7 june 1999 - digital.library.unt.edu
TRANSCRIPT
Signal Based Motion Compensation forSynthetic Aperture Radar
Final Report
Department of EnergyGrant Number DE-FG03-96ER82294
7 June 1999
TSC-B022-199-O024
Technology Service Corporation11400 West Olympic Blvd., Suite 300
Los Angles, CA 90064(310) 954-2200
Goleta EngineeringP. O. BOX6208
Santa Barbara, CA 93111(805) 967-0600
DISCLAIMER
This report was prepared as an account of work sponsoredby an agency of the United States Government. Neitherthe United States Government nor any agency thereof, norany of their employees, make any warranty, express orimplied, or assumes any legal liability or responsibility forthe accuracy, completeness, or usefulness of anyinformation, apparatus, product, or process disclosed, orrepresents that its use would not infringe privately ownedrights. Reference herein to any specific commercialproduct, process, or service by trade name, trademark,manufacturer, or otherwise does not necessarily constituteor imply its endorsement, recommendation, or favoring bythe United States Government or any agency thereof. Theviews and opinions of authors expressed herein do notnecessarily state or reflect those of the United StatesGovernment or any agency thereof.
Portions
DISCLAIMER
of this document may be illegiblein electronic image products. Images areproduced from the best available originaldocument.
—
SUMMARY
The purpose of the Signal Based Motion Compensation (SBMC) effort is todevelop a method to measure and compensate for both down range and cross rangemotion of the radar in order to provide high quality focused SAR imagery in the absenceof precision measurements of the platform motion. Currently SAR systems require veryprecise navigation sensors for motion compensation (mocomp). These sensors are veryexpensive and are often supplied in pairs for reliability. In the case of GPS they can bejammed, further degrading performance. This makes for a potentially very expensive andpossibly vulnerable SAR system. SBMC can eliminate or reduce the need for theseexpensive Nav sensors thus reducing the cost of budget minded SAR systems.Alternately SBMC can increase the robustness of higher performance SAR systems by(1) increasing the performance of existing mocomp algorithms, (2) offering a back up toNav failure such as GPS jamming and (3) provide an alternate for redundant Nav sensors.
The DOE Phase II SBIR SBMC effort began on 22 July 1997. During theprogram trips were made to and meetings held at both Sandia and Raytheon – McKlnneyTexas (former TI). Data has been secured from Raytheon - McKinney on their Sea Vueradar and APS-137B (V) 5 AIP SAR.
The Sea Vue radar has a sidelooking strip mode and a spot mode with down rangeresolutions of 24, 12 and 6 feet (7.2, 3.6 and 1.8 m). Sea Vue has analog rangecompression and provides range compressed I and Q data out of the A/D. Data has beenreceived with no mocomp applied and fill Nav data recorded fromaLN-100 EmbeddedGPS INS (EGI) motion measurement system (MMS). This will allow processing of the Iand Q data via both MMS based mocomp and SBMC. The desired output will be threeimages: no-mocomp, MMS mocomp and SBMC, for direct comparison.
Raytheon has also collected no-mocomp I and Q data from the APS-137 B(V)5SAR, and released it to GE/TSC. This data is at 10 ft (3 m) resolution with a chirpedpulse, thus requiring range compression in the TSC processing.
An additional and very important source of data is synthetic data developedinternally at TSC. This approach provides precisely defined multiple point target datagenerated in an exact controlled environment. This synthetic data is used to develop andoptimize the SBMC algorithm, prior to feeding real I and Q recorded raw phase historydata from the above sources thru the SBMC algorithm.
In a parallel effort Sandia is modi~ing their PGA algorithm to provide somedegree of 2-D SBMC. Currently the PGA provides 1-D cross range phase errorcompensation. The heart of the SBMC algorithm that Goleta Engineering / TSC isdeveloping is a down range tracker to provide down range mocomp. The goal is to blendthe SNL and TSC / Goleta Engineering efforts for a very robust SBMC. The two, PGAand Range Tracker, working together will provide a very capable SBMC algorithm.
ii
As an alternate to the PGA, a Doppler tracker and multiple iteration map driftautofocus algorithm were developed. The Doppler tracker was developed to stabilize theDBS filters used in the range tracker for improved range track performance. This alsoprovides a first order mocomp. A two iteration map drift autofocus approach provedadequate to focus the final image. Thus, in its final configuration the SBMC algorithmconsists of three main parts:
- Doppler tracking and compensation- Range tracking and correction- Autofocus
The SBMC algorithm was developed using both the Sea Vue data and thesynthetic data. The synthetic data proved extremely helpfid in developing the algorithm.Results were generated using a 4 point target cluster of synthetic data, a 100 dispersedpoint target array of synthetic data and a batch of Sea Vue recorded data. Good Dopplertracking, range tracking and autofocus were achieved.
The results on this program demonstrated the capability of the SBMC approach.A very robust algorithm can be developed based upon SBMC and any available Navsensors. The algorithm is tuned to a particular application. It is adapted to a particularradar and aircraft Nav system. This SBMC approach will enable a low cost SARcapability to be provided for budget minded applications. Alternately it can also beapplied to high performance SAR systems for improved capability. It will extend currentMMS mocomp and autofocus performance and provide a backup capability tocompensate for Nav system performance degradation, such as from component failure orGPS jamming.
TABLEOFCONTENTS
SUMMARYTABLE OF CONTENTSLIST OF FIGURESLIST OF TABLESLIST OF KEY ACRONYMS AND SYMBOLS
1
22.12.22.32.42.52.5.12.5.22.5.32.5.42.5.52.5.62.62.6.12.6.22.6.32.6.42.6.52.6.62.6.72.72.7.12.7.22.7.32.7.42.7.52.8
33.13.23.33.43.53.63.7
INTRODUCTION
SIGNAL BASED MOCOMPSBMCConceptThe Four Parts of SBMCApplication to Candidate SAR Image Formation Processing (IFP)Ground Based Signal Processor DefinitionDown Range MocompDown Range Mocomp Design ApproachMotion CompensationRange TrackingCoarse Resolution Range-Doppler MapsS13MC Down Range Algorithm DescriptionSBMC VariantsRange Motion AnalysisMotion ModelMotion SensitivityHigh Frequency Range Motion Sensitivity AnalysisLow Frequency Range Motion Sensitivity AnalysisTotal Range Motion Sensitivity ModelExpected Range Track Measurement AccuracyMotion Analysis ConclusionsApplication to the Sandia Twin Otter SARExisting Sandia MocompSandia Data Collection for Phase IITypical Twin Otter ProcessingNo IMU or GPSDown Range Mocomp Algorithm Design Options for the OSASEA VUE SAR
SBMC ALGORITHMDoppler TrackerFrequency Shift MeasureSmoothing FilterDoppler CorrectionRange TrackerRange CorrectionRange Track and Correction Data Results
Page #
iiivvi
. ..Vlll
ix
1-1
2-12-12-32-32-52-62-62-72-82-82-92-1o2-112-112-122-122-132-142-152-152-162-162-172-182-182-192-19
3-13-13-33-33-43-53-73-8
iv
3.83.9
44.14.24.3
55.15.25.35.45.5
Autofocus AlgorithmAutofocus Data Results
RAW DATA DESCRIPTIONSimulated DataSea Vue DataAIP SAR Data
SBMC RESULTSFour Target ClusterMany TargetsSea Vue Radar ResultsExample Matlab Program Output ListingAIP SAR Results
References
Appendix A SBMC Matlab ProgramFull SBMC Matlab ProgramDoplr_trackRange_trackAutofocusMMS MocompNo_mocomp
Page#
3-123-15
4-14-14-1o4-14
5-15-15-15-15-75-8
R-1
A-1
v
LIST OF FIGURES Page #
2-12-22-32-42-52-62-72-82-92-1o2-112-122-132-142-153-13-23-33-43-53-63-73-83-93-1o3-113-124-14-24-34-44-54-64-74-84-94-1o4-114-124-135-1
5-2
SAR Mocomp Approach for Spot and Strip Modes 2-1Generic SAR Processing with Signal Based Mocomp 2-2Fundamental (range-Doppler) SAR Processor with SBMC 2-4Two-stage Overlapped Subaperture SAR Processing with SBMC 2-4Polar Format SAR Processor with SBMC 2-5SAR Algorithm for SBMC Development 2-6Implement Range Motion Measurement Via Multiple-Image Slip Detection 2-7SBMC Down Range Algorithm Block Diagram 2-9Compensation for Range Motion 2-1oMotion Model Spectrum 2-12Motion Sensitivity Model 2-14Required Motion Reduction 2-15Sandia Mocomp Overview 2-17SV SAR Processing 2-20Sea Vue SAR Overlapped Aperture Processing 2-21Doppler Spectrum (left) and after phase shifi to zero Doppler (right) 3-2Measured LOS Velocity, Raw (left) and Smoothed (right) 3-2Computed LOS Phase Shift (left) and error (right) 3-2CR Compressed Images from First Two Sub-Apertures 3-9Cross Correlation, 3-D (top), Collapsed Doppler (bottom) 3-1oCross Correlation after Thresholding, all Dopplers 3-11Measured Range Slip per Doppler Filter (17 of 32 above Threshold) 3-11Example Range Tracker Results 3-12Illustration of Cross Correlation Data (left) and Cross Range Slip (right) 3-15Estimated QPE (left) and Static Focused Image (right) 3-16First Iteration QPE (left) and Corrected Image (right) 3-16Second Iteration QPE (left) and Corrected Image (right) 3-16Simulated Data Geometry 4-5Cross Track Displacement 4-5Cross Track Velocity 4-6Four Targets Raw Data 4-6Unfocused DBS Image of Four Targets 4-7Raw Data Image for Many Targets 4-8DBS Image for Many Targets 4-8Many Targets DBS Image at p = 2000 or x = 1 Km 4-9Geometry for Simulated Data with Cross Track Motion 4-9Illustration of Raw Data from Sea Vue files 4-12DBS Image of Sea Vue Data 4-14AIP SAR Raw Data (kOOOl.ph) 4-15DBS Image of AIP SAR Data (kOOOl.ph) 4-15Four Target Cluster Results. Top center is no-mocomp, lower left is 5-2SBMC and lower right is MMS-mocompFour Target Cluster Results for P = 4096. Top center is no-mocomp, 5-3lower right is SBMC and lower right is MMS-mocomp
vi
Page #
5-3
5-4
5-5
5-65-75-8
5-95-1o
Four Target Cluster Tracker Results. Doppler Tracker ontheleft and RangeTracker on the right. The solid line is the Tracker Value, the short dashed line isthe predicted CRP value and the large dashed line is the cross track motionMany Targets Results. Top center is no-mocomp, lower left is SBMC and lowerright is MMS-mocompMany Targets Tracker Results. Doppler Tracker on the left and Range Tracker onthe right. The solid line is the Tracker Value, the short dashed line is thepredicted CRP value and the large dashed line is the cross track motionMany Targets Image for P = 4096Doppler tracker (left) and Range Tracker (right) for P = 4096Sea Vue Radar Images. Top center is no-mocomp, lower left is SBMC and lowerright is MMS-mocompRange Tracker for SBMC Sea Vue ImageAIP SAR SBMC Images (kOOOl.ph)
5-3
5-4
5-4
5-55-55-6
5-65-9
vii
2-12-24-14-24-34-44-5
LIST OF TABLES
Sinusoidal Motion ModelTypical Parameters for SNL ProcessingRadar Parameters for Simulated DataProcessing and Motion ParametersParameters for Sea Vue Data Used - Subaperture ValuesRadar and Processing Parameters ComparisonSea Vue Data Collection Header File Format
Page#
2-112-184-24-74-1o4-114-13
. . .Vlll
LIST OF KEY ACRONYMS AND SYMBOLS
ACRA/D, ADCAFAFPAHRSAIPAMANTAZBSRBWCITCOACRCRLCRPCRRCRSSCTMDOEDBSDDSDRDRADRRDRSSDSEGIELEXFFTFMFSFSNGPSHI,QIFFTIFPIMUINsISARISLR
Azimuth Compression RatioAnalog to Digital ConverterAutofocusAntenna Foot PrintAttitude and Heading Reference SystemAirborne Improvement ProgramAmplitude ModulationAntennaAzimuthBeam Sharpening RatioBandwidth or BeamwidthCoherent Integration TimeContrast Optimization AlgorithmCross RangeCentral Reference LineCentral Reference PointCross Range ResolutionCross Range Sample SpacingCorner Turn MemoryDepartment of EnergyDoppler Beam SharpeningDirect Digital SynthesisDown RangeDefense Research AgencyDown Range ResolutionDown Range Sample SpacingDoppler ShiftEmbedded GPS and INSElevationExciterFast Fourier TransformFrequency ModulationFrequency ShiftFrequency Shift NumberGlobal Positioning SystemaltitudeInphase, QuadratureInverse FFTImage Formation ProcessorInertial Measurement UnitInertial Navigation SystemInverse SARIntegrated Sidelobe Ratio
ix
LLOLOSMBCMDAMOCOMPMMSNFFTNPRINRGOSAPPFAPGAPKSLPRFPRIPROCPsPSLRPTRQPERRCVRREcRFR-DRIGRNGRSsSARSDASEAVUESIRSNLSOFSvRTISTSCTSCILATx fcTIT-OTRKUK
Length of projected synthetic apertureLocal OscillatorLine of SightMain Beam ClutterMap Drift AlgorithmMotion CompensationMotion Measurement SensorNumber of samples in the FFTNumber of PRIsNumber of Range GatesOverlapped SubaperturePulsePolar Format AlgorithmPhase Gradient Autofocus AlgorithmPeak Sidelobe LevelPulse Repetition FrequencyPulse Repetition IntervalProcessorPhase ShiftPeak Sidelobe RatioPoint Target ResponseQuadratic Phase ErrorRangeReceiverReceiverRadar (Radio) FrequencyRange - DopplerRadar Imagery GeneratorRangeRange ShiftSampleSynthetic Aperture RadarSampled Data Assembly (MD)A Raytheon Commercial SAR SystemSignal to Interference RatioSandia National LabsSubaperture Overlap FactorSea VueRaytheon TI Systems (now just Raytheon)Technology Service CorporationTSC / Los AngelesTransmit center frequencyTexas InstrumentsTwin OtterTrackUnited Kingdom
x
vVL, VLOSXMTR
VelocityLine of Sight VelocityTransmitter
xi
1 INTRODUCTION
This is the final report documenting the results on the DOE Phase II SBIRprogram on Signal Based Motion Compensation (SBMC). The Phase II effort buildsupon the preliminary results obtained during the preceding Phase 1 effort. The objectiveof the Phase I and Phase II effort is the detailed analysis, design and demonstration of theSBMC algorithm.
This report begins in Section 2 with a summary of the SBMC concept andproceeds to summarize the individual items investigated. Then in Section 3 the SBMCalgorithm as developed is defined. The partial results discussed in Section 3 show datafrom the three main parts of the overall SBMC algorithm: the Doppler tracker, the rangetracker and the autofocus algorithm. The data that was used to develop the algorithm isdescribed in Section 4. The final SBMC results are presented in Section 5. The results inSection 5 show sets of three images for comparison: no-mocomp, MMS mocomp andSBMC.
The SBMC Matlab program is attached at the end of the report as Appendix A. Itincludes the master program plus the subprograms for Doppler track, range track and autofocus. Also included are the subprograms for MMS mocomp and No-mocomp that areused for comparison.
1-1
2 SIGNAL BASED MOCOMP (SBMC)
2.1 SBMC Concept
For strip mapping the motion compensation, or mocomp for short, is to a centralreference line (CRL) and for spot the mocomp is to a central reference point (CRP) asillustrated in Figure 2-1. The core of SBMC is to do range and Doppler tracking tostabilize the range gates and Doppler filters on the ground during the CIT and the entiremap fi-ame time to achieve resolution, geometric fidelity, and dynamic range. Thus ineffect SBMC builds upon, expands upon and adds to SAR autofocus in developing theSBMC algorithm. Figure 2-2 illustrates a generic SAR processor with signal basedmocomp added.
