are



considered below. State partials are partials of the state vector with respect to the solve-for parameters (the attitude coefficients), and are also considered below.

14.5.2.1 Landmark observation partials

The landmark observation partials are summarized below. Partials of EW with respect to roll, pitch, and yaw.

sss sMEWEWsMEWEWsMEWEW⋅⋅=

∂∂

⋅⋅=∂

∂⋅⋅=

∂∂

111 arccos,arccos,arccos ψθφψθφ

Where 1φM , 1θM and 1ψM are the first row vectors of the following matrices respectively:

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⋅−⋅−⋅+⋅⋅−⋅−⋅⋅−

⋅+⋅⋅⋅−⋅⋅=

∂∂

=θφθφ

ψφψθφψφψθφψφψθφψφψθφ

φφ

cossincoscos0coscossinsinsincossinsinsincos0

sincossinsinsinsinsincossincos0E

EMM

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛

⋅−⋅⋅⋅⋅⋅−⋅⋅⋅−⋅⋅⋅−

=∂

∂=

θφθφθψθφψθφψθψθφψθφψθ

θθ

sincossinsincossincoscossincossinsinsincoscoscoscoscossincossin

EE

MM

⎟⎟⎟

⎠

⎞

⎜⎜⎜

⎝

⎛⋅−⋅⋅⋅−⋅⋅−⋅−⋅+⋅⋅⋅+⋅⋅−⋅−

=∂

∂=

000sinsincossincossincoscossinsincoscoscossinsinsincoscoscossinsinsinsincos

ψφψθφψφψθφψθψφψθφψφψθφψθ

ψψ

EE

MM

Partials of NS with respect to roll, pitch, and yaw

( ) ( ) ( ) ( ) ( ) ( )[ ]

( ) ( ) ( ) ( ) ( ) ( )[ ]

( ) ( ) ( ) ( ) ( ) ( )[ ]ssss

ss

ssss

ss

ssss

ss

sMsmsMsmsmsm

NS

sMsmsMsmsmsm

NS

sMsmsMsmsmsm

NS

⋅⋅⋅−⋅⋅⋅⋅⋅+⋅

=∂∂

⋅⋅⋅−⋅⋅⋅⋅⋅+⋅

=∂

∂

⋅⋅⋅−⋅⋅⋅⋅⋅+⋅

=∂

∂

23

23

23

3223

22

3223

22

3223

22

1

1

1

ψψ

θθ

φφ

ψ

θ

φ

Where the quantities 2φM , 2θM and 2ψM represent the second row vector of the matrix

φEM , θEM and ψEM and likewise the third row vectors of these matrices are denoted by the respective quantities with subscript 3.

to complete the set of observation partials with respect to the orbit and attitude state vectors, the partials of the misalignment terms maEWδ , maNSδ with respect to the misalignment angles are also required. These are:

EWNSNS

EWNSNS

NSEW

NSEW

ma

ma

ma

ma

ma

ma

ma

ma

cossin,

coscos,cos,sin =

∂∂

−=∂

∂−=

∂∂

−=∂

∂θ

δφ

δθ

δφ

δ



14.5.2.2 Earth Edge observations partials with spherical Earth model

The partials of the Earth edge observables eEW and wEW , or of the pseudo-observables sH ,

dH can be derived from differentiating. This involves obtaining partials of the quantities ξ and γ already defined. To simplify notation, we shall break up the attitude state vector into two

parts [ ]ψθφ=v and [ ]mama θφμ = . Thus, we can write [ ]μβ v= . Also, for convenience, we define maNSNSNS δ−=' .

