presented by, mr. sandip aghav department of electronic science, university of pune, pune
DESCRIPTION
Development of On-board orbit determination system for Low Earth Orbit (LEO) satellite Using Global Navigation Satellite System (GNSS) Receiver. Presented by, Mr. Sandip Aghav Department of Electronic Science, University of Pune, Pune. Orbit Determination Techniques. Ground Based. - PowerPoint PPT PresentationTRANSCRIPT
Development of On-board orbit Development of On-board orbit determination system for Low Earth Orbit determination system for Low Earth Orbit (LEO) satellite Using Global Navigation (LEO) satellite Using Global Navigation Satellite System (GNSS) ReceiverSatellite System (GNSS) Receiver
Presented by,
Mr. Sandip AghavMr. Sandip Aghav
Department of Electronic Science,Department of Electronic Science,
University of Pune,University of Pune,
PunePune
Introduction
Doppler Measurement
Orbit Determination Techniques
Ground Based
Laser Ranging
Sun sensor, star sensor
Space borne
GNSS Measurements
Classification of Orbit determination techniques
Problem Definition
A method is proposed to use onboard GPS Receiver stand-alone with a direct measurement of position, velocity and acceleration data for orbit determination instead of using differential technique and combined observational technique.
Use of Simplified force models for orbit determination and reduce the extra Burdon from hardware.
Application Target Area: Remote Sensing Satellites
Range: 500 Km to 1200 Km
Positional Accuracy: <50m and Velocity: 1m/sec
Disadvantages of Ground Based Orbit Determination Techniques
Common disadvantage: Data can be collected from satellite only when the satellite is in the
line of sight of the controlling Ground Station.
Methods Disadvantages
Doppler Shift Measurements •Tropospheric, ionospheric and multipath errors •Accuracy frequency dependent.
Triangulation Method •Large number of Ground stations and their maintenance
Laser Ranging Technique •weather conditions, •troposphere errors, •laser system drift, •station position errors, etc
Why GPS based position determination
Ground station is reduced of several operational burdens.
All time data collection is possible The cost of planning experimental observations
is substantially reduced. Scheduling the ground station operations and
data collection is easier and can be done in advance as needed.
Autonomous orbit determination possible
Need of Autonomous On-board satellite Navigation system
On-board collection of data reduces many errors in the orbit determination.
On Board real time orbit determination is possible.
Data processing can be done on-board.
On-board orbit correction is possible.
Concept of Autonomous Navigation System
Objectives of the proposed work
To design/simulate orbit determination algorithm to be used on-board for satellite navigation.
To design/simulate GPS data filtering technique to be placed on-board satellite.
To select a simplified satellite orbit models for on-board processing.
feasibility of Use of above mentioned software on-board a satellite to make the navigation autonomous.
Methodology
Orbit Integration Orbit Estimation
R-K method,R-K method, Cowell’s Method
Least Square, Kalman FilterKalman Filter
Flow chartSTART
ACQUIRE A PRIORI STATE AND COVARIANCE ESTIMATES AT t0
SET k=0, i.e Initialization
k=k+1ACQUIRE A MEMBER OF OBSERVATION VECTOR Yk
PROPAGATE STATE VECTOR TO tk, CALCULATE STATE
TRANSITION MATRIX Φ (tk, tk+1)
CALCULATE EXPEXTED MEASUREMENT Xk AND PARTIAL
DERIVATIVES OF Xk WITH RESPECT TO Xk-1(tk)
PROPAGATE STATE NOISE COVARIANCE MATRIX Q(tk, tk-1)
PROPAGATE ERROR COVARIANCE MATRIX Pk-1(tk)
CALCULATE GAIN MATRIX K
UPDATE X*k-1 TO BECOME kth STATE ESTIMATE
UPDATE ERROR COVARIANCE MATRIX Pk
PROPAGATE Xk(tk) TO ANY TIME OF THE INTREST
LAST OBSERVATION?
END
Y
N
Kalman Filter and
Orbit Estimation
Orbit Estimation Method
Estimation is the calculated approximation of a result which is usable even if input data may be incomplete or uncertain.
Uncertain: Model, Measurement, Perturbations, etc.
Kalman Filter: Orbit Determination
Kalman Filter Basics:
“An optimal recursive data processing algorithm”
An efficient recursive filter that estimates the state of a linear dynamic system from a series of noisy measurements.
Very well suited for Real Time Data Filtering.
Estimate the state and the covariance of the state at any time T, given observations, xT = x1, …, xT
Kalman FilterMathematical Background
H relates the state to the measurement z at step k.
R is the measurement noise covariance.
Kalman Filter: Non Linear System
State Vector Propagation/Update:
15
2
31
2
22
23 r
z
r
RJ
r
xx e
xx
yy
2
22
2353
2
31
r
z
r
RJ
r
zz e
Abovementioned equation of motion is numerically integrated using Runge-Kutta 4th order method.
Integration is taken over initial to final time. Results were tested for various time step.
Seed Orbital Elements
Six orbital elements semi major axis (a) eccentricity (e) inclination angle (i) longitude of ascending node (Ω)
argument of perigee ()
time of perigee passage ()
As a function of time ‘t’ from standard ground station.
From six orbital elements, ECEF coordinates of the satellites are calculated.
Position vector r(t) = x(t)i + y(t)j + z(t)k
Position measurements using on-board GPS receiver
Collects data from GPS receiver (RINEX format) as a function of time ‘tc’ Conversion of RINEX format data into position and velocity (ECEF
coordinates).