SPOTMOCOMPCRP
------------------------------------------------------f---------------------
SAR SLARSTRIP MAP .. .
-------------------------------- .
$(t) = ~ R(t)A
ALONGTRACK
.j$~....”.-:-.
--------------- ~----.......
........”....
....”....”,,......”...’
v < ➤
L OR CIT
STRIP/ MOCOMP
CRL
A
; CROSS; TRACK
.............
Figure 2-1 SAR Mocomp Approach for Spot and Strip Modes
2-1
—— —INS / GPS
I
➤ ––__––_ &––_––-SBMC , AUTO-4
IFOCUS
II . — ——— —
A’v v PREDICTED
MEASURED
I PHASERESIDUAL
MOCOMP I HISTORYPHASE
COMPUTE - ERRORSI[ J
IRAw I 7 vDATA A-F
IN PREFILTER RANGE CORNER 0MOCOMP2
AZIMUTH~ (MOCOMPI)- COMPRESS + TURN - COMPRESS
MEMORY
rI
,,
L-JPOSTPROC
OUTPUT. NO IMU IMAGE t. OPTIONALINSAND/ORGPS
Figure 2-2 Generic SAR Processing with Signal Based Mocomp
Figure 2-2 represents the basic processing architecture in which SBMC will beimplemented. Most SAR processors incorporate three main functions: prefilter, rangecompress and azimuth compress. The azimuth compression function is the heart of theSAR processing and is the main area where the alternate image formation processingalgorithms differ. Azimuth compression is comprised of a corner turn memory (CTM)followed by a cross range algorithm such as range-Doppler, overlapped subaperture(OSA) or polar format algorithm (PFA). The cross range processing algorithm assumesthat the data is range compressed and aligned in range. This range alignment is usuallydone by controlling the A/D with a signal derived from an inertial Nav sensor.
There are the three leading autofocus algorithms: PGA, map drift and contrastoptimization. Figure 2-2 shows the SBMC added on as an extension to the autofocusalthough in general the SBMC can be added to a radar that does not have autofocus. Ifautofocus is present the SBMC will work with the autofocus. If autofocus is not present,the SBMC will include the autofocus function. SBMC will provide the range andDoppler correction signals necessary to compensate for motion both down range andcross range such that high quality imagery is obtained. Also, shown in Figure 2-2 areoptional INS and GPS inputs. SBMC can work with these inputs or without them. Thebaseline SBMC will work without any Nav inputs. The baseline radar resolution is 3 m.
Therefore the primary requirements to incorporate SBMC are:(1)(2)(3)(4)
wide bandwidth auto-focus for Doppler trackingadded range trackerreplace Nav drive (inputs) for other functions such as PRF controlfigure out the location of where the map was made
2-2
2.2 The Four Parts of SBMC
There are four parts to SBMC and these are: the aircraft interface, coarse SBMC,fine SBMC and position location.
The aircraft interface is tailored to a particular platform. Available Nav aids willbe used to set up the mapping scenario and provides inputs to set up the processing andmocomp. For example, some systems may have a GPS Nav sensor on board. Othersmay have and attitude and heading reference system (AHRS), pitot tube velocity, or otherdata that could be used by the SBMC.
Coarse SBMC involves primarily a range slip measurement and correction butalso possibly a coarse Doppler correction. There will be an adjustment for “missing”Nav inputs using the available Nav data. It maybe desirable to control the A/Ds andprovide a prefilter down conversion reference. SBMC must then provide these signals.Also some applications perform some mocomp in the transmitter and receiver. If so,these correction signals must also be supplied.
Fine SBMC is a wideband phase or Doppler measurement and compensation. Itis currently being implemented with 2-D PGA autofocus under development at SNL.
For position location the focused and linearized maps from SBMC can becorrelated with stored reference maps. This will provide an exact geometric location andregistration of the maps. Also this will provide the aircrafi with an exact location of itslocation when the maps were made
2.3 Application to Candidate SAR Image Formation Processing (IFP)
A block diagram of the fundamental range-Doppler SAR processing with signalbased mocomp is given in Figure 2-3. Raytheon (former TI) Systems uses fimdamentalrange-Doppler processing in the Sea Vue SAR. The signal based mocomp includes rangetracking and wideband auto-focus (Doppler tracking) and will provide the mocompinputs to the processor.
The two stage overlapped subaperture (OSA) SAR processor with SBMC addedis illustrated in Figure 2-4. This IFP algorithm is used on the SNL Twin Otter and theRaytheon (TI) AIP SAR. SBMC will provide the motion compensation inputs (MCI) tothe processor via the mocomp computer. SBMC will also provide the correction signal tothe range shift multiply.
The polar format SAR processor with SBMC is illustrated in Figure 2-5. Thepolar format IFP algorithm is used by the PGA development group at SNL in theirground processor. In Figure 2-5 the range compensation signal is shown going to thefrequency domain multiplier.
2-3
11
sDA
Q a: :,: ‘1....................jRANGE ;
CORNERMOCOMP
CROSSPREFILTER TURN RANGE AMPL
~COMPRESS;MEMORY
MULTIPLYFFT DETECT
.. .. .. . .. .. . .. . . . .. ..
rMOCOMP 1‘ 4 MOCkP 2+
iINPUT lmur
I1
1II11 Y
POST~.-.-.--------------------------.----------, PROCESSING
RANGETRACKER
2 1 OUTPUTt 1 IMAGEI 1
I SIGNALBASEDMOCOMP1
I I------ ------ ------ ------ .- .-. _ ._ ---- ._ ._. _ ,
Figure 2-3 Fundamental (range-Doppler) SAR Processor with SBMC
PRESUMMER INTWINOTTER/ NO PRESUMMER INB(V)5
/ /I –t
+ + COARSE + +s
+ + +RANGE 3-D FINE
CROSS RANGE CORNER MOCOMPD SHIFT
CROSSRANGE MULTIPLY
AMPL
A MULTIPLYCOMPRESS TURN RANGE
FFTDETECT
+ + + MEMORY FILTERING
Q
T/ i
I MCIMCI t----.-
]&Q/
mTMCI
mAUTOFOCUS
TOMOCOMP 4——_——COMPUTER ‘ SIGNALBASEDMOCOMP
LaT
OUTPUTIMAGE
Figure 2-4 Two-stage Overlapped Subaperture SAR Processing with SBMC
2-4
I ~. .-—
-+ :4 + +
POLAR DOWN RANGE CORNER:MULT: FFT TURN
CROSSRANGE AMPL, [ LE-FORMATTING
MEMORYFFT DETECT
+, + + ~ +
Q ‘-----v
7POST
PROCESSING
SIGNAL+ BASED
TO SWEEPGENERATOR(PFALWAYSWORKS WITHSTRETCH)OR TO DIGITAL = ~,,:.,,.
MULTIPLIERINPROCESS~R
Figure 2-5
2.4 Ground Based Signal
“u,,”,
IMAGE
*ADD RANGE TRACKERTO AUTOFOCUS
Polar Format SAR Processor with SBMC
Processor Definition
A ground based signal processor called SARP was developed to be used as aplatform for the development and utilization of the SBMC algorithm. SBMC is a mainarea where the ground processor will be utilized, some with simulated radar data, butmostly with real recorded SAR raw data. The ground based signal processor acceptsdigital data inputs and processes them to form the final output image. This ground basedprocessor has the flexibility to accommodate multiple image formation algorithms andautofocus algorithms, and allows for the development of the signal based motioncompensation algorithms. The image formation algorithms which can be implementedare: the fimdamental range-Doppler which is used on the Raytheon Sea Vue radar, theoverlapped sub-aperture which is used on the SNL Twin Otter and Raytheon APS- 137AIP SAR, and the Polar Format. The autofocus algorithms that can be implemented are:PGA, Map Drift and Contrast Optimization. A candidate block diagram of the signalprocessing which the ground processor can perform is given in Figure 2-6. Thisprocessing, when the options are properly selected, will allow data from all three sourcesto be processed. In effect the autofocus algorithm is inserted serially betweenMOCOMP2 and the final Az Compression.
2-5
I&Qm I&Q
OUT
RANGESBMC CTM
AzCOMPRESS — MOCOMP2 — COMPRESS ~
,,
4,,0
, 1I ,-_____..,,1 1:, : AUTO- : t____
: FOCUS :-----”
t--------,OPTIONSBYFUNCTIONALBLOCK
1. MOCOMP1 OR NO MOCOMP12. PREFILTER OR NO PREFILTER3. GROWTH ONLY - NO POLAR REFORMAT OR FIRST STAGE FFT4. CHIRP RANGE CORRELATO~ DERAMPED RANGE FFT OR NO RANGE COMPRESS5. SBMC OR NO SBMC6. MAIN CTM - GROWTH TO 3-D CTM FOR TWO STAGE OSA PROCESSING7. MOCOMP2 OR NO MOCOMP28. LINE BY LINE AZ COMPRESS OR FFT BATCH PROCESSING--.. -.-———--—.----——-----— ------
9. ADD AUTOFOCUS PROCESSING
Figure 2-6 SAR Algorithm for SBMC Development
2.5 Down Range Mocomp
2.5.1 Down Range Mocomp Design Approach
The pilot flies to a designated spot and tries to fly at a desired heading, velocityand altitude. The mocomp starts with precomputed values of the along track velocity Vx,the line of sight velocity to the CRP or CRL, VLos, the range to the CRP or CRL, r,, andgrazing angle Y to the CRP or CRL. Or if GPS is present, the values will be computedfrom the GPS inputs.
Coarse resolution DBS maps are made at up to 0.5 sec CIT and full down rangeresolution. This is 1 m for the Twin Otter, 2 m for Sea Vue, or 3 m for B(V)5. Next, twosuccessive images are cross correlated in the down range dimension and the range error isdetermined. This process is illustrated in Figure 2-7. In this illustration, the down rangepart of AR is measured and compensated by the down range mocomp and the cross rangecomponent is compensated by the autofocus. The range error will be generated at a 2 Hzor higher rate commensurate with the spectrum of the expected platform motion.
2-6
T2
TI
+
VAICIMAGE 2
r-r lmGE1ARL-.–––4 ~
——-— —_--—--—-——._——--——
I_ _____/
AR IS THE MAP SHIFT DUE TO AIRCRAFT MOTION ERROR
IT IS A 2-D KIN TO THE MAP DRIFT AUTOFOCUS ERROR
AR CAN BE MEASURED TO A SMALL FRACTION OF ARESOLUTION CELL
Figure 2-7 Implement Range Motion Measurement via Multiple-Image Slip Detection
A key part of this range cross correlation involves the nature of the coarseDoppler – fine range resolution maps, particularly the point target content of theseimages. Alternates in the DBS beam sharpening ratio maybe required, and possibleamplitude thresholding prior to cross correlation may also be tried. As an alternate tocross correlation, the individual point scatterers can be tacked from map to map.
After computing the range error on a pair of images, a smoothing filter can beadded to computed a smoothed range slip. This might be an a, ~ filter to compute rCand VLO.S.It will be necessary to determine the coefficients a, ~ and maybe provide theseas inputs to the Mocomp computations, which are usually performed in a C-30 processor.
It maybe possible to obtain a measure of Vx from the PGA autofocus. Thisrequires interpreting the quadratic phase error as coming from a cross range velocity errorand not a LOS acceleration. Further, it may be possible to obtain a measure of VLos fromthe linear phase error in the PGA. This would be combined with the VLO.Scomputedfrom the range tracker.
2.5.2 Motion Compensation
The SBMC involves two steps coarse and fine. The coarse step is the rangetracker (range error measurement and compensation) and the fine is the 2-D PGA. Thesetwo steps operate in series. The coarse range tracker will take out the coarse range-Doppler errors and the 2-D PGA will take out the rest. The primary purpose of thecoarse range track SBMC step is for no-GPS. With GPS based mocomp, the coarserange tracker is of marginal necessity. Its primary purpose with GPS mocomp is as abackup in case GPS is jammed.
2-7
The input Doppler spectrum will not be centered at zero Doppler due to theuncertainty or initial error in velocity. For the SNL collected data, it is assumed that theDC line will be filtered out, but this needs to be verified. The input spectrum either needsto be shifted to zero or the proper filters selected out of the Doppler FFT.
In the SNL OSA algorithm, the order of processing is complex multiply to reducethe LOS error to zero, followed by first stage Doppler FFT and then range compressionFFT. Since the LOS velocity isn’t known, the question is whether to do the range FFTfirst or the first stage Doppler FFT. The range FFT will be larger typically 2K and thecoarse Doppler smaller typically approx 64. Efficiency-wize it is better to do the Az FFTfirst and the range FFT next on the selected 32 or so useful Doppler filters. In either casethe range tracking requires high res range data.
2.5.3 Range Tracking
The main new ingredient for SBMC is range tracking. The down range motion ofthe radar will be measured by analysis of the signal return and an error signal generatedto compensate for this motion. This range tracking and compensation will adjust thereturn to a fraction of a range gate such that the cross range SBMC processing can thentake out the more serious cross range phase errors. The SBMC cross range processing isprimarily autofocus. The SBMC autofocus will be wideband to take out not onlyquadratic phase errors but higher frequency ones as well.
The key is to develop a way of measuring the range motion. The main approachis to form coarse resolution range-Doppler images and cross correlate them in range.Alternately a search can be of the coarse resolution range-Doppler maps for likely pointtarget returns in the range-Doppler space and these point targets tracked from successiverange-Doppler maps. The key is to form these range-Doppler maps at a short enoughintegration time to capture the motion. A nominal design point is to make the coarseresolution maps at approximately a 20 Hz rate.
2.5.4 Coarse Resolution Range-Doppler Maps
The coarse maps are actually at fine or high range resolution and coarse Dopplerresolution. The range resolution is at that of the final image so that the range tracking canoperate on the best data. The Doppler resolution is determined by the desired dynamicbandwidth. So for a 20 Hz data rate as an example, the Doppler resolution isapproximately 20 Hz. The cross range resolution can be determined from this, i.e. CRR=R6sand
As an example, consider Ks = 1.2,1= 0.03 m, V = 100 m/s and CIT = 1/20 see, then thesynthetic beamwidth is 3.6 mr or 0.2 deg which is nominally about a 10 to 1 beam
2-8
sharpening ratio. At a range of 10 Km the CRR is 36 m which is quite a bit broader thanthe DRR.
Alternately a higher res DBS can be used but at an overlapped higher data rate.For example, the coarse DBS maps can be done at 0.5 sec CIT, but overlapped 10 to 1 togive a 20 Hz data rate. It is unclear how responsive this would be, i.e. how well wouldthis respond to 10 Hz motion. So, this would need to be analyzed. For now, to start, thesimple non-overlapped 20 Hz approach will be pursued.
2.5.5 SBMC Down Range Algorithm Description
Down range SBMC processing, as illustrated in Figure 2-8, begins after downrange (DR) compression, The down range motion from a straight line path is measuredby cross correlating successive range-Doppler (R-D) maps. These maps have coarseCRR but fine DRR. It is desirable to avoid cross range cell slippage between successiveR-D maps. This makes life easy. To do this it is necessary to keep the distance between
(overlapped) sub-apertures AL< CRR so that successive R-D maps can be crosscorrelated readily.
,.-.-----, IRNG ;Az!COMP ; COMP ~
PRI DOPLR I ,
A A,--------I
I
T,
T ‘“,,
CTM ,RANGE RANGE ,
CTMRANGE
FFT (R-D ,CORLATR ERROR ERROR
MAP) CALCLATR FILTER ..________-..._______;
1.2.3.4.5.6.7.8.