Note that the Euler matrix elements ijm , are functions of v only, and that 'NS is a function of

μ only. The partials of 'NS with respect to attitude angles are given by:

μδ

μ ∂∂

−=∂

∂=

∂∂ maNSNS

vNS ',0'

And μ

δ∂

∂ maNS has been obtained before. Based on the foregoing, the following expressions

have been derived for the partials of ξ with respect to attitude:

μξ

μξξ

ξξ

∂∂

⋅=∂∂

⎟⎠⎞

⎜⎝⎛

∂∂

⋅−∂

∂⋅

⋅=

∂∂ D

DvD

vm

Dvtan,sin

cos1 13

Where the partials of ijm , with respect to v are given by:

[ ]

[ ]

[ ]0sincoscossin

sinsincossincossincoscoscoscossinsinsin

cossinsinsincoscoscoscossincoscossinsin

33

23

13

θφθφ

ψφψθφψθφψφψθφ

ψφψθφψθφψφψθφ

⋅−⋅−=∂

∂

⋅−⋅⋅⋅⋅⋅+⋅⋅−=∂

∂

⋅+⋅⋅⋅⋅−⋅+⋅⋅=∂

∂

vm

vmv

m

And the partials of D with respect to attitude are given by

( )μ

ξμ

ξξ

∂∂

⋅⋅+⋅⋅−=∂∂

∂∂

⋅+⎟⎠⎞

⎜⎝⎛

∂∂

⋅−∂

∂⋅⋅=

∂∂

''cos'sincos

sin'sin'coscos

2333

132333

NSmNSmNSDv

mv

mNS

vm

NSvD

The partial of γ with respect to the attitude state vector are calculated in a similar fashion and summarized below:

μγμγ

γγ

∂∂

⋅⋅

=∂∂

∂∂

⋅⋅

=∂∂ D

DvD

Dv tan1,

tan1

Finally, the partials of the half-sum and half-difference pseudo-observables with respect to the attitude state vector can be expressed in terms of partials already derived:



⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

∂∂∂∂

=∂

∂

⎟⎟⎟⎟

⎠

⎞

⎜⎜⎜⎜

⎝

⎛

∂∂

+∂∂

∂∂

=∂∂

μγ

γ

βμ

δμξ

ξ

βvH

EWvH d

ma

s ,

14.5.2.3 State partials

Partials of the attitude state vector β with respect to the Fourier and polynomial attitude coefficients can be easily written down by inspecting the attitude model equation given above. The results are:

( )

( )

( ) pk

ijjk

i

fijjn

i

fijjn

i

nkta

nntns

nntnc

,...,2,1................

,...,2,1............sin

,...,2,1...........cos

=⋅=∂∂

=⋅=∂∂

=⋅=∂∂

ωδβ

ωδβ

ωδβ

Where i, j index the ith or jth attitude angle.


of 97 MTG SUN-GLINT STUDY

15 MTG SUN-GLINT STUDY

15.1 Introduction As part of the Young Graduate Traineeship, an algorithm for finding the susceptible regions over water bodies to present sun-glint was also studied for Meteosat Third Generation satellite. The following analysis was aimed at studying the sun-glint zone definition over water bodies and its impact on the satellite requirements. The tool is called MTG-SG.

15.2 Sun-glint definition Sun-glint is the mirror reflection of sunlight by suitably tilted facets of the water surface into the sensor. This reflection can create dramatic views or obscure features of interest. It is most common and predictable over water bodies, although it can appear over urban areas. The precise location of the sun-glint track is calculated bearing in mind the ocean surface roughness and the imaging geometry defined by the Sun’s position and the sensor’s viewing direction.

As stated above, sun glitter is the mirror reflection of sunlight into the sensor by facets of the water surface that are suitably tilted. Thus the surface wave spectrum, or the surface roughness, as well as the viewing geometry of the image determine the sun glitter radiance. A perfectly smooth surface would contain only one glint. But if the water surface is rippled by even the slightest wind, reflected images become wrinkled and indistinct. A light source, such as the Sun, is then reflected from multiple spots on the surface (Figure 15-1). Sun glitter can dominate the radiance received from the water if the viewing direction of the sensor is within about 20° of the direction of sunlight reflection from a flat water surface. The sensor does not, of course, see the individual highlighted facets, but the average over a resolution cell. The more facets with the suitable slope values there are, the stronger the sun glitter radiance received by the sensor. The probability of occurrence of such facets is closely related to the probability distribution function of slopes. Here, we are going to use the Cox and Munk model.