GPS receiver measurements are in Geodetic co-ordinate system. It needs to be converted in to geocentric coordinate system.
Again calculate of position, acceleration and velocity vectors by same method which is used for reference orbit calculation.
Use Extended Kalman filer algorithm to estimate the optimal state vector.
Error calculation and error minimization
Generate new corrected orbit
Simplified force model:
Pure Keplerian and Newtonian model of Satellite orbit is selected.
Gaussian nature with zero mean nose model is selected.
J2, J3, J4 Earth Gravity model is selected.
4th Order Runge-Kutta method is selected with fixed step size.
Kalman filter: Initial Calculations
0 0 0 1 0 0
0 0 0 0 1 0
0 0 0 0 0 1
-8.29E-07 4.91E-08 7.36E-07 0 0 0
4.91E-08 -1.01E-06 1.90E-07 0 0 0
7.36E-07 1.90E-07 1.84E-06 0 0 0
1 0 0 0 0 0
0 1 0 0 0 0
0 0 1 0 0 0
0 0 0 0.01 0 0
0 0 0 0 0.01 0
0 0 0 0 0 0.01
1.027118 1.027118 1.027118 1.027118 1.027118 1.027118
1.027118 1.027118 1.027118 1.027118 1.027118 1.027118
1.027118 1.027118 1.027118 1.027118 1.027118 1.027118
1.027118 1.027118 1.027118 1.027118 1.027118 1.027118
1.027118 1.027118 1.027118 1.027118 1.027118 1.027118
1.027118 1.027118 1.027118 1.027118 1.027118 1.027118
Table 2: Initial Covariance matrix
1823.2 470.7 7066.7 -6.6 2.9 1.5
Table 1: Initial State Vector
Table 3: Propagated error Covariance matrix
Table 4: System Jacobian matrix
0 2 4 6 8 10
x 104
6828.94
6828.96
6828.98
6829
6829.02
6829.04
tsec
Sem
i-m
ajo
r axis
(a)
in K
m
Time Vs Semi-major axis
0 2 4 6 8 10
x 104
9.0154
9.0155
9.0156
9.0157
9.0158
9.0159
9.016
9.0161
9.0162x 10
-3
tsec
eccentr
icity(e
)
Time Vs eccentricity
0 2 4 6 8 10
x 104
28.474
28.474
28.474
28.474
28.474
28.474
28.474
28.474
28.474
28.474
tsec
Inclination A
ngle
(i)
in d
egre
es Time Vs Inclination Angle
0 2 4 6 8 10
x 104
35.9118
35.9118
35.9118
35.9118
35.9118
35.9118
35.9118
35.9118
35.9118
35.9118
tsec
Rig
ht
Assention o
f A
scendin
g N
ode(O
MG
) in
degre
es
Time Vs Right Assention of Ascending Node
0 2 4 6 8 10
x 104
-44.572
-44.571
-44.57
-44.569
-44.568
-44.567
-44.566
-44.565
tsec
Arg
um
ent
of
perigee(o
mg)
in d
egre
es
Time Vs Argument of perigee
0 2 4 6 8 10
x 104
0
20
40
60
80
100
120
140
160
180
tsec
Tru
e A
nom
oly
(v)
in d
egre
es
Time Vs True Anomoly
0 2 4 6 8 10
x 104
6824
6825
6826
6827
6828
6829
6830
tsec
Sem
i-m
ajo
r axis
(a)
in K
m
Time Vs Semi-major axis
0 2 4 6 8 10
x 104
7
7.5
8
8.5
9
9.5x 10
-3
tsec
eccentr
icity(e
)
Time Vs eccentricity
0 2 4 6 8 10
x 104
28.435
28.44
28.445
28.45
28.455
28.46
28.465
28.47
28.475
tsec
Inclination A
ngle
(i)
in d
egre
es Time Vs Inclination Angle
0 2 4 6 8 10
x 104
28
29
30
31
32
33
34
35
36
tsec
Rig
ht
Assention o
f A
scendin
g N
ode(O
MG
) in
degre
es
Time Vs Right Assention of Ascending Node
0 2 4 6 8 10
x 104
-60
-55
-50
-45
-40
-35
-30
tsec
Arg
um
ent
of
perigee(o
mg)
in d
egre
es
Time Vs Argument of perigee
0 2 4 6 8 10
x 104
0
20
40
60
80
100
120
140
160
180
tsec
Tru
e A
nom
oly
(v)
in d
egre
es
Time Vs True Anomoly
Fig:1: Orbital Elements with Pure Keplerian Equations
Fig:2: Orbital Elements with J2 Effect
Fig: Effect of Secular variation J2 ,J3, J4 on orbit geometry
-1-0.5
00.5
1
x 104
-1-0.5
0
0.51
x 104
-4000
-2000
0
2000
4000
-1-0.5
00.5
1
x 104
-1
-0.5
0
0.5
1
x 104
-4000
-2000
0
2000
4000
-1-0.5
00.5
1
x 104
-1
-0.5
0
0.5
1
x 104
-4000
-2000
0
2000
4000
x[Km]y[Km]
z[km
]
(a) Pure Keplerian
(b) J2
(a) J2,J3,J4
Conclusion Orbit Integration using Kepler’s and Newton’s Laws of
motion. GPS RINEX data file decoding. Extended Kalman Filter Representation Calculation of Jacobian Matrix for system equation. Calculation of Jacobian Matrix for system equation from
actual measurement (RINEX data file). Calculation of System Matrix. Calculation of initial Noise matrix and error covariance
matrix.
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