THE DATA IS LOADED ONE PHI LINE OF RANGE GATES AFTER THE OTHERTHE DATA IS FFT’D ACROSS PRI’s, ONE RANGE GATE AIWER THE OTHERTWO SUCCESSIVE RANGE DOPPLER MAPS ARE FORMEDCORRESPONDING RANGE LINES FROM SEQUENTIAL CORRESPONDING DOPPLER FILTERS ARE CORRELATEDA RANGE ERROR IS CALCULATED AS A FUNCTION OF CROSS RANGE DOPPLER FILTER AND TIMETHE RANGE ERROR IS SMOOTHED (a - ~ FILTER)THE DATA IS RANGE COMPENSATED BY THIS RANGE ERROR - A DOWN RANGE INTERPOLATION(MAYBE) THE DATA IS PHASE COMPENSATED IN THE ORTHOGONAL PRI DIMENSION - A COMPLEX MULTIPLY
Figure 2-8 SBMC Down Range Algorithm Block Diagram
The cross correlation proceeds Doppler filter by Doppler filter. The SBMC R-Dmaps will be modeled after the first stage of the SNL Twin Otter (T-O) OverlappedSubaperture (OSA) processing. Nominal parameters for the T-O are: L1 = 7.7 m, AL =2.6 m (3 to 1 overlap) and CRR1 =22 m. For the T-O case since AL << CRR1, i.e. 2.6 m<<22 m, the data from successive CR FFT’s will lineup good enough in the CR
direction such that the down range cross correlation can proceed without concern forcross range cell slippage. Thus if a longer L 1 with finer CRR were to be used, heavyoverlapping to keep AL << CRR1 will still keep life easy.
The result from each Doppler filter is edited and then averaged across Dopplerfilters. The down range error from successive R-D maps will be filtered in an u–p or
2-9
ct+y filter or an equivalent smoothing filter. The range compressed data will then beadjusted via a DR interpolation to take out the measured DR motion. This is illustrated inFigure 2-9.
AIRCRAFTGROUND TRACK
RANGE DATAAFTER
RANGE TRACK
v
\
DATA INCTM AFTER ;RNG TRK
I \
(.-----L,.~.es____--T:_=hi__= _____ ..:..
1 ..- ...... 1
J1 --- ---I..... ..... I
.... ... . ..... ... . . .I
\-.....
.. ..\
-..... ..
NEAR FARRANGE RANGE
RANGE DATABEFORE
RANGE TRACK
DATA INCTM BEFORE ;RNG TRK .
+..————.—. :—II
:I
A :1I +—--+-4 i
1;:1
A
1.
POINTTARGET - ;:J
LOCATIONONSUCCESSIVEF’RIs
CONSTANTTIMEDELAY
TARGET MOTION MIRRORSAIRCRAFTMOTION
Figure 2-9 Compensation for Range Motion
2.5.6 SBMC Variants
To provide controlled data for the down range mocomp development,synthetically generated point target data or Radar Imagery Generator (RIG) data can beused. RIG is a TSC program to generate SAR imagery from 3-D geometric models usingelectromagnetic (EM) code. This ability to generate simulated data provides a veryusefid capability in general.
To optimize the range slip measurement performance, CIT1 or L1 can be varied.As an option to this, it maybe possible to go to finer first stage CRR with heavieroverlap. The measured tracking error at the finer res can be compared with the coarserres error to determine which approach is best.
Instead of cross correlating whole maps, an alternative approach is to hunt for anduse bright scatterers. Also it may be desirable to try thresholding first prior to crosscorrelating. This is similar to the hunt for bright scatterers. The algorithm can crosscorrelate or track individual bright scatterer cells from map to map, or it can centroidbright scatterers from each map prior to comparing successive maps.
2-1o
For performance evaluation the SBMC image can be compared with a motioncompensated good image. It would be desirable to measure the noise added by SBMC, ifan approach can be conveniently formulated. Remember that the 2-D PGA will take outsome residual noise.
2.6 RANGE MOTION ANALYSIS
2.6.1 Motion Model
A motion model has been developed in Mathcad. To date measured data from theSNL Twin Otter and a CV 580 has been used to develop this model. The model is builtupon sinusoidal motion with peak values of R = 40 m, V = 4 m/s and A = 0.2 g. Basedupon analysis of a limited amount of measured dat~ the Twin Otter has a nominal motionof 2 m/s at a nominal frequency of 0.0345 Hz. The CV 580 has a nominal motion of 3 mat a nominal frequency of 0.017 Hz. The model is summarized in Table 2-1 andillustrated in Figure 2-10.
Table 2-1 Sinusoidal Motion Model
DATA OBTAINED ON TWO AIRCRAFT:
TWIN OTTER 3mAT.017Hz ( YIELDS 0.32 m/s AND 0.003 G )
CV 580: 2 nds AT 0.034Hz ( YIELDS 9.36 m AND 0.043 G )
SINUSOIDAL MODEL DEVELOPED:
R. =40
V. ‘4
A. =0.2
RR(f) ‘R.
V.R~~ =—
2m f 1
10.A ~RA(f’) .’
,2X f. ,21
max displacement in meters
max velocity in m/s
max acceleration in gees
spectrum in meters
spectrum in meters
spectrum in meters
spectrum in meters
2-11
100
10
: 0.1
,.,.–4
1.10–5
SINUSOIDAL MOTION WITH PEAK VALUES
RO=40 rn VO=4 mls AO=0.2 9
MOTION MODELI I I I
‘6 ],.,. I I I I
“ TWIN OTTER
‘ CV 580
, ,.0001 001 01 1 10 100
2.6.2 Motion
fFREQUENCY(Hz)
Figure 2-10 Motion Model Spectrum
Sensitivity
Range motion imparts both a phase and an amplitude change on the return. Thetraditional mocomp / autofocus measures and takes out the phase change. The samplingby the A/D converter will impart the amplitude change on the return. The sensitivity canbe developed by analyzing the return from a point target. As the A/D sample moves overthe target, there will be and amplitude change depending on where the samples fall on thepoint target response (PTR). For sinusoidal range motion there will be a sinusoidalamplitude change. The sinusoidal amplitude can raise the PTR cross range sidelobesdepending on whether the motion is pure sinusoidal or random and on the frequency ofthe motion. Low frequency amplitude change does not appear to effect the PTR much.However, a low frequency range change can move the target across a range cell limitingthe effective CIT and hence the achievable cross range resolution. This resolution lossfrom low frequency motion is more pronounced during the linear part of the sinusoid andless of an issue during the quadratic part.
2.6.3 High Frequency Range Motion Sensitivity Analysis
Jitter in range on the A/D samples can produce Amplitude Modulation (AM)across the synthetic aperture. This is a PRI to PRI variation and not a pulse to pulsevariation. Let the amplitude from a point target as fimction of range be given by a = f(R).Then a variation in R produces a variation is amplitude
Aa = f~R) AR
2-12
The fractional amplitude change is given by
Aa f’(R) ~—= —a f(R)
which for a sinusoidal variation can be set equal to the desired sidelobe level PKSL. Thiscan be solved for the allowed amplitude change or jitter
~ . PKSL
f ‘(R)
f(R)
A gaussian pulse shape is given by
where DRR is the 3 dB pulsewidth. The derivative is given by
f ~R) = - ~ R f(R)
The equation for the allowed high frequency range jitter, setting ARH = AR, becomes
PKSL
‘RH = 41n2R
DRR2
The max value of the gaussian pulse occurs at R = DRR / 2 {(ln2) which isapproximately the 3 dB point. Therefore the required range jitter becomes
AR~ =I
PKSL DRR2Jin
which for a PKSL of- 30 dB and a compressed pulsewidth of 1 m becomes 0.02 m.Thus a sinusoidal PRI to PRI range jitter of this value will produce -30 dB sidelobes fora point target near the center of the A / D or down range samples.
2.6.4 Low Frequency Range Motion Sensitivity Analysis
The low frequency range motion sensitivity is based on the target moving out of arange cell and hence limiting the CIT and cross range resolution. Consider sinusoidalmotion of the form R = ARL sin 27cft,where ARL is the peak value and f is the frequencyof motion. Let the allowed motion during a CIT be DRR, then the equation for theallowed peak value as a function of frequency becomes
DRR 1AR~ = ——
CIT 27rf
2-13
It maybe possible to develop a more exact equation relating AR~ to f by analyzing theexact amplitude roll off of a point target response as a function of the distance of thepoint target from a range sample location.
2.6.5 Total Range Motion Sensitivity Model
The range motion sensitivity model is the sum of the low frequency part and thehigh frequency part, i. e.
ARs = ARL + ARH
The motion sensitivity is given in Figure 2-11, and the required motion reduction MR,which is the ratio of the motion to the motion sensitivity, is given in Figure 2-12.
,.,., L1.10-3
CROSS RANGE
CIT = 10 SECS
CROSS RANGE SENSITIVITY
i—
001 0.1 1 10f.
100
F’FWQUENCYOFM(YIION(HZ)
DOWN RANGE
-30dB DRR=2m
DOW RANGE SENSITIVITYw 1 I i I
10–
1 –
11 -
0001 001 0.1 1 10 10U
f
FREQuENCY OF MOTION (W
Figure 2-11 Motion Sensitivity Model
2-14
CROSS RANGE DOWN RANGE
CIT = 10 SECS PKSL = -30 dB DRR=2m
RO =40 m VO=4 mls Ao =0.2 g
REQRD MOTION REDUCTION (MR) T=l O sec
‘“’04 ~ ‘“’04-1.103
FM R(O&_ ,00 _
‘5
10 –
I I
‘ O.fci 0.01 01 t 10 100 ‘ owl 0.01 01 1 10 lot
f f
FREQUENCY (Hz) FREQUENCY OF bfOTION (Hz)
Figure 2-12 Required Motion Reduction
2.6.6 Expected Range Track Measurement Accuracy
To a first order the range track accuracy 8R is on the order of
iiR = ~~~ DRR2.5 & m
where n is the number of pixels where the range is measured from, S/1 is the signal tointerference ratio which limits the range measurement accuracy for each pixel and DRRis the down range compressed resolution. As an example, for n = 100 and SIR= 6 dB thecell splitting accuracy is 1/50. For a resolution of 1 m, the range measurement accuracyis 0.02 m. This value is just equal to the high frequency range measurement sensitivity of0.02 m. For a measurement time of 0.1 see, the velocity accuracy is 0.2 m/s. Smoothingfrom successive measurements can improve this accuracy even fi.u-ther.
Considering a beamwidth of 5 deg and a velocity of 77 rds, the width of the mainbeam clutter (MBC) is 6.71 n-ds. Thus a velocity accuracy of 0.2 rrds should keep thisspectrum centered quite well. A PRF of 600 Hz, for example, corresponds to a velocityof 9 m/s. The MBC velocity spread pretty well matches the 600 Hz data rate (a 1.34 oversample ratio).
2.6.7 Motion Analysis Conclusions
The down range sensitivity to motion is much less than that for cross range, i.e.
cross range 0.0001 m down range 0.04 m
2-15
Basically the required motion reduction and max bandwidth is:
cross range 3,000 / 1 & 20 Hz down range 10/l &lHz
The required mocomp is therefore much less for down range than for cross range. Thedown range mocomp Nyquist bandwidth should therefore be about 2 Hz and thecorresponding CIT for successive image cross correlation is therefore 0.5 sees.
2.7 Application To The Sandia Twin Otter SAR
2.7.1 Existing Sandia Mocomp
The Sandia approach to mocomp is divided up into two parts, one called motionmeasurement and the other mocomp.
The Motion Measurement System (MMS) combines two sensors, an IMUoutputting data at about 1 KHz and a GPS outputting data at 1 Hz. The two outputs areblended into a Nav solution. The Nav solution has the “noise” from the GPS 1 secupdates. Sandia removes this 1 Hz noise with a proprietary filter. The MMS generatesfour main variables for the mocomp:
Vx the along track velocity
VLos the Line of Sight (LOS) velocity to the map CRP or CRL
rC the range to the map CRP or CRL
Y the grazing angle from the CRP / CRL
The mocomp is performed in a C-30. It requests data from the MMS at the Azsample rate, which is the data rate out of the presumer. This request rate is nominally at400 to 800 Hz. The MMS predicts ahead 1.5 clock periods and computes the fourvariables for this time. They are then sent back to the mocomp C-3 Oat the request ratebut delayed slightly. The nominal latency is 1.5 to 2 ms.
The C-30 mocomp computes the control variables, which are applied in thetransmitter, receiver and image formation processor. The primary LOS phasecompensation is applied in the receiver ahead of the ND. The waveform and LO signalsare generated using direct digital synthesis (DDS) techniques. The mocomp controls theRF start frequency, FM slope, and A/D rate.
The MMS provides for antenna stabilization. Thus the C-30 mocomp generatesno antenna control. The Sandia mocomp is illustrated in Figure 2-13.
2-16
1
El 1 KHzIMU
11
I1tI
1 radarAzII sample rateof
~ 400 to 800 Hz r-uIFP
(OSA + PGA)
P)Pl EX I REC I
t
I
bC-30 J*
NAV SAR data11 b (MOCOMI) V.x1
r%
1 VLOSproprietary 1
filterremoves :r.
1 Hznoise 1 Y
1‘x
L1GPS 1 Hz- ANT
MOTIONantenna stabilization
MEASUREMENT I-JSYSTEM (MMS)
Vx = along trackvelocity
VLOS = lin;of sightvelo;ity
r.= range to map center
W = grazing(depression)angle
Figure 2-13 Sandia Mocomp Overview
2.7.2 Sandia Data Collection for Phase II
The Twin Otter has a presumer and the data is recorded out of this presumer. If themocomp is turned off, i.e. the four variables frozen, and the presumer left in, there is agood chance that the presumer will filter out the antenna main beam return, and nothingbut noise and sidelobe clutter recorded. This is what happened during Phase I. Tocorrect for this problem, the presumer has been modified to basically allow it to beshorted out or bypassed. This for Phase II, when the mocomp is turned off, the presumerwill be shorted and the full PRF line to PRF line spectrum recorded. This data will berecorded with a reduced PRF and possibly reduced range samples to accommodate thebandwidth limitations of the data recorder. Sandia will setup the data collectionparameters to permit recording as much of this no presumer data as possible.
A second approach is to just terminate the IMU inputs in the MMS and run off ofGPS only. In this case the mocomp will not be turned off but allowed to run with GPSdriven inputs. What this means is that the four variables will not be frozen but allowed tochange at the GPS rate.
Thus we are defining two levels of SBMC, one with GPS only inputs and thesecond with out any inputs, GPS or IMU. The 2-D PGA approach requires that the rangemotion be confined to only a few range cells. Thus for robustness a separate rangemocomp ahead of the 2-D PGA is required to take out the larger motion of several tens ofmeters. Basically the 2-D PGA can work with and compensate for only about 1 meter
2-17
range motion. Typical motion as defined by the motion model is expected to be in the
neighborhood of+ 40 m.
2.7.3 Typical Twin Otter Processing
Some nominal or typical parameters for the SNL Twin Otter Processing aresummarized in Table 3. If the SBMC is integrated in the OSA processing, the rangetracking can be done by cross correlating the OSA generated subaperture images inrange. This will improve the efficiency of the range tracking. Alternately the SBMC canuse the points selected by the OSA for the PGA. This point selection is done by the OSAon the subaperture images and passed onto the PGA. The parameters calculated for thistypical scenario of Table 2-2 show a nominal ten to one beam splitting from a 64 pointfirst stage FFT with an output rate of 28 Hz.