Glitter patterns are roughly elliptical, with an aspect ratio that depends on the source elevation angle. For example, the sun produces a circular glitter pattern when it is directly overhead (90° elevation angle) and produces an elongated elliptical pattern near sunset or sunrise (small elevation angle). This all assumes a uniformly rough surface; quite often, however, wind gusts increase the roughness or surface slicks reduce the roughness in a localized region.

For a high light source, the angular length of a glitter pattern is equal to four times the angle of the maximum wave slope (Figure 15-1). Waves inclined both toward and away from the observer create glints, resulting in a factor of two times the maximum wave slope; the additional factor of two is a result of angular doubling on reflection. The ratio of the glitter-pattern width to its length is given by the sine of the source elevation angle. If the light source is at the same elevation as the observer, the glitter pattern dimensions are half as large as with an infinitely high source, but the width-to-length ratio is the same. As the sun or moon drops lower in the sky, the glitter pattern gets progressively narrower until the width-to-length ratio reaches a minimum when the source elevation angle is twice the maximum wave slope. Beyond this angle, as the sun or moon approaches the horizon, the glitter pattern becomes shorter because of shadowing and eventually disappears.

Taking into account that the maximum wave slope can be determined from the geometry of glitter patterns, Charles Cox and Walter Munk found a more quantitative way of using glitter patterns to derive a statistical model for the complete wave-slope distribution. They used cameras in the bomb bay of a World War II surplus B-17G aircraft to photograph sun glitter on the Pacific Ocean near Hawaii. By relating the photographic density to the probability of a sun-



glint wave slope, Cox and Munk derived a wave-slope probability density function (PDF). This experiment was limited to measuring slopes smaller than about 28° because the light from larger slopes, which occur with lower probability, was lost in the background.

Figure 15-1: Sun-glint process

By examining multiple images in this way at different wind speeds, Cox and Munk were able to show that the PDF for ocean wave slopes can be described as a Gaussian plus higher-order skewness and kurtosis terms. The actual PDF tends to have higher probability for very small and very large slopes than a Gaussian distribution. Furthermore, the along-wind distribution is skewed, showing a higher probability for downwind slopes than for upwind slopes. This makes sense because the wind pushing the small wind waves causes them to lean downwind. The PDF variance (mean-square slope) increases approximately linearly with wind speed, indicating that the surface gets steadily rougher as the wind blows harder.

15.3 Sun-glint algorithms

15.3.1 General Algorithm

15.3.1.1 Algorithm definition

Cox and Munk have proposed a model that considers the sea surface as a collection of facets, each with individual slope components xz and yz . The probability distribution of facet slopes

( )yx zzP , , depends on:

• Wind speed

• Wind direction

In a target-fixed, local coordinates system with the Y axis aligned with the Sun azimuth, given the Sun zenith angle sθ and the sensor zenith angle vθ and azimuth angle vφ specifying the reflected ray, a wave facet specified by the zenith angle β and azimuth angle α (taken clockwise from the Sun) of its outward normal, the condition for that facet to reflect sunlight in the direction ( )vv φθ , towards the sensor is:

φθθθθϖ Δ⋅⋅+⋅= cossinsincoscos2cos svsv

Where ϖ is the mirror reflection angle and φΔ is defined as vs φφ − . See Figure 15-3.



Figure 15-2: Observation zenith angle and sun zenith angle definition

According to the law of reflection, the vector difference between the reflected and incident rays must lie along the facet normal. From this, it is possible to express the facet angles α and β as a function of the incident and reflected directions.