Table 2-2 Typical Parameters for SNL Processing
PARAMETER
Wavelengthv,
Data RateAx
NFFT1CITI
Subaperture OverlapSubaperture Rate
L10,1
Cklcm
6,L
CIT
UNITS
mKtsHzm
ms
Hzm
Emmmrmsec
VALUE
0.031506000.1364
0.113/1287.72.210221
0.11802.3
2.7.4 No IMU or GPS
One of the first issues involved with this option is how to generate the VLos LOSphase correction and the VXcross range PRF correction. The VLOS correction isrequired to center the received Doppler spectrum to zero Doppler. This can be done byway of a “clutter tracker” function. The first stage FFT outputs can be used to generatethis error. This can be done by taking the filters between -32 and Oand Oand +32 andmeasuring the power in each half. A velocity error is generated by scaling the differenceover sum ratio of the two powers. This error is used to reposition the spectrum. Afterseveral iterations the spectrum should shift to zero. Once at zero the range track alpha-beta filter should maintain Doppler track.
2-18
2.7.5 Down Range Mocomp Algorithm Design Options for the OSA
It maybe possible to obtain Vx from the PGA autofocus. This requiresinterpreting the quadratic phase error as coming from a cross range velocity error and notfrom a LOS acceleration. Also, it may be possible to obtain a measure of VLos from thelinear phase error in the PGA. This would be combined with the VLos computed fromthe range tracker.
It maybe possible to use an U, ~, y filter to estimate aLos. This would assist indetermining if the PGA QPE is from LOS acceleration or cross range velocity. The rangeerror can be computed from adjacent apertures or overlapped subapertures. Theseoverlapped apertures could be the overlapped subapertures of the OSA.
In fact it may be possible to use the first stage coarse Doppler filtered data fromthe OSA. This would make for a very efficient algorithm. Nominally the first stage CITis -0.1 sec with a 3 to 1 overlap and an output data rate -30 Hz. Another option is touse the OSA point select points and track them as opposed to cross correlating the imagesin range.
And further it may now be practical to compute the depression angle for the C-30mocomp. This angle is probably too small to be of practical interest for typical longrange mapping.
2.8 SEA VUE SAR
The Sea Vue (SV) SAR processing as extracted from a document by DaveSteinbauer of Raytheon-McKinneyl is illustrated in Figure 2-14. In order to minimizerange cell migration effects, only the central portion of each batch processed is retainedas illustrated in Figure 2-14. For the high resolution cases, the synthetic aperture isgreater than the section of processed image that is retained out of the FFT batchprocessed. So, in order to generate a continuous strip image for the high resolutionmodes, multiple overlapped apertures are required. The aperture overlapping isillustrated in Figure 2-15.
—
1SV-SAR Algorithm Description Document, Dave Steinbauer, Raytheon – McKinney Texas.
2-19
Nominal 600 hzPRF l&Q
1024 range bins(firm
Phase Adjust1024 range bins
*g ==
“ Range Closure+ AiPxail Motion ,
1024range bins
-m
,,-’” ReducedPRF
32-pOint Prefilter
/’Huge Dual-
Poti CircularCorner TumMemory
IFirst Full
> Aperture
I
1024 range bins
DopplerInfo
1II,,
Phase Adjust
‘ Quadratic “T“ Range Focus ‘d. Fine Motion. Autofocus
1,
I
\\
SV-SAR SubpatchSignal Processing Flow
\
Repeal forEach OverlappedFull Apertwe
~.
FullX-rangeImagePatch
I I
!I’ ,Range _
[ Subp?.tck where Range! ~cRP I Migration defocus ~L is. 0.25 cells
I-Defocused due to
Range Migration
“ De-Warp. Beamshape Weighh”g+ Non-Linear Intemsiiy
\-End Image Built From
on and on Overlapped (Multi-look)Subpatches
Figure 2-14 SV SAR Processing
2-20
ground trackvector
)1’
ground track vector
1
aperture26
\.\
/’
.
I
Blow-up of area
26* incr_subpatch_flig ht_dist—
.
E decimated pulse at which‘aperture 25 is started
z’ overage used to tweak focus vectors+ ‘]/4)
IL 25* incr_subpatch_fiig ht_dist
incr_video_flig ht_dist —
~1 &\—
+=~ = decimated pulsesL-===-
-+=rawpulses at final prFspacin9
aperture25
-— 2* incr_subpatch_flight_dist
— 1 * incr_subpatch_flight_dist
y ~ position at which“Begin SAW pressed
Figure 2-15 Sea Vue SAR Overlapped Aperture Processing
2-21
3 SBMC ALGORITHM
In this section the SBMC algorithm as developed will be described. Thefollowing parts of the algorithm will be presented: Doppler Tracker, Doppler Correction,Range Tracker, Range Correction, Autofocus.
3.1 Doppler Tracker
The Doppler tracker was developed late in the program to assist the range tracker.The reason for this is that the range tracker works on DBS maps from successivesubapertues and it is necessary to keep these DBS filters stationary on the ground for thesubaperture pairs.
A key part of the Doppler tracker is the initialization. Once the tracker locks up itwill then track changes in Doppler from one subaperture to another. Initialization is easyif the Doppler error is less than a PRF and the clutter spread s also less than the PRF.Then the Doppler tracker will accurately measure the correct LOS velocity.
After initialization, the Doppler tracker works by measuring the centroid of theclutter spectrum on each subaperture. The initial Doppler estimate for each subaperturecomes form the previous subaperture. Thus the Doppler tracker measures the change inDoppler form the previous value.
The centroid measurement is obtained by first forming an FFT in each range gate,with typical NFFT’s being 32, 64 or 128. Weighting is applied prior to the FFT to reduceDoppler sidelobes. The FFT output is amplitude detected and then summed in eachDoppler filter across all range gates. Thresholding is applied to reduce the effects ofsidelobe or aliased Doppler clutter.
Doppler Track Algorithm
1.2.
3.
4.5.6.
7.8.9.10.11.
Measure Frequency Shifl of first subaperture, FS 1Phase Shift second subaperture by FS 1 to zero DopplerMeasure AFS2 of second subaperture
Compute frequency shift for second subaperture, FS2 = FS 1 + AFS2Frequency shifl third subaperture data by FS2Measure AFS3 of third subaperture
Compute frequency shift for third subaperture, FS3 = FS2 + AFS3Continue until last subaperture frequency shift is formed, FSNSmooth all N values of FSGenerate continuous value of FS(p) where p is the pulse numberPhase shift entire aperture of P pulses by FS(p)
The Doppler clutter spectrum is illustrated in Figure 3-1 for the first subaperture,before and after phase correction to zero Doppler.
3-1
Spectrum of First Subaperlure before Phase Cor
’50 ~-50
-55
-60
-65
mu
-70
-75
-so
-85 I Io 20 40 60 80 100 120 140 -85
FFT Filter Number(
Spestrum of First Subaperlure afler Phase Cor
20 40 60 80 100 120FFT filter Number
Figure 3-1 Doppler Spectrum (left) and after phase shift to zero Doppler (right)DOPPLER TRACKER RESULTS (Raw)
‘“’~
-1 Io 20 40 60 60 100 120
SubapeWre Number
1
DOPPLER TRACKER RESULTS (Smoothed)
-1 Io 500 1000 1500 2000 2500 3000 3500 4000 f
Pulse Number
Figure 3-2 Measured LOS Velocity, Raw (left) and Smoothed (right)
Measured LOS Phase in Doppler Tracker1000
Ioh
~ -1000 -:‘5g
m -2000:Em~ .~ooo
-4000 -
-50000 500 1000 1500 2000 2500 3000 3500 4000 ~
Pulse Number
Measured LOS Phase Errori” Ooppler Tmcker
‘so~
20C
5(
1c
Pulse Numbe!
/“-”
Figure 3-3 Computed LOS Phase Shift (left) and error (right)
3-2
)
I
3.2 Frequency Shift Measure
The frequency shift is measured by determining the centroid of the Dopplerclutter spectrum.
Frequency Shift Measure
1. Compute clutter spectrum of subaperture data d(s,p)
D(s,m) = ffi(d(s,p) W@))
Were D is the frequency spectrum of d, m is the filter number from 1 to M where M is =DP the number of pulses in the subaperture, and W is a weighting or window function toreduce Doppler filter sidelobes. The fft is performed on each range gate independently,corner turn fashion. Thus we have transformed range-pulse into range-Doppler.
2. Amplitude detect D or find the magnitude
M(s,m) = abs(D(s.m)) = ID(s,m) 1
3. Sum all range gates in each Doppler filter
M(n’z) = ~M(s, m)s
4. Threshold the data by returning either M if M > Thresh or Oif M < thresh.
MT(m) = max(M(m), Thresh) - Thresh
Where the threshold is chosen to be 1/10(-20 dB) of the peak value of M
Thresh = 1/10 max(M(m))
5. Compute the centroid from
~p MT(P)
FS=P;~T(p)
3.3 Smoothing Filter
The smoothing filter computes the average value for each point by summing anumber of samples around the sample point and then dividing by the number of samplesselected for averaging. Special considerations are applied at the beginning and end of thesequence. A symmetrical 9 point smoothing filter is used. R2 is the name assigned the
3-3
variable in the smoothing filter, i.e. R2 = VLOS and N is the number of subapertures, i.e.N = P/DP.
Smoothing filter
R2 (1) = R2 (1);R2 (2) = (R2(l)+R2( 2)+ R2(3) )/3;
R2 (3) = (R2(1)+R2( 2)+ R2(3)+R2 (4)+R2(5) )/5;R2 (4) = (R2(1)+R2( 2)+ R2(3)+R2(4)+R2 (5)+R2(6)+R2(7) )/7;for e = 5:N-4
R2 (e) = (R2(e-4) +R2(e-3) +R2(e-2)+R2 (e-l) +R2(e)+R2( e+l)+R2(e+2) +R2(e+3) +R2(e+4) )/9;
endR2(N-3) = (R2(N-6) +R2(N-5)+R2 (N-4) +R2(N-3) +R2(N-2)+R2(N-1) +R2(N))/7;R2(N-2) = (R2(N-4)+R2 (N-3)+R2 (N-2) +R2(N-l)+R2(N))/5;R2(N-1) = (R2(N-2) +R2(N-1)+R2 (N)) /3;R2 (N) = R2 (N);
3.4 Doppler Correction
Thelast step inthe Doppler Tracking algotiti isthe Doppler comection. This issimply aphase shift operation.
DopplerCorrection Algorithm
1. Alinear phase shift $overthe subaperture is computed fromthe measured frequencyshift
VLOS = ~~ PRF2 DP
427#Los(P) = - ~ vLosp~P
or
where FS is the measured frequency shift, DP is the number of pulses per subaperture, Ais the RF wavelength, PRI = l/PRF and p is the pulse number.
2. The data is phase shifted by multiplying the raw data, d, by a mocomp vector, mcv,range gate by range gate
nzcv(p) = cos($Lo~ (p)) + i sin(~~o~ (p))
mocomp _ d(s, p) = ma(p) d(s, p)
where mocomp_d is the Doppler corrected data.
3.5 Range Tracker
The range tracker measures the change in range between successive subaperturepairs. Thermge chageis computed fiomfill rmgeresolution coarse Dopplerresolution DBS maps. The range change is computed independently on correspondingDoppler filters between the two adjacent subaperture DBS maps. These DBS maps are ofapproximately the same area on the ground. If the Doppler correction is applied correctlyand the azimuth compression ratio, ACR = L / CRR, is small, the Doppler filters willoverlay. The DBS maps are thresholded prior to cross correlation.
The two DBS maps are cross-correlated in the down range dimension. The crosscorrelation range shift as measured in each Doppler filter is then summed across all validDoppler filters after Doppler filters with low signal levels returned are eliminated first viaa second thresholding process. The delta range from each successive subaperture pair isadded to the previous one to generate a total range change profile across the full aperture.Thus for N subaperture pairs, N values of delta R and N values of R are formed. The Nvalues of R are then smoothed with a smoothing filter and these data points interpolatedto provide a continuous range change over all P pulses in the aperture.
Range Tracker Algorithm
1. Setup the subapertures allowing for sub aperture overlap
N = SOF P/ DP
Where N is the number of subapertures, SOF is the sub aperture overlap factor, i.e. 2 or 3,P is the total number of pulses in the full aperture and DP is the number of pulses persubaperture.
2. Setup to loop over subaperture pairs, P1 :P2 and P2:P3 where P2 - P1 = P3 - P2 =DP.
3. Compute the FFT of each subaperture pair forming two range-Doppler maps
Al (s,m) = fft(d(s, P1 :P2) W(y))A2(s,m) = fft(d(s, P2:P3) W(p))
4. Amplitude detect and threshold each subaperture range-Doppler map
Ml = abs(Al) = IAl [M2 = abs(A2) = IA2 [
Ml~ = max(Ml, thresh) – threshM2T = max(M2, thresh) – thresh
where the threshold is selected to be 1/16 or –24 dB below the peak signal value in eachrange-Doppler data matrix
threshl = 1/16 max(Ml)thresh2 = 1/16 max(M2)
5. Take out the mean value for each range-Doppler map. This will eliminate the trianglebuild-up resulting form the cross correlation process.
M1..}v(s,m) = MI T(S,m) – meanl (m)M2..W(s,m) = M2~(s,m) – mean2(m)
where the means are computed individually on each Doppler filter m, by summing overall range gatess in each Doppler filter and dividing by the number of range gates S.
rneanl(rn) = +; MIT(S>??Z)
mean2(rn) = ; yf2, (s>@
6. Cross correlate the two range-Doppler maps in the down range dimension,s,independently for each Doppler filter, m.
C(r,m) = xcorr(M1..W(s,m), M2..W(s,m))
where r is the down range variable, r = 1:(2S – 1).
7. Threshold the Cross correlated data to eliminate low level or noise like returns
CT= max(C, thresh) – thresh
where the threshold is selected to be l/t or–12 dB below the peak correlation output
thresh = 0.25 max(C)
8. Now locate the peak in the cross correlation output, only considering data near zerorange which occurs at r = S. Only the three center lags are considered here
r= S-l: S+l.
xv cT(r>~)RS(m) = ‘
;C~ (~, m)
where Doppler filters with zero data are eliminated, i.e. with ~C7 (r, m) = O.r
3-6
This data is then summed across the good k Doppler filters to obtain one value of deltarange shift for this subaperture pair
RS = mean(RS(k))
9. Sum the delta range, RS(b), from each subaperture, b, to form the cumulative rangechange from all subaperture pairs.
RS _ sum(b) = ~ RS(b)1
10. Continue this process for each sub aperture pairs, b, until all N – SOF have beenformed.
1. Fill in the last few data pairs, 1:SOF, using linear extrapolation
2. Smooth the data
3. Fill in the data using linear interpolation to go from N values of Range Change to Pvalues. Thus there is now a value of range change associated with each pulse.
3.6 Range Correction
Range correction can be applied using an interpolation algorithm to shift the datain range by the desired amount as determined by the range track algorithm. Historicallythis type of interpolation has been provided by a four point sync interpolator whichoperates separately on the I and Q data. An alternate is to use a “fast” interpolator whichis comprised of an FFT, complex multiply or phase shift, and an IFFT. The fastinterpolator is described here. It operates on each down range line one at a time
Range Correction Algorithm
1. Read in S down range samples of data for a single pulse, p, d(s,p)and compute the fft
D(k>p) = ffi(d(s,p))
2. Generate the required phase shift for each pulse
PS(p) = 2 n lag(p)/ S
where the lag or normalized range shift per range sample is given by
lag(p) = RS(p) / DRSS
3-7
where RS is the range shift as a function of pulse number determined from the rangetracker and DRSS is the down range sample spacing.