The angle β formed by the facet normal and the z-axis is computed as:

ϖθθ

β2cos22

coscoscos

+

+= sv

Figure 15-3: Sun-glint geometry

Smooth-surface calculations are relatively simple, but a rough surface requires integration over the randomly oriented specular facets. An effective emissivity for the rough surface can be determined by multiplying the Fresnel emissivity for each wave slope by the slope Probability Density Function (PDF), and integrating over the full range of possible slopes, weighted by the projected wave-facet area. The isotropic Gaussian term from the Cox-Munk model for wave-slope probability density function is given by:

( )( )2

2

2tan

221 σ

θ

πσθ

n

nP−

⎟⎠⎞

⎜⎝⎛=



This PDF describes the probability of a wave facet having slope nθ with respect to the zenith

for any wave-slope variance (mean-square slope) 2σ . In the Cox-Munk model, the mean-square slope depends linearly on wind speed sW according to:

( )004.000512.0003.02 2 ±⋅+= sWσ

Higher-order terms in the slope PDF are required to simulate a more realistic rough surface but their relatively small contribution to the slope integral allows these terms to be dropped for the sake of simplicity.

15.3.1.2 Limitations

Shaw and Churnside demonstrated that the mean square slope also depends on the air sea temperature difference, so the result from Cox-Munk model are valid strictly for neutral stability (equal temperatures of the water surface and immediately overlying air).

Moreover, as the complete Cox-Munk model, does not provide a complete description of the wave slope distribution:

• Swell, not related to local wind, is not taken into account;

• The model is valid for a deep ocean where interaction with the sea bottom is negligible. In reality, the wave profile is distorted when the sea bottom gets close to the surface.

15.3.2 Complete two dimensional algorithms


This is the algorithm that must be applied when the wind speed and direction is known or foreseen. So, it uses external knowledge of the wind speed and direction, and the illumination and observation geometry of each pixel, to estimate the level of sun-glint contribution to the surface reflectance.

The slopes of the wave facet in the X and Y directions ( )yx zz , can be expressed as a function

of the facet azimuth α and zenith β as follows:

βαβα

tancostansin⋅=⋅=

y

x

zz

Which leads to:

vs

vy

vs

svx

z

z

θθφθ

θθθφθ

coscossinsin

coscossincossin

+Δ⋅−

=

++Δ⋅

=

Let W be the wind speed modulus. It is expressed as:

( ) ( ) ( )22 ,,, jiWjiWjiW uc +=



Let χ be the wind direction in the local frame ( χ taken clockwise from the sun). If the sun system (x,y) is rotated through an angle χ to a new system (x’,y’) related to the wind direction, then the Cox and Munk model provides facet slopes xz' and yz' in this wind system as:

( )( ) yxy

yxx

zzz

zzz

⋅+⋅−=⋅−=

⋅−⋅=⋅−=

χχβχα

χχβχα

cossintancos'

sincostansin'

If we define the next parameters:

( )

( )

u

y

c

x

u

uwithuuu

c

cwithccc

z

z

Wji

Wji

ση

σξ

σσ

σσσ

σσ

σσσ

'

'1016.3

000.0,

1092.1003.0

,

31

010

31

010

=

=

⎩⎨⎧

⋅==

⎯⎯→⎯⋅+=

⎩⎨⎧

⋅==

⎯⎯→⎯⋅+=

−

−

Then the probability that the facet reflects specularly the incident radiation in the sensor direction is:

( )( ) ( ) ( ) ( )( ) ( )( )3624

111413624

136112

112

2404

2222

2440

303

221

22

21','

+−+−−++−+−−−−⋅+

−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

ηηηξξξηηξηξ

σπσ

CCCCC

cuyx zzP

With the next coefficient:

23.040.0

033.004.0

12.00086.001.0

04

40

103

0031

0300303

22

121

0211

2102121

==

⎩⎨⎧

−==

⎯⎯→⎯⋅+=

=⎩⎨⎧

−==

⎯⎯→⎯⋅+=

CC

CC

WCCC

CC

CWCCC

with

with

The sun-glint reflectance is then:

( ) ( ) ( )yxvs

sv zzPr ','coscoscos4

,, 4 ⋅⋅⋅⋅

⋅=Δ

βθθωπφθθρ

Where the Fresnel reflection coefficient ( )ωr can be considered as a constant of value 0.02 for incidence between 0º and 50 º.