3. Phase shift the fft spectrum by the above phase shift
D_shift(k,p) = D(k, p) J’sfp)k
4. Inverse fft the result
D_shift(s,p) = ifft(D_shift(k,p))
5. Repeat for the next pulse until all pulses are corrected.
3.7 Range Track and Correction Data Results
An illustration of the range tracker results is included in Figures 3-4 thru 3-7.These plots were generated using raw SAR data recorded from a flight test of the SeaVueRadar developed by Raytheon of McKinney TX, DBS maps from two successivesubapertures are illustrated in Figure 3-4. The DBS images were generated using 32point FFTs in the cross range direction. The number of down range samples is S= 128.The cross correlation form these two images is illustrated in Figure 3-5. The figure onthe top is a 3-D rendering of the cross correlation output, C(r,m), as a function of downrange and cross range. The bottom figure shows a pot of the data where it has beencollapsed across Doppler filters into the down range domain, C(r,:). This plot afterthresholding is illustrated in Figure S-6, i.e. CT(r) = max(C, thresh) – thresh. Theresultant range slip as a function of Doppler filter is given in Figure 3-7 for those filtersthat contained sufficient amplitude.
A plot of the range tracker results as a fi.mction of pulse number is illustrated inFigure 3-8. This plot was generated using simulated many targets data. The predictedand measured values are shown for comparison. The platform cross track motion isshown as a large dash line, the LOS range motion is shown as a solid line and themeasured range motion is shown as a short dash line. The measured range changefollows the predicted value fairly closely.
3-8
CR FFT Image Ml
1
1
20
40
60
80
~00
120
Cross Range
Figure 3-4 CR Compressed Images from FirstTwo Sub-Apertures
3ml
200
1m
c1
-1oo300
. ...’,,. .
. . . .. .
. . ...’.. . . . .
. . . . .
,. ..’”.. . . . .
. . . . .. . . . . .
..”’i. . . . .
.,,. . . . .
XCORR. . .,, . . . . .:. .
,.,’ ,.. . .,.,
“40
100 “20
Range
250
200
150
00
50
0
50
-1oo
00
XCORR
Doppler
o 50 100 150 200 250 300
Range Samples Out of Correlator for all 32 Dopplers
Figure 3-5 Cross Correlation, 3-D (top), Collapsed Doppler (bottom)
3-1o
18C
16C
140
120
100
80
60
40
XCORR THRESHOLDED Thresh2 = “Thresh2”1 I 1 , 1
20
00 50 100 150 200 250 :
Figure 3-6 Cross Correlation after Thresholding, all Dopplers
15
10
5
0
-5
-lo
R slip(k) Thresh2 = 100
# , 1 , I I 1 I
‘w0 , , , , I a
2 4 6 8 10 12 14 16
10
Figure 3-7 Measured Range Slip per Doppler Filter (17 of 32 above Threshold)
3-11
RANGE TRACKER RESULTS Thold=l/16 Thresh2=0.25o
-1
-2
-3
~4
! -5
S42
-7
-8
-9
-100 500 1000 1500 2000 2500
Pulse Number
Figure 3-8 Example Range Tracker Results
3.8 Autofocus Algorithm
There are several autofocus algorithms in use today. The principal ones being the PhaseGradient Autofocus (PGA) developed by SNL, the Map Drift Algorithm (MDA)originally developed by Hughes Aircraft and the Contrast Optimization Algorithm (COA)perfected by the DRA in the UK. A simple map drift algorithm was developed fortemporary use on this program. The final objective being to replace this with a PGAsupplied by SNL. The map drift algorithm as used on this SBMC program will bediscussed here.
The map drift algorithm as used here was adapted from the range track algorithm.The final synthetic aperture is divided in half into two sequential subapertures of equalsize. Images are formed from these two half apertures and these images are then crosscorrelated in the cross range dimension, range gate by range gate. A cross range slip ismeasure for each range gate and the resultant values averaged to develop a final value.This final value range slip for the two half apertures is scaled to develop a QPE. Aquadratic phase fimction is then generated for the full aperture. The data is then correctedby this quadratic phase finction and a full aperture image formed. Multiple iterations canbe performed to converge the QPE. Up to four were tried on this effort and it was foundthat two was sufficient. The final result is a two iteration MDA. The max allowed lag
value was large for the first iteration and then reduced for the second iteration, withnominal values for the two lag limits being 20 and 5.
To assist in convergence and estimated focus can be applied prior to the start ofautofocus. Alternately, the Doppler tracker may take out most of the quadratic phaseerror. When a Doppler tracker is used, then the estimated focus is not applied separately.It is either Doppler tracker or estimated focus.
Autofocus Algorithm
1. Divide the data into two half apertures of P/2 pulses by S samples each.
2. Form Images of each half aperture using cross range fft’s, PI :P2 and P2:P3 where P2-P1 = P3– P2 = P/2.
3. Compute the FFT of each half-aperture forming two range-Doppler images
Al(s,m) = ffi(d(s, P1 :P2) W(p))A2(s,m) = fft(d(s, P2:P3) W@))
4. Amplitude detect and threshold each half-aperture range-Doppler images
Ml = abs(Al) = IAl IM2 = abs(A2) = I A2 I
MIT = max(Ml, thresh) – threshM2T = max(M2, thresh) – thresh
where the threshold is selected to be 1/16 or –24 dB below the peak signal value in eachrange-Doppler data matrix
threshl = 1/16 max(Ml)thresh2 = 1/16 max(M2)
5. Take out the mean value for each range-Doppler map. This will eliminate the trianglebuild-up resulting form the cross correlation process.
Ml ..W(s,m) = MIT(s,m) – meanl(s)M2..W(s,m) = M2T(s,m) – mean2(s)
where the means are computed individually on each range gates, by summing over allDoppler filters m in each range gate and dividing by the number of Doppler filters P/2.
meanl(s) = ~xkfl,(s,m)P12 m
3-13
nzean2(s) = ~ ~M2,(s,m)P12 n,
6. Cross correlate the two range-Doppler maps in the cross range dimension, m,independently for each range gate,s.
C(r,n) = xcorr(Ml ..W(s,n), M2,.W(s,n))
where n is the down range variable, n = 1:(P + 1).
7. Threshold the Cross correlated data to eliminate low level or noise like returns
CT= max(C, thresh) – thresh
where the threshold is selected to be 1%or–12 dB below the peak correlation output
thresh = 0.25 max(C)
8. Now locate the peak in the cross correlation output, only considering data near zerorange which occurs at n = P/2. Only the center lags are considered here
n= P/2- Ll:P/2+Ll
where L 1 is the lag limit for the first iteration.
~ n c, (s, n)Ds(n) = n
~ Cr (s>~)
where range gates with zero data are eliminated, i.e. with ~ CT(s, n) = O.n
9. This data is then summed across the good k range gates to obtain one value of deltaDoppler shift for this subaperture pair -
—
DS = mean(DS(k))
10. A quadratic phase correction is then formed for p = 1:P
qpc(p) = ~$~DS(p-1-P/2)2
11. A correction focus vector is formed
cfv = cos(qpc(p)) – i sin(qpc(p))
12. The data is then phase shifted with this function
3-14
d_focus(s,p) = d(s,p) cfv(p)
13. A second iteration is then formed using d_focus as the input data array with steps 1thru 12 above repeated exactly except that a second lag limit L2 is used.
14. Additional optional iterations can be used if desired.
15. The final image is formed by performing a cross range FFT on each range gate
D_focus(s,m) = flt(d_focus(s,p))
3.9 Autofocus Data Results
To illustrate the autofocus algorithm data from the SeaVue radar is used. Typicaldata horn the cross range correlation is illustrated in Figure 3-9. In the plot on the rightthe cross correlator amplitude as a finction of Doppler filter with a number of range gatescollapsed is shown. A restricted window about the cross correlation centroid is shown.A zero shift would be centered at 512. On the right is the cross range slip as a functionof range gate number for those range gates that passed the threshold criterion. Theserange slips are then averaged and that result scaled to compute a QPE.
Figure 3-10 illustrates the estimated QPE and the resultant incorrectly or partiallyfocused image prior to autofocus. Figure 3-11 shows the first iteration QPE and resultantcorrected image. Figure S-1 2 shows the second iteration QPE and resultant final focusedimage. The estimated QPE was 124 radians, the first iteration measured QPE error was68 radians and the second iteration measured QPE error was 8 radians.
CROSS CORRELATION OUTPUT MEASURED CROSS RANGE SLIP
120001
1Ocmo
woo .
CROSSRANGE DOWN RANGE
Figure 3-9 Illustration of Cross Correlation Data (left) and Cross Range Slip (right)
120I
100
80
60
40
20 .
00 200 400 600 800 1000 I
Figure 3-10 Estimated QPE (left) and Static Focused Image (right)
140
&lo .
M“
-80 .
40
-40
40 .
-700 200 400 600 awl 1ooo 1
Figure 3-11 First Iteration QPE (left) and Corrected Image (right)
-9 I0 200 400 600 800 1000
Figure 3-12 Second Iteration QPE (left) and Corrected Image (right)
3-16
4 RAW DATA DESCRIPTION
The SBMC algorithm was developed using both simulated or synthetic data andreal data, both collected in a broadside SLAR geometry. The synthetic data wasgenerated internally by TSC/LA. The data was generated to provide digital, pulsecompressed, I and Q, raw phase history data. This data was to be similar to the real dataprovided externally from Raytheon / McKinney TX from their commercial Sea Vueradar. Sea Vue also supplies digital, pulse compressed I and Q, raw phase history data.Both sets of DAT are nominally at 2m resolution.
The synthetic data was generated in two sets for use on this program. The firstwas a cluster of 4 point targets with nominal separation of 10 meters approximately linedup in the down range dimension. The second set of data was 100 randomly dispersedtargets over an area of approximately 128 m down range by 1.86 Km cross range.
The main purpose in using the simulated data was to generate controlled data withselected aircraft motion and target scene parameters. The simulated data could easilygenerate cross track motion with the accompanying motion thru range resolution cells.This was very important for the development and testing of the down range tracker whichis a primary and central part of the SBMC being developed here.
SeaVue provided strip map data with 1024 down range samples by a largecontinuous succession of along track pulses or PRIs. Emphasis was on data from onescene from one just one set of the data supplied.
Data has also been received from the APS-137 BV(5) AIP SAR developmentalradar at Raytheon/ McKinney TX. Data was also generated by SNL for use on thisprogram but has not been received or processed.
4.1 Simulated Data
Simulated data for a “line” of 4 point targets and Many Targets (100) wasgenerated and provided for processing. This data was comprised of 128 down rangesamples by 5000 along track pulses. The parameters for this data are listed in Table 4-1.A sinusoidal cross track motion of t 10 m at 30 Hz was added. Each pulse consisted of aheader file followed by a data file of 128 I,Q samples. The header file contained data onthe geometry and platform motion. This enabled MMS (as from an INS) type mocomp tobe available as well allowing simultaneous SBMC and MMS Mocomp to be performedfor comparison.
4-1
Table 4-1 Radar Parameters for Simulated Data
PARAMETER UNITS VALUE COMMENT
Data file 5,000 pulsesAz Beamwidth deg 2.3 e~
mr 40.1
PRF Hz 500PRI 2VA 1% 93.137 305.5 fps
VL Max ds 1.884 10 m at 0.03 HzData Collection Time sec 10 5000 * PRIData Collect Distance m 931
NPRI = NFFT 32CIT sec 0.064 p~ * Np~
L 5.96 VA* CITH k 4.181R 40+ 40.218
RF GHz 9.65
A m .03109
BW MHz 100Pw us 20
NFFTR 2048DRR m 1.8 1.2 * (c/2)/ BW
DRSS m 1.4648 (c/2) * PW / NFFTRSynthetic Bearnwidth deg 0.133 (3s , Ks = 0.89
mr 2.32
CRR m 93.2 @R=40.2KmCRSS m 105 A6Pm * R/ NFFTAFP m 1614 R 9R
A9PW deg 4.78 pRF/(2VA/k)mr 83.45
BSR 17.3 9R / esACR 0.0639 L/CRR
4-2
0102030405060708091011
The header record for each pulse is:
PRF (Hz)number of range bins per pulse in binary fileA/D sample rate (Hz)range of first range bin (m)deramp reference range (m)platform position along track (m) xplatform position cross track (m) Yplatform height above ground (m)platform velocity along track (m/s) Vxplatform velocity cross track (m/s) Vyplatform velocity vertical (m/s)
The coordinates used are x for along track by y for cross track. The complex phasehistory data is of the form in matrix notation d(s,p) where s stands for down range samplenumber from 1 to 128 and p stands for along track pulse number from 1 to 5000. Thecorresponding header information is h(s,p) wheres is the number 01 to 11 above. Thuseach pulse consists of 11 header numbers followed by 128 data samples.
The location of the four scatters is:
x (m) Y@l w
450. 40000. 1.460. 40010. 1.440. 40020. 1.470. 40030. 1.
For the Many Targets scene, one hundred 1 m2 targets were randomly distributedover an area of approximately 128 m downrange by 1.86 Km along track. The geometryfor the simulated targets data collection is illustrated in Figure 4-1. The cross trackdisplacement is plotted in Figure 4-2 and the cross track velocity is plotted in Figure 4-3.The raw data is plotted in Figure 4-4, showing the range migration of the four targets dueto the radar cross track displacement. Thus there is significant motion thru down rangeresolution cells. The unfocused DBS image is given in Figure 4-5 clearing showing thefour targets. Now what will happen when a longer synthetic aperture is attempted, is thatthere will be motion thru range resolution cells degrading the compressed image quality.This is what is illustrated next.
The parameters for different aperture sizes are summarized in Table 4-2, where Pstands for the number of pulses for each aperture. The smaller values of P are used in thesubapertures that are used in the Doppler and Range trackers. The nominal design pointis P = 2048 which provides the nominal 2 m resolution. One issue associated with thelonger apertures is the image rotation about a CRP for a Spot mapping. The amount ofrotation at the edges of the Many Targets data scene for a CRP at the scene center is
4-3
listed in the last column. This rotation effect will be apparent in some of the imagesillustrated. The down range motion as a function of aperture size is also listed, showingthat there is appreciable range walk for the design point of P = 2048.
One other point of interest associated with Table 4-2 is the synthetic aperturelength L and the cross range sample spacing CRSS. The CRSS is approximately thecross range resolution CRR and the ratio of L to the CRR is the azimuth compressionratio ACR. When the ACR is less than one, no focusing is required. However when theACR is greater than one, then focusing is required. Thus for P <128 no focusing isrequired, whereas for P >128 focusing is required.
The raw data for the Many Target is shown in Figure 4-6 and the correspondingDBS image is shown is Figure 4-7. These images are not to scale. The scene extentdown range is 128 m and for cross range it is 1.86 Km. The simulated data does not havean antenna pattern included and hence the whole scene is included. The image size isdetermined by the PRF. At a velocity of 93 n-ds at X-band, the PRF ambiguity region isapproximately 4.8 degrees or 3.3 Km at a range of 40 Km. Thus the PRF Doppler extentis quite a bit larger than the scene Doppler extent.
Since the aircraft is moving toward the scene, Zero Doppler is not directlybroadside to the along track direction but actually looking back slightly about 1.2 deg.This puts zero Doppler at x = –809 m at the target scene y of 40 Km, relative to the initialy = Oat t =0. As the aircraft proceeds along track, zero Doppler will actually move intothe scene. This is illustrated by the DBS image taken at p = 2000 or x = 1 Km, shown inFigure 4-8. Here the lower part of the scene is starting to fold about the PRF line at 500Hz. This data was run using Matlab. Some of the processing parameters listed during theprogram are included here:
>>Matlab file: Donprl .mDate, Time: 4 Feb 99, 4PMData File: ManyTargs.matStart Sample Number: 1Start Pulse Number: 2000Number of Samples: 128Number of Pulses: 128Down Range Sample Spacing (m): 0.9868Cross Range Resolution (m): 23.2102Cross Range Sample Spacing (m): 26.0789Synthetic Aperture Length (m): 23.6568
The geometry of the simulated data with cross track motion is illustrated in Figure4-9. The information in this figure is helpful in understanding the results to be presentedshortly.
4-4
/$
930 mData
Collectio]
Interval
Vx
4 TargetsCluster >
10
Many TargetsDataArea
...