This algorithm accepts as an established reference the Cox and Munk model. That model does not provide a complete description of the wave slope distribution:



• Swell, not related to local wind, is not taken into account;

• The model is valid for a deep ocean where interaction with the sea bottom is negligible. In reality, the wave profile is distorted when the sea bottom gets close to the surface.

15.3.3 Two dimensional first-order algorithm


When the wind direction is not known, the first-order in the slope probability is retained as the best approach, since it is much less sensible to its variation.

It is obtained by replacing the probability function in the two dimensional algorithm with its simplified version:

( ) 2

22

21','

ηξ

σπσ

+−

⎟⎟⎠

⎞⎜⎜⎝

⎛=

cuyx zzP


This algorithm suffers the same limitations that the complete two dimensional algorithm.

15.3.4 Simplified algorithm


When no information is available on the wind speed direction, a simplified version of the Cox and Munk algorithm can be used. The main assumption is to consider the facet slope nθ equal to the angle β formed by the facet normal and the Z axis.

βθ =n

Therefore:

βββθ 2

222

coscos1tantan −

==n

From previous equation in βcos we have that:

( )ϖθθ

βcos22coscos

cos2

2

++

= sv

Therefore:

( )

( )( ) ( )

( )2

2

2

2

2

coscoscoscos2cos12

cos22coscos

cos22coscos1

tansv

sv

sv

sv

θθθθϖ

ϖθθ

ϖθθ

β+

+−+⋅=

++

++−

=

By substituting, we obtain:



( ) ( )( )2

222

coscoscoscoscossinsincoscos12tantan

sv

svsvsvn θθ

θθφθθθθβθ+

+−Δ⋅⋅+⋅+⋅==

So the probability of a spatial sample being contaminated by sun-glint is given by: ( ) ( )

( )22

2

coscoscoscoscossinsincoscos12

2

1 sv

svsvsv

sgPθθσ

θθφθθθθ

σπ+⋅

+−Δ⋅⋅+⋅+⋅−

⎟⎠⎞

⎜⎝⎛

⋅=

And the sun-glint reflectance is given by:

sgvs

sg Pr⋅

⋅⋅⋅⋅

=βθθ

πρ 4coscoscos4


The limitation of the complete 2 dimensional Cox and Munk algorithm apply. Although this algorithm accepts as an established reference the Cox and Munk model, it uses a simplified formulation in which the direction of the wind speed is not known, and therefore not provided as input.

15.4 MTG sun-glint simulation The simplified algorithm described in 3.4 is used on the MTG-SG tool. The calculation that can be found on this tool presents the following parts.

• Obviously, the MTG sun glint calculation problem is simplified since MTG is orbiting the Earth in a geostationary trajectory and can be considered as a resting point at geostationary altitude in the Earth-Centered Earth-Fixed reference frame (ECEF).

• The Sun must be propagated over the simulation time in order to obtain its position on inertial frame and later on, transform from this inertial frame to the ECEF reference frame.

• With both position vectors (sun, satellite) in ECEF, the observation zenith angle, sun zenith angle and relative azimuth can be calculated for each point on the Earth surface. Taking advantage of the fact that MTG is a geostationary satellite, a grid over the Earth is defined by Table 15-1:

• With all this information, the sun-glint reflectance can be calculated applying the last equation and bearing in mind the two previous equations for probability and nθ .

From To Grid step

Latitude -45º 45º 1º

Longitude -90º 90º 1º

Table 15-1: Grid over the Earth definition parameters

15.4.1 Input parameters %Fresnel water reflection coefficient reflec_coef = 0.02; %Minimum reflectance to plot



reflec_to_plot = 0.0005; %Latitude subsatellite point lat_sat = 0; %Longitude subsatellite point lon_sat = 0; %Wind velocity wind_vel = 7.5; %[m/s] %Simulation time time_simu = 365; % [dias] %Simulation integration time time_step = 1800; %[sec] %Initial epoch time_Epoch = datenum('2011/01/01-00:00:00.000', 'yyyy/mm/dd-HH:MM:SS.FFF'); %Earth (central body) gravitational constants [m^3/s^2] CONST.TierraMu = 398600.448073446e9; CONST.J2 = 0.00108263602298; CONST.J3 = -2.532435345754395e-006; %Sun and Moon gravitational constants (LuniSolar attraction) [m^3/s^2] CONST.SolMu = 132712438000.0e9; CONST.LunaMu = 4902.799063e9; %Solar Radiation constant [w] CONST.SolRadConstante = 1327/2.99792458e5*1.49597870e8^2; %Equatorial radius [m] CONST.ReqTierra = 6378137.0; % Semi major axis WGS84 [m] CONST.A = 6378137; % Semi minor axis WGS84 [m] CONST.B = 6356752; % Earth’s flattening WGS84 CONST.F = 1.0/298.257223563; % Eccentricity WGS84 CONST.E = 0.0818191908426; %Earth's magnetic characteristics [rads] [Wb·m] CONST.EarthDipoleLong = 168.60*pi/180; CONST.EarthDipoleCoelev = 109.55*pi/180; CONST.EarthDipole = 7.943e15; %Earth's time related variables CONST.DaysPerYear = 365.2422 ;CONST.SecondsPerDay = 86400.0; CONST.EarthAngularVelocity = 0.72921158E-4; % [rad/s] %Light speed [m/s] CONST.SLight = 299792458.0; %Other constants CONST.rad2deg = 180 / pi; CONST.deg2rad = pi / 180; CONST.f1 = 1.57542e9; CONST.f2 = 1.2276e9; CONST.RelPotentialTerm = -6.2636803e7; %m^2/s^2 % Constant to calculate GMT CONST.gmst00 = 24110.54841; CONST.gmst01 = 8640184.812866; CONST.gmst02 = 0.093104; CONST.gmst03 = -6.2d-6; CONST.rAoki0 = 1.002737909350795; CONST.rAoki1 = 5.9006d-11; CONST.rAoki2 = -5.9d-15;



15.4.2 Output

Figure 15-4: MTG-SG tool video file



Acknowledgements

One year ago, I took a plane to the Netherlands with the aim of showing my engineering skills working on one of the more challenging and motivating subject any aerospace engineer can dream. A subject where not only AOCS but also ground processing and estimation have a shared role: Image Navigation and Registration. Although I had worked before on this and I knew I was going to broaden my knowledge on this area, I did not know how broad this discipline could be and how much I was going to learn. But this traineeship provided me not only technical knowledge but something else. When I left Spain I could not suspect that the experience of spending a year of my life studying and working in the ESA-ESTEC would enrich me so much. Most of this enrichment has come from all the different and exceptional people that I have met during this time.

Among all of them, I would especially like to thank my supervisor Donny Aminou for making this traineeship possible and Pieter Van der Braembussche and Berthyl Duesmann who took good care of me, answering all my questions. Because if supervisors are the people who supervise you then what is the English word for the people who patiently teach you, guide you and treat you as an equal?. I did my best to get the most from you and I finished richer just for meeting you. I would also like to thank Jean-Loup Bezy for giving me this opportunity.

Last but not least, my work experience at ESTEC gave me the opportunity to meet some of the most brilliant scientists who are doing an amazing work to understand the planet in which we live; I thank all people belonging to Instrument Pre-development and Future missions sections for their support and kindness, I have been very lucky to work among you and luckier to be given a position to continue working with you in the future.

Finally thank you to my family and the people that in spite of the distance have always been with me.