128m
w40 Km
Figure 4-1 Simulated Data Geometry
CROSS TRACK DISPLACEMENT
—
—
—
1395
930
465
0
-465
,
, , I , , , ,
500 1000 1500 2000 2500 3000 3500 4000 4500 5(
Pulse Number
1860m
00
Figure 4-2 Cross Track Displacement
4-5
20
40
60
80
100
120
CROSS TRACK VELOCITY
, I I I ,
I
o 500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Pulse Number
Figure 4-3 Cross TrackVelocity
Raw Data Image
500 1000 1500 2000 2500 3000 3500 4000 4500 5000
Cross Range
Figure 4-4 Four Targets Raw Data
4-6
Unfocused Image
20
40
60
80
‘100
120
20 40 60 80 100 120
Cross Range
Figure 4-5 Unfocused DBS Image of Four Targets
Table 4-2 Processing and Motion Parameters
P CIT CRSS ARLOS ARROT(see) (:) (m) (m) (m)
16 0.032 3.0 214 0.06 0.07
32 0.064 6.0 105 0.11 0.13564 0.128 12 53 0.24 0.27128 0.26 24 27 0.48 0.54
256 0.51 48 13.3 0.96 1.1512 1.0 95 6.5 1.9 2.21024 2.0 186 3.26 3.8 4.3
2048 4.i 372 1.63 6.8 8.7
4-7
Unfocused Image
1
1
/$
930 mData
CollectionInteNal
G
20 40 60 80 100 120
Cross Range
Figure 4-8 Many Targets DBSImage atp=20000rx=l Km
A~vx=93 m/s
PRF =
3340 m
4.8 deg7.8mls .........”’’”’””’””500 Ha,,..........-”-”’””-’”’ ,330Hz
Figure 4-9 Geometry for Simulated Datawith Cross Track Motion
4-9
4.2 Sea Vue Data
Data was collected by Raytheon/ McKinney TX on their commercial Sea Vueradar. Data was specifically recorded with the mocomp turned off for use on thisprogram. The parameters of the Sea Vue radar, reflecting the subaperture processing, aresummarized in Table 4-3. Data was also collected by the SNL Twin Otter radar and theRaytheon /McKinneyAPS-137B V(5) AIP developmental SAR system but not used yeton this effort. Parameters for all three radar are compared in Table 4-4.
Table 4-3 Parameters for SeaVue Data Used - Subaperture Values
PARAMETER UNITS VALUE COMMENT
Data file 1hex first lK pulsesAz Beamwidth deg 2.3 e~
mr 40.1
PRI ms 3.255PRF Hz 307.2VA fps 358 0.01 @ 0.5 Hzv~ fps 0.65 0.1 @ 0.5 Hz
Data Time sec 3.33 1024*PRINPRI = NFFT 32
CIT sec 0.10416 PRI NPRIL ft 37.29 VA CITR Kft 120
2.. ft 0.1025
Synthetic Beamwidth deg 0.070 esmr 1.223
CRR ft 147 Ks = 0.89CRSS ft 165AFP ft 4817 R eR
Aep~ deg 2.52 pRF/(2V*/L)m 43.95
BSR 32.8 eR / esACR 0.254 L/CRRVL fps 0.65
VL * Data time ft 2.17
Note: (1)(2)(3)(4)(5)(6)(6)
Synthetic beam crossover <-3 dB due to unweighting synthetic aperture
Should have aliasing with low PRF of 307 Hz. Ae~R~/ eR = 1.10AFP = Antenna Foot PrintACR = Azimuth Compression RatioCRR = Cross Range ResolutionCRSS = Cross Range Sample SpacingBSR = Beam Sharpening Ratio
4-1o
Table 4-4 Radar and Processing Parameters Comparison
PARAMETER UNITS SANDIA RAYTHEON RAYTHEONTWIN OTTER SEA VUE AIP SAR
MODES STRIP & STRIP & STRIP &SPOT SPOT S POT
FREQUENCY GHz 15,9.75,9.6,34.7 9.6 9.75
RESOL m 1, 1/3 1.8 R3 no deramp (3m)
RANGE, R Km 4-15 10-90 <93 (50 nm)
VELOCITY, V Kts 100-200 150-300 200-350
AZIMUTH BROADSIDE, BROADSIDE, BROADSIDE,~45”to*1350 *30” +30”
SWATH Km 1.5 1.56 2.6 @ 10 ft resol(1024 pixels)
NRG 1,800 1,024 = 1,600
MAX CIT see 1, 3 10 Classified
A/D SPEED MHz 66.7 100 Variable
A/D BITS 81&Q 81&Q 81&Q
PULSE COMP. STRETCH ANALOG DIGITAL - Derampand FFT
PREFILTER YES, NO YES NO
AZ ALGORITHM OSA OVERLAPPED OSAFFT BATCH
MOTION SENSOR IMU / GPS LN-1OOG IMU / GPS
MOCOMP XMTR, RCV~ AF PRF, A/D>PF & XMTR, PRF, AF,PRF, A/D, PROC FFT A/D, Tx fc
PIXEL SPACING ratio 1.5, 1.2,2.0 1.2 1.84 strip, 1.5 spot
AZ BEAMWIDTH Deg 5,2.5, 8 2.3 2.2EL BEAMWIDTH Deg 15 5 5PEAK POWER Watts 100 15K 50 KPRF Hz IIK 500 500PULSEWIDTH usec 25 20 20
4-11
During the SBMC development, emphasis was on just one data scene. The dataconsisted of the first 1 K pulses from the file named 1hex. The number of range cellsused was just 512 of the 1024 collected. The raw data size 512 x 1024 was selected tomatch the down range and cross range resolution in the final image and minimizeprocessing time. An image of the raw data is given in Figure 4-10.
Raw Data Image
50
100
150
350
400
450
500
100 200 300 400 500 600 700 800 900 1000
Cross Range
Figure 4-10 Illustration of Raw Data from Sea Vue files
The data recorded for each radar pulse consists of a header file followed by 1024I,Q samples. There are 58 parameters recovered from the header file for possible usewith the SBMC program. The header file listing is given in Table 4-5. In this table e = 2and E = 10. This header file contains the nav data recorded from the LN-100 EGInavigation system. This nav data can be used to provide the necessary parameters forMMS mocomp for comparison with the SBMC.
4-12
Table 4-5 Sea Vue Data Collection Header File Format
NUMBER NAME DESCRIPTION
1 count incrementingintegerevervPRI, “u.
2 I hour3 I minute I I, 1
4 secrmi
5 day6 month Note: One must be added to this number7 year8 fNU mode_wdl (Refer to LN1OOGMessage 101 word9 vel Zmetag descri@ion—10 x_vel lsb = ;e-18 Feet/see11 y_vel lsb = 2e-18 Feetkec12 z_vel lsb=2e-18 Feet/see13 olatform az Isb=2e-15 Semicircles14 roll – Isb=2e-15 Semicircles15 pitch Isb=2e-15 Semicircles16 true_heading Isb=2e-15 Semicircles17 mag_heading lsb=2e-15 Semicircles18 x_accel Isb = 2e-5 Feet/see/see19 y_accel Isb = 2e-5 Feet/see/see20 z_accel Isb = 2e-5 Feet/see/see21 x_cnex lsb = 2e-3022 y_cnex lsb = 2e-3023 z_cnex lsb = 2e-3024 longitude lsb=2e-31 Semicircles25 inertial ah lsb = 4 Feet26 gc_stee~lng_err27 x_axis_res_tilt28 y_axis_res_tilt29 lNU_mode_wd230 roll_rate lsb = 2e-I 3 Semicircles/see31 pitch_rate Isb=2e-13 Semicircles/see32 yaw_rate Isb = 2e-13 Semicircles/see33 raw latitude Isb = 4,65661EA-1Osemicircle34 raw~longitude kb = 4.65661EA-10semicircle35 crl_range c30 floating point in ft36 resolution SIX FT=O,TWELVE FT=l ,
TW~NTYFOUR_FT=~, FORTYEIGHT_FT=337 sar mode STRIP=O,SPOT=l38 squint_angle c30 floating point in degrees39 scene elevation intege~ Isb = 1ft40 prf – c30floatingpoint in Hz41 ffi_size c30 floating point42 dec_factor integer43 filter_index integer44 cells to im c30 floating ~oint—-. . -.45 cellsto_multilook c30 floating point46 ip fi;al_aper_length c30 floating point47 in;lal Va c30 floating point in ft/sec48 R– c30 floating point in ft49 Es c30 floating point in radians50 Vn c30floatincooint in ttkec, e,
51 I Ve c30 floatirw ooint in tVsecI 1
~r––-–52 I Vd c30 floating point53 I VI I c30 floatin~ noint
I -.—I
. . . . . . . . . . . .
;6 antcmd ham< inte9er in 1—
57 encoder58 ant tilt
in tlkec I
1 r .= . . .... in ft/sec54 I Va c30 floating point in Wsec55 I PRI i c?(I flmiting point in sec
-------- I ....-=-. ... .2bit barnsr integer in 12bit barns
I c30 floating uoint in radians
4-13
DBS Image
50
100
150
350
400
450
500
20 40 60 80 100 120
Cross Range
Figure 4-11 DBS Image of Sea Vue Data
4.3 AIP SAR Data
Raytheon McKinney has recorded and supplied data from their APS-137 B(V)5AIP SAR development program. Data was specifically generated for this program underno-mocomp conditions. An image of the raw data from the I,Q phase history data filekOOOOl.ph is shown if Figure 4-12. This data represents 1024 of compressed down rangesamples by 1280 pulses. The raw data contained a large DC bias which was filtered out.The raw data image shown here is after that DC Line filter. A DBS image is illustrated inFigure 4-13. This DBS image is for the lK range gates at a beam sharpening ratio of 256to 1.
4-14
.&.Lm
Down Range.Om --lso ul .00 ~ (J00 0 eo go000000 00
No0
.000
Down Range
5 SBMC RESULTS
The simulated data with cross track motion was then processed with SBMC. TheSBMC used consisted of the following steps: Doppler Tracking, Doppler PhaseCorrection, Range Tracking, Range Correction and Autofocus. The range correction isvia a fast correlation algorithm. Autofocus consists of a two iteration map drift type. Forcomparison, three images are shown: No-mocomp, MMS mocomp and SBMC.For No-mocomp, an estimated static focus is applied. For MMS mocomp, the actualgeometry inputs were used, i.e. Vx and Vy, such as would be available from an INS.
5.1 Four Target Cluster
For most cases run, the principal parameters selected are: P = 2048 correspondingto a cross range sample spacing CRSS of 1.63 m and a cross range resolution CRR of1.45 m for uniform weighting for the final FFT, starting at P = 1, a subaperture DP = 32for the Doppler and range trackers. The down range sample spacing DRSS is approx 1 mand the resulting down range resolution DRR is approx 1.8 m.
The results from the four target cluster are shown in Figure 5-1, for P = 2048 andDP = 32. The results for P = 4096 are also shown in Figure 5-2. In this case the CRSS isreduced to approx 0.8 ~ and the CRR to 0.7 m. Notice that the SBMC continues to focusproperly. It is not known why the MMS-mocomp is defocused.
The Doppler and Range Trackers results are shown in Figure 5-3. Again, thesubaperture size is DP = 32 pulses. Thus for P = 2048 pulse there are 64 subaperturesacross the fill aperture. The tracker values are the solid lines. The short dashed lines arethe range to the cluster CRP and the large dashed line is the cross track range of the radar.
5.2 Many Targets
The results for the Many targets case are illustrated in Figure 5-4, for P = 2048,the design point. The corresponding range and Doppler Tracker Results are shown inFigure 5-5. The SMBC Many targets image for 4096 pulses is illustrated in Figure 5-6.The corresponding Doppler and range tracker results are shown n Figure 5-7. For thislater case, the number of pulses per subaperture is 64, the subaperture overlap factor is 1,the number of subapertures in the trackers is 64, the down range sample spacing is 0.9868m and the cross range sample spacing is 0.81496 m.
5.3 Sea Vue Radar Results
Results from using real radar data are shown in Figure 5-8. This data wasspecially generated and supplied by Raytheon (formerly TI) McKinney TX from theircommercial Sea Vue radar. The data was recorded without mocomp but with all the Navvariables recorded. This made it possible to generate the three images of no-mocomp,MMS-mocomp and SBMC. The no-mocomp was generated using an incorrect value forthe aircraft velocity to provide an estimated static focus. The SBMC involves Doppler
5-1
tracking, range tracking and autofocus. The SBMC is primarily autofocus as the downrange cross track motion was less than a range cell. The range tracker results aresummarized in Figure 5-9. This figure shows the estimated down range motion asdeveloped by integrating the Sea Vue supplied header value for VLos, the range errorfrom each subaperture pair and the final smoothed range error. It is this final smoothedrange error which is used in the range correction interpolation.
Emm&d NMIIccmnDhate
Exwmded SBMC ham
20
)(x
1X
cm,, Ran&Expanded W MWCMWb age..— —
20
40
1Oc
12C
20 40 60 80 100 120Cms Range
20
40
lMI
120
20 40 60 80 1C4 120CmSs Ranse
Figure 5-1 Four Target Cluster Results. Top center is no-mocomp, lower left is SBMCand lower right is MMS-mocomp
5-2
Expsnded SBMC Ima$?Cm.ssRange
ExpandedMMS MominPimage
CrossRsngs Cross Range
Figure 5-2 Four Target Cluster Results for P = 4096. Top center is no-mocomp, lowerleft is SBMC and lower right is MMS-mocomp
-1 I0 500 1000 1300 2000 2500 3000 3500 4000
0
-2
.4
.6
-8
-10
-12
Figure 5-3 Four Target Cluster Tracker Results. Doppler Tracker on the left and RangeTracker on the right. The solid line is the Tracker Value, the short dashed line is the
predicted CRP value and the large dashed line is the cross track motion
5-3
ExpandedNoinocomp Image
20 40
Figure 5-4
20Expanded S BMC image
40 60 80 100 12(J(SO<sRamze Expanded MMS Mocmnp Image.... ---
20
120
20 40 60 so 100 120Cross Range
lower left is SBMC and
Cross Range
Many Targets Results. Top center is no-mocomp,lower right is MMS-mocomp
121 I Io 500 1000 1500
-10 I2000 2500 0 500 1000 1500 2000 2500
Figure 5-5 Many Targets Tracker Results. Doppler Tracker on the left and RangeTracker on the right. The solid line is the Tracker Value, the short dashed line is the
predicted CRP value and the large dashed line is the cross track motion
5-4
Expanded SBMC Image
20 40 60 80 100 120Cress Range
Figure 5-6 Many Targets
DOPPLER TRACKER RESULTS (Smoothed)
-1 Io 500 1000 1500 2000 2500 3000 3500 4000 4500
Pulse Number
mage for P = 4096
,
RANGE TRACKER RESULTS Thold=l/la Thresh2=0.25
‘~
Pulse Number
Figure 5-7 Doppler tracker (left) and Range Tracker (right) for P = 4096
5-5
N3mccomp Image (Est[msledVLOS and Sialic Focus)
SBMCDopk Trk, Rng Trk& Autofocus
Cress RangeSSMC Innge @awe Track and Autofocus)
NO MOCOMPEstimated Focus
MMS MOCOMP
MMS MCCOIIIP Image
Cross Rawe 100 204 300 40U 500 @Xl 703 800 SW ICQOCress Rawe
Figure 5-8 Sea Vue Radar Images. Top center is no-mocomp, lower left is SBMC andlower right is MMS-mocomp
RANGE TRACKER RESULTS Thold=l/16 Thresh2=0.25
5
4 -
3 -
2 -
El -
w ,,.,,............................ -’~-.--’”.D ....................................... ., ..”’’’’”’’””’’”’”’........................ ........................:0 - ““’”””::.::’”’”:::::::::::~ “’
....... .... .... . ........................................ ....
IYcg -, -
n
-2 -
-3 -
-4 -
-50 200 400 600 800 1000 1200 1400
Pulse Number
Figure 5-9 Range Tracker for SBMC Sea Vue Image
5-6
5.4 Example Matlab Program Output Listing
When a Matlab program is run, various parameters and steps indications areselected and these are printed out. The Matlab program print out for the Sea Vue datajust shown is listed below:
>}Matlab file: SBMC_SV.mDate, Time: 7 April 1999, 9AMData File: newsv_8.matStart Sample Number: 1Start Pulse Number: 1Number of Samples: 512Number of Pulses: 1280Number of pulses per subaperture: 128Subaperture Overlap Factor: 1Number of Subapertures in Trackers: 10Down Range Sample Spacing (m): 1.5244Cross Range Sample Spacing (m): 1.4664Cross Range Resolution (m): 1.3051Range (Km): 34.1479PRF (Hz): 307.231Aperture Velocity, Va (m/s): 109.171Coherent Integration Time, CIT (s): 3.333Synthetic Aperture Length, L (m): 363.8668Data Collection Length, X (m): 454.8334Cross Range Image Size (m): 1501.5548Down Range Image Size (m): 780.4878DV1OSto CRP due to L (m): 1.1633Providing static focusDoppler TrackingUsing Hamming WeightingVLOS_l (m/S): 0.55377Delta VLOS_l (m/s): -0.036915VL_initial (m/s): 0.51685Vy(l): 0.22931LOS Doppler Phase Correction
5-7
Range TrackingNumber of Subapertures in Range Tracker: 10Range Tracker Scale Factor: 1Using Hamming WeightingRange InterpolatingBeginning AutofocusIteration #l Lag Limit (# of cells): 60Iteration #2 Lag Limit (# of cells): 10Cross Range Autofocus - First IterationFirst Iteration Autofocus QPE (rad): -26.8211Cross Range Autofocus - Second IterationSecond Iteration Autofocus QPE (rad) -5.5193Generating Autofocus ImageGenerating MMS Mocomp ImageMMS Range InterpolatingMMS Mocomp to a LineMMS Mocomp to a PointDynamic Focus QPE(p=l)(rad):-195.1554Dynamic Focus QPE (p=P) (rad): -194.4245Generating MMS Mocomp ImageEstimated LOS Velocity: 0.17321Generating No_mocomp ImagePlotting Results
5.4 AIP SAR Results
The AIP SAR raw data described in the last chapter was operated on by theSBMCalgorithm. This algorithm contained the following functions: DCline filter,static focus, down range tracker, autofocus. The results of this SBMC processing areillustrated in Figure 5-10. This figure shows three images, all at 1 K by 1 K pixels. Thetop image is an unfocused one where simply a cross range FFT is used. The middleimage is a static focused image where an estimated quadratic focusing function isapplied. This estimated focus is developed based on nominal parameters. The finalimage on the bottom is after the SBMC processing. The matlab program print out forthese images is as follows:
}}Program file: aip 4.mDate, Time: 13 Apfil 99, 2PMData File: aipdata5.matStart Sample Number: 1Start Pulse Number: 1Number of Samples: 1024Number of Pulses: 1024Number of pulses per subaperture: 32Subaperture Overlap Factor: 1Number of Subapertures in Trackers: 32Down Range Sample Spacing (m): 2Cross Range Sample Spacing (m): 6.9543Cross Range Resolution (m): 6.1893Range (Km): 152.7PRF (Hz): 300Aperture Velocity, Va (m/s): 100Coherent Integration Time, CIT (s): 3.4133Synthetic Aperture Length, L (m): 341.3333Data Collection Length, X (m): 341.3333Cross Range Image Size (m): 7121.1645Down Range Image Size (m): 2048DV1OSto CRP due to L (m): 0.22353Providing static focusStatic focus QPE (rad): -38.4741Range TrackingNumber of Subapertures in Range Tracker 32Range Tracker Scale Factor: 1Using Hamming WeightingRange InterpolatingBeginning AutofocusIteration #1 Lag Limit (# of cells): 60Iteration #2 Lag Limit (# of cells): 10Cross Range Autofocus - First IterationFirst Iteration Autofocus QPE (rad): -24.9356Cross Range Autofocus - Second IterationSecond Iteration Autofocus QPE (rad): -2.6978Generating Autofocus ImageUsing Hamming WeightingComputing Unfocused hnageComputing Static Focused ImagePlotting Results
5-8
UNFOCUSED
ESTIMATEDSTATIC FOCUS
DYNAMICSBMC(Range trackand Autofocus)
Unfocused CR FFT Image of kOOOO.ph data
100 200 300 400 500 600 700 600 900 1000Cross Range
Static Focused CR FFT Image of kOOOi3,ph data
Cross Range
SBMClmage (Range Track and Autofocus)
Cross Range
Figure 5-10 AIP SAR SBMC Images (kOOOl.ph)
5-9
It is interestingto see the convergence of the autofocus algorithm inthisprintout.The magnitude of thepeak quadraticphase forthe estimatedstaticfocus was 38.5radians. For the first iteration of the autofocus algorithm it was 24.9 radians and for thesecond iteration it was 2.7 radians. For comparison, the usual error budget for SARresolution preservation is n/2 or 1.6 radians of QPE.
5-1o
REFERENCES
1. “Real Time Motion Compensated SAR”, J Kirk, 1973 TSRSR, pp 701-721.
2. “Algorithms for Focused Linear Synthetic Aperture Radar Imaging”, C J Oliver et al,
SPIE Conf - Algorithms for SAR Imaging Vol 2230-04, Orlando 1994, pp 60-71.
3. “Phase Gradient Auto-focus - A Robust Tool for High Resolution SAR PhaseCorrection”, D Wahl et al, IEEE AES, Jul 94, pp 827-835.
4. “A Map Drift Autofocus Technique for Correcting Higher Order Phase Errors”, CMancill and J Swiger, 1981 TSRSR, pp 391-402.
5. “Single Pass Fine-Resolution SAR Autofocus, G Bendor and T Gedra, 1983NAECON.
6. “A SAR Image-Formation Algorithm that Compensates for the Spatially-VariantEffects of Antenna Motion”, B Burns and J Cordaro, SPIE 94 Vol 2230, pp 14-24.
7. Spotlight-Mode Synthetic Aperture Radar: A Signal Processing Approach, C Jakowatzet al, Kluwer Academic Publishers, Norwell Mass, 1996.
8. “Motion Compensation of Airborne Synthetic Aperture Radars Using Autofocus”, DBlackwell and S Quegan, GEC Journal of Research, Vol 7 No 3, 1990.
9. “An Ultra-Fine Resolution Ku/Ka-Band SAR with Real-Time Image Formation”, D FDubbert et al, 1994 TSRSR, pp 345-360. (SNL Twin Otter test bed radar)
10. “Application of Phase Gradient Autofocus to High Resolution Synthetic ApertureRadar Imaging”, P H Eichel et al, 1990 TSRSR, pp 397-403. (Extend 1-D PGAto 2-D. Further focus ASARS-2 beyond map drift).
11. “Synthetic Aperture Radar Motion Compensation Using Autofocus”, (Phase I) FinalReport, DOE SBIR 96-113, CN: DE-FG03-96ER 82294, TSC Inure: 197-0011,May 1997.
R-1
APPENDIX A SBMC Matlab Program
Six Matlab programs are included. The first is the main Matlab program asgenerated for the simulated data. It is called:
FULL SBMC MATLAB PROGRAM, SBMC.m
This main program calls five functions. Theses five functions are:
Doplr_trackRange_trackAutofocusMMS MocompNo_mocomp
The Matlab program for each of these five fi.mctions is also included in this appendix.The Matlab programs include words describing them and some of the individual steps.Also there are numerous statements for figures or plots that are included in theseprograms.
A-1
% FULL SBMC MATLAB PROGRAM - Including MMS-mocomp and No-mocomp% John Kirkdisp( [’Matlab file: SBMC.m’])disp( [’Date, Time: 7 April 1999, 7 PM’])
% This is a program to incorporate down range and cross range mocomp.% Specifically a Doppler tracker, range tracker and autofocus are used.% The Doppler and range track data are measured on a subaperture basis and% smoothed and filled over the full P.% A Tansform interpolator is used to insert the range correction.% A simple map drift autofocus with two iterations is used.% This program calls; Doppler track, Range_track, autofocus, MMS–mocomp% and No-mocomp. First, load ~aw data file:
%load fixed.mat;%disp( [’Data File: fixed.mat’])load ManyTargs.mat;iisp( [’Data File: ManyTargs.mat’])DRSS = 0.9868; % Down Range Sample Spacing in meters (JCK calculated)d = 0.03109; % wavelength in meters for RF = 9.65 GHz
% Set up the batch of raw data. Header data is h(s,p) and Raw I,Q data is d(s,p)% where s is fast time down range sample number and p is cross range or pulse or PP.I% or slow time number. First pick out a data winddow.
S1 = 1;5 = 128;32= S1 + s - 1;s = S1:S2;pl = 1;
P = 4096;P2 = PI + P - 1;~=Pl:P2;
DP = 64;SOF = 1;Y = SOF*(P/DP);
40 = d(s,p);30 =h(:,p);i=AO’ .’;?=HO ;5=1:s;?=l:P;
3 = h(05,1);PRF = h(Ol, l);PRI = l/PRF;Ja = h(09,1);Lambda = w;
.6
%
Start range sample numberNumber of range samples
Pulse Start NumberNumber of pulses (or PRIs)
Number of pulses (or PRIs)per subapertureSubaperture overlap factorNumber of subapertures in loop
Comples conjugate of raw I,Q data
Reduce data size to S x P
Initial Range in mInitial value for PRF in HzInitial value for PRI in secInitial value for aperture velocity in mpswavelength in m
kRSS = (R*lambda)/(2’Va*PRI*(P) ); % Cross Range Sample Spacing for LS = 0.89; % for unweighed FFT
1RR =
ispispispisp
(R*Ks’lambda)/(2*Va*PRI*(P) ); % for full aperture of P pulses
‘Start Sample Number: ‘,num2str(Sl)])‘Start Pulse Number: ‘,num2str(Pl)])‘Number of Samples: ‘,num2str(S)])‘Number of Pulses: ‘,num2str(P)])
iisp( [’Number of pulses per subaperture: ‘,num2str(DP) ])iisp( [’Subaperture Overlap Factor: ‘,num2str(SOF)] )iisp( [’Number of Subapertures in Trackers: ‘,num2str(N)])iisp( [’Down Range Sample Spacing (m): ‘,num2str(DRSS)])iisp( [’Cross Range Sample Spacing (m): ‘,num2str(CRSS)])ii.sp([’Cross Range Resolution (m): ‘,num2str(CRR)])
>____________________________________________________________________________________
Doppler Tracker - Measure LOS phase and adjust I,Q data
I
i = l)oppler_track (SOF, P, DP, S, PI, PRF, w, d, h, N);
;--------------------------------------------------------------------------------
T Range track the data
W_Sum = Range_track(d, SOF, S, P, DP, DRSS);
;________________________________________________________________________________
; Range correct the data via Interpolation using the new Transform Interpolatorlisp( [’Range Interpolating’])
= 1:s;= l:P;
.ag(p) = RS_Sum(p)/DRSS; % sample quantizati.on for sine interpolator output
) = fft(d, S, 1);
‘or p = l:P;
I
PS(p) = 2*pi*lag(p)*(l/S);for s = 1:S;D shift(s,p) = D(s, p) *exp(+i*PS(p) *s) ;—% D shift(:,p) = D(:, p)*(cos(PS(p)) - i*sin(PS(p) ));
shift = ifft(D shift, S, 1);
d int = d shift’.’; % Complex coniu~ate back—
,--------------------------------------------------------------------------------
Autofocus the data. Static focus the data prior to beginning AutofocusThe proceed with two iteration map drift autofocus.
lisp( [’Beginning Autofocus’])
L1 = 20; % Lag limit, Iteration #ldisp( [’Iteration #l Lag Limit (# of cells): ‘,nurn2str(Ll)l)
L2 = 4; % Lag Limit Itration #2lisp( [’Iteration #2 Lag Limit (# of cells): ‘,num2str(L2)])
.uto focus d = auto focus(d int, S, P, Va, PRI, R, lambda, Ll, L2, CRSS) ;— . — —
, SBMC = auto focus d;
-------
—
.----—----
—
-----------------------------------------------------------------
Compute MMS Mocomp Imagelisp( [’Generating MMS Mocomp Image’])
[ = AO;
, MMS = MMS mocom~(S. P, h, d, DRSS, lambda, R);
-------
—
,-------—.
. ..., 7 ,..
-----------------------------------------------------------------
Compute No Mocomp Image – with estamated linear MCL and static focus only
‘L = (h(lO, l) + h(lO,P))/2; % Static (Nominal or average) cross track velocilisp( [’Estimated LOS Velocity: ‘,num2str(VL)])
nomo = No_mocomp(AO, S, P, VL, Va, lambda, R, PRI);—
________________________________________________________________________________
Typical DBS Image for DP pulses
---
.——
.-
t
.-
---
Y
---
= 1:s;l== (P/2)+l:DP;
1A3 = fft (AO,DP, 2) ; .6
%for g = 1:S% A3 (g,:) = fftshift(A3 (g, :)); %%endA3 = abs(A3);Thold = (1/16 )*max(max(A3)); 06
A_DBS = max(A3, Thold)–Thold; .6
Raw I,Q data is d(s,p)
Shift left and
Pick thresholdT’hold image
%____________________________________________________
% Plot Resultsdisp( [’Plotting Results’])
p=l:P;
X = h(06, p); % Radar positiony = h(07, p);X = 450 - h(06,1); % Initial Range aY = 40000 - h(07,1);Z = 4181.14;R start = (XA2 + Y“2 + ZA2).”0.5;R–= ((450 - X). ‘2 + (40000 - y).~2 + ZA2).A0.5; %
DR CRP = R - R start;— % Predicted Range—
DR_CRL = -h(07, :); % Cross Track Di
figure(5)plot(p,DR_CRP(:), ‘k-’,p,DR_CRL, ‘b-- ’,p,RS_Sum( :), ‘r:’title( ’RANGE TRACKER RESULTS Thold=l/16 Thresh2=0xlabel( ’Pulse Number’) ;ylabel( ’Down Range (m) ‘);
figure(6)colormap(gray) ;image(A SBMC*2*64/max(max(A_SBMC) ));title(’~BMC Image (Range Track and Autofocus) ‘);xlabel(’Cross Range’) ;ylabel(’Down Range’);
P= (P/2):(P/2)+127;A8 = A SBMC(S,P);
figure(7)colormap(gray) ;image (A8*2’64/max(max(A8) ));title( ’Expanded SBMC Image’) ;xlabel( ’Cross Range’ );ylabel( ’Down Range’);
figure (8)Iplot(p, (20*log10(A8 (45:90, :)+0.000001) ));axis([l 128 -90 –60]);qrid;title( ’Cross Range PTR’);xlabel(’Cross Range’ );ylabel(’dB’) ;
right halves
value
.----—---
at each
.t start
Range at, change
splaceme
);.25’);
.--——-
pulse
eachto CR
~nt fr
----—--
from s
pulse.P at X
‘om CRL
------
tart
= 450
-----
figure (9)?lot(s, (20*log10(A8 (:,l:128 )+0.000001)));axis([l 128 -90 -60]);grid;title( ’Down Range P’I’ R’);xlabel (’Down Range’) ;
~ = l:P;
figure (10)Zolormap (gray) ;Lmage (A_MMS*2 *64/max (max (A_MMS ))):itle( ‘MMS Mocomp Image’) ;<label (’Cross Range’ );?label( ’Down Range’);
;
3 = (P/2)-196:(P/2)-69;111 = A MMS(S,P);J = 1:178;
Figure(n)
k
olormap(gray) ;“mage (All*2*64/max(max(All) ));itle( ’Expanded MMS Mocomp Image’label(’Cross Range’);
{label (’Down Range’);
> = l:P;
Figure (12)~olormap (gray);Lmage(A_nomo*2*64 /max(max(A_nomo):itle(’No-mocomp Image (Estimate<label (’Cross Range’) ;{label(’Down Range’);
) . (P/2)-640:(P/2)-513;L>p = (P/2)-127:(P/2);!10 = A_nomo(s,P);
1:128;
Eigure(13):olormap(gray) ;Lmage (A10*2*64/max(max(AIO) ));:itle( ’Expanded No–mocomp Image’ )klabel(’Cross Range’);{label(’Down Range’);
J = l:DP;
Rigure(14)-olormap(gray) ;
[
mage (A_DBS*2*64/max(max(A DBS))itle(’DBS Image at p = P/27);label( ’Cross Range’);{label( ‘Down Ranqe’ );
);
));:d VLOS
;
);
and Static E‘Ocus) ‘);
function [data_out] = doplr track (SOF, P, DP, S, PI, PRF, w, d, h, N)—
& Doppler Tracker John Kirk 22 March 1999iisp( [’Doppler Tracking’])30F = 1; % Until added to this function
6 This is a program to Doppler track the data and apply the LOS phase correction& for application prior to the range tracker. It makes an initial Doppler measurei and then predicts ahead to the next subaperture. The initial measurement uses two; iterations. Each subsequent measurement only measures a delta and then adds this to\ the predicted value to come up with a final value for that subaperture. When the loop~ is finished the data is smoothed with a 9 point filter and then filed out for each\ pulse using linear interpolation. A phase correction is then generated and applied\ to the whole aperture.
~____________________________________________________________________________________
i Initialize New Doppler Tracker. Measure VLOS for first subaperture in two steps.i Initialization is critical - to lock up the tracker and avoid PRF/2 and foldover\ problems.
> = l:DP;?g = hamming; % Weighting function~isp( [’Using Hamming Weighting’])
? = 1:s;?1 = 1;?2 = PI + DP –1;) = P1:P2;
il = d(:,Pl:P2);) =l:DP;
for g = 1:S;dl_W(g,p) = dl(g,p).*Wg(p)’;
>ndj = 1:s;
il = dl w;—
!1 = fft(dl(s,p), DP,2);11 = abs(Al);
% Raw I,Q data is d(s,p)
) = l:DP;
;uml = sum(Ml, l); % All range bins for each doppler filter:hold = (1/10)*max(max(Suml)); % Pick threshold value, -20 dB;uml = max(Suml, Thold)-Thold; % T’hold image;um2 = sum(p.*Suml) ;~um3 = sum(Suml) ;
$FS1 = Sum2/Sum3 -((DP+l)/2);‘S1 = Sum2/Sum3;;disp( [’Frequency Shift (m): ‘,num2str(FSl)])
11 = (w/2)*(FSl/Dp)*pRF;
jdisp([’VLOS_l (m/s): ‘,num2str(Vl)])
j_______________________________________________________________
: Phase shift the first subaperure data By VI for second iteration.; shift the data to near zero Doppler.
‘RI = l/PRF;.ambda = w;
~elta R = V1*PRI;ielta–LOS phase = 4*pi*(l/lambda)*delta R;,0S_p=ase7p) = -delta LOS phase’p; –——
This should
, Create mocomp to a line vector, mcl(p)
lC1(p) = COS(LOS phase(p)) + i* (sin(LOS_phase(p) ));—
:or s=l:S;for p = l:DP;
mocomp_d(s ,p) = mcl(p)*dl(s,p);end
:ndi=l:S;)=l:DP;
11 = mocomp_d;
----------_----_________________________—____
Secon<
~or g =dl_W
!nd= 1:s;
iteration
1:s;
g,p) = dl(g,p).*Wg(p)’;
[1 = dl W;—
,3 = fft(dl(s,p), DP,2); % Raw I,Q data is d(srp)
“or g = 1:sA3(g, :) = fftshift(A3 (g,:)); % Shift left and right halves
nd= 1:s;
[3 = abs(A3);:uml = sum(M3,1); % All range bins for each doppler filter‘hold = (1/10)*max(max(Suml)); % Pick threshold value, -20 dB:uml = max(Suml, Thold)-Thold; % T’hold data~um2 = sum(p.*Suml) ;~um3 = sum(Suml);
‘S1 = Sum2/Sum3 -((DP+l)/2); % measure (delta) frequency shift about PRF/2Ivl = (w/2)*(Fsl/DP)*PRF;disp( [’Delta VLOS_l (m/s): ‘,num2str(DVl)])
-----------------------------------------------------------
Now add VI and DV1 to form initial VLOS
~ = l:N-SOF+l;
‘L = VI + DV1; % LOS Velocity for first subaperture (SA).isp([’VL_initial (m/s) : ‘,num2str(VL)])fv = o;[cl = 0;
-------------------------------------------------------------------------------
Now loop over SA #2 to SA #last
or b = 2:N-SOF+lC =b - 1;
disp ([’Subaperture: ‘,num2str(b)l)
‘3 = c*(DP/SOF) + 1;‘4 = P3 + DP - 1;
_______________________________________________________________
Phase shift the next subaperure data By VL(b-1) . First generate phase historyfor second subaperture from first SA measured LOS Velocity
=P1:P2;
;=1:s;
ielta R = VL*PRI;lelta–LOS phase = 4*pi*(l/lambda)*delta_R;,0S_pFase7p) = -delta LOS phase’p;—.
Create mocomp to a line vector, mcl(p)
lC1 (p) = cos(LOS_phase(p)) + i* (sin(LOS_phase (p)) );
Select next subapertures data
[1 = d(:,P3:P4);)=l:DP;
Phase shift second SA data to zero doppler
‘or s=l:S;for p = l:DP;
mocomp_d(sr p) = mcl(p)*dl(s,p);end
!nd
, = l:DP;
= 1:s;
12 = mocomp d;—
FFT Shift to PRF/2 and compute DV about DP/2
“or g = 1:s;d2(g,p) = d2(g,p). *Wg(p)’;
nd= 1:s;
,1 = fft(d2(s, p),DP,2); % Raw I,Q data is d(s,p)
or g = 1:sAl(g,:) = fftshift(Al (g,:)); % Shift left and right halves
nd= 1:s;
11 = abs(Al);uml = sum(Ml,l); % All range bins for each doppler filter‘hold = (1/10)*max(max(Suml)); % Pick threshold value, -20 dBuml = max(Suml, Thold)-Thold; % T’hold imageum2 = sum(p.*Suml) ;um3 = sum(Suml) ;
IFS = Sum2/Sum3 - (DP+l)/2;
v = (w/2)*(DFs/DP)*PRF;
‘L = VL + DV; % Update old VL with DV to new valuenew value‘Los(b) = VL;
nd
__________________________________________________________________________
Generate VL data for ploting
Los(l) = VI;S = VLOS;
= l:N-SOF+l;
CRP = h(lO, (DP*b)) + (h(09,1)/h(04,1))*(450 - h(06, (Dp*b) ));—
figure (1)plot (b,VS(b), ’k-’ rb,h(lO, DP*b),’b--’,b,V CRP(b),’r: ’);title( ’DOPPLER TRACKER RESULTS (Raw)’);–xlabel (’Subaperture Number’) ;ylabel( ’Measured LOS Velocity (m/s)’);
%___________________________________________________________________ ______________
% Data smoothing and filling
b=l:N;
R2 = VS; % Borrowed this routine from RANGE TRACKER, hence use of R.
% for SOF must fill in last N-SOF+l
%R2 (N-2) = R2(N-3);%R2(N-1) = R2 (N-2);%R2(N) = R2(N-l);
% Generate smooth version of VLOS
elements
R2(1) = R2(1);R2(2) = (R2(l)+R2(2)+R2(3))/3;R2(3) = (R2(1)+R2(2) +R2(3)+R2(4 )+R2R2(4) = (R2(1)+R2(2) +R2(3)+R2(4 )+R2for e = 5:N-4
R2(e) = (R2(e-4) +R2(e-3)+R2(e-2 )-endR2(N-3) = (R2(N-6) +R2(N-5)+R2 (N-4 )+R2(N-3) +R2(N-2)+R2(N-1) +R2(N))/7;R2(N-2) = (R2(N-4) +R2(N-3)+R2 (N-2) +R2(N-l)+R2(N))/5;R2(N-1) = (R2(N-2)+R2(N-l)+R2(N))/3;R2(N) = R2(N);
5))/5;5)+R2(6)+R2(7))/7;
R2(e-l) +R2(e)+R2(e+l)+R2 (e+2)+R2(e+3)+R2(e+4))/9;
% Generate continuous version of RS Sum—
R1 = [R2,R2(N)];%Rl = R2;
for c = l:Nm(c) = (Rl(c+l) - Rl(c))/(DP/SOF);for k = ((c-l)*(DP/SOF))+l:c*(DP/SOF) ;
RS Sum2(k) = RI(c) + m(c)*(k–(c-l)*(DP/SOF) );% R~n(k) = R(b);
endend
VLOS = RS Sum2;—
o~ _____________________________________________________________________
% Plot Measured VLOS and compare to V_CRP and Vy. (Header file is h.)
p = l:P;
V CRP = h(09,1) *(((450 - h(06rp))/h(04,1)) + h(lO,p)/h(09,1));—
V CRP 1 = V_CRP(l);d~sp(~’V_CRP( 1) ’,num2str(V_CRP_l) ])
vy_l = h(lO, l);disp([’Vy(l): ‘,num2str(Vy_l)] )
figure (2)plot (p,VLOS(:),’k–’,p, h(lO, :), ’b-–’rp,V_CRP, ‘r:’);title( ’DOPPLER TRACKER RESULTS (Smoothed) ‘);xlabel( ’Pulse Number’ );ylabel( ’LOS Velocity (m/s)’);
.6_________________________________________________________________________________________
>0 Doppler Correction. Compute line of sight phase correction over full aperture P.iisp( [’LOS Doppler Phase Correction’])
= 1:s;= l:P;
?RI = l/PRF;lambda = w;
5elta_R2(p) = VLOS(p).*PRI;ielta_LOS_phase2 (p) = 4’pi*(l/lambda)’delta_R2 (p);iOS_phase2 (l) = 0.0001;for p=2:P;
I LOS_phase2(p) = LOS_phase2(p-l) - delta_LOS_phase2 (p);~nd>=l:P;
: Plot Phase Vector
figure (3)~lot(p, LOS_phase2) ;:itle(’Measured LOS Phase in Doppler Tracker’) ;<label(’Pulse Number’);{label (’LOS Phase (radians) ‘);
b Compute Delta V error and plot phase difference
N error = V CRP - VLOS;— —
ielta_R3(p) = DV_error(p) .*PRI;ielta LOS phase3(p) = 4*pi*(l/lambda)’delta R3(P);—3S_pEase7-(1) = 0:0001;
for p=2:P;LOS_phase3(p) = LOS_phase3 (p-l) – delta_LOS_phase3 (p);
:nd>=l:P;
k Plot Phase Error Vector
Figure (4)~lot(p, LOS_phase3) ;:itle( ’Measured LOS Phase Error in Doppler Tracker’) ;<label(’Pulse Number’) ;{label(’LOS Phase Error (radians) ‘);
i> Create mocomp vector, mcv(p) and phase shift data to zero Doppler
Rev(p) = COS(LOS phase2 (p)) + i* (sin (LOS_phase2(p) ));—
for s=l:S;for p = l:P;
mocomp_d2(s,p) = mcv(p)*d(s,p);end
Id=1:s;=l:P;
i = mocomp d2;—
iata out= d;—
_--_--—_--—— ------------------------------------------------------------------
Function [data_out] = Range_track (d, SOF, S, P, DP, DRSS)
k Down Range Track John Kirk 7 April 1999
iisp( [’Range Tracking’])
\ This is a function to track the data in range. The range track algorithm measuresk the range slip between two successive subaperture DBS map by cross correlating the~ images in down range DBS filter by DBS filter. Only filters above a threshold arej retained. The algorithm loops over successive pairs of subapertures. The measu~ed\ range error from each iteration is added to that from the prevous one. The algorithm? contains the ability to use overlapped subaperturesr apply weighting before the FFTs,; threshold the FFTs, smooth the data with a 9 point smoothing filter and fill in thek data points within the subapertures via linear interpolation.
; ---------------------------------------------------------------------------------------
~ Range track the data.
5 = 1:s;)= l:P;
J = SOF*(P/DP); % Number of subapertures in loopiisp( [’Number of Subapertures in Range Tracker: ‘,num2str(N)])
{TSFiisp
Jg =iisp
= 1.0;[’Range Tracker Scale Factor: ‘,num2str(RTSF)]
hamming; % Weighting funct.[’Using Hamming Weighting’])
on
:or b = l:N-SOF % Loop over subaperture pairsC= b - 1;
jdisp ([’subaperture: ‘,num2str(b)])
> = 1:s;‘1 = c*(DP/SOF) + 1;)2 = P1 + DP -1;) = P1:P2;
> Compress first subaperture batch of raw data in cross range dimension with an FFT.
11 = d(s,Pl:P2);= 1:s;
) = l:DP;
!or g = 1:s;d W(g,p) = dl(g,p).*Wg(p)’;—
)nd= 1:s;
il=dW;.
~1 = fft(dl(s,p), DP,2);
ifOr g = 1:SAl(g,:) = fftshift(Al (g,:));
;end= 1:s;
11 = abs (Al);‘hold = (1/16)*max(max(Ml));
fl = max(Ml, Thold)–Thold;
Set up the second batch raw data
= 1:s;‘3 = PI + (DP/SOF);
)4 = P3 + DP -1;
% Raw I,Q data is d(s,p)
% Shift left and right halves
% Pick threshold value to be 1/16 of peak% T’hold image
) = P3:P4;
, Compress the second batch of raw data in cross range dimension with an FFT.
12= d(s,P3:P4);= 1:s;
) = l:DP;
‘or g = 1:S;d2_W(g,p) = d2(g,p).*Wg(p)’;
:nd= 1:s;
[2 = d2_W;
L2 = fft(d2(s, p),DP,2); % Raw I,Q data is d(s,p)
for g = 1:SA2(g,:) = fftshift(A2 (g,:)); % Shift left and right halves
end= 1:s;
12 = abs(A2);‘hold = (1/16)*max(max(M2)); % Pick threshold value[2 = max(M2, Thold)-Thold; % T’hold image
Compute the range slip between the two images. Cross correlate the two maps inranger Doppler filter by Doppler filter. First take out the mean of the two images.
[l_mean = mean(Ml, l);[2 mean = mean(M2,1);—
or g = l:DPMl_new(:,g) = Ml(:,g) - Ml mean(g);M2_new(:,g) = M2(:,g) - M2~mean(g);
:nd
‘or g = l:DPc(:,g) = xcorr(Ml_new (:,g),M2_new (:,9));
nd
~ = l:DP;= l:2*s_l;
‘hresh2 = 0.25*max
‘2 = max(C,Thresh2
max(C)); % Pick threshold value of 1/4
-Thresh2; %Threshold the cross correlated data
Now locate peak of XCORR. Restrict to just a few lags about center.
‘=s-1:s+1; % 3 center lags
uml = sum(r*C2(rr:),l);um2 = sum(C2(r, :),l);
._slip = O;
.=1; % Eliminate columns (Doppler filters) below thresholdor m=l:DP
if(Sum2 (m) -= O) 90 -= means not equeal toS_l = Suml (m);S 2 = Sum2(m);R–slipl = RTSF*DRSS* ((S 1./S 2)-S); % Note scale factor of RTSF*DRSS%~R = ( m + 0.5 - (DP/2~)*w/7; % add correction for beam dispersion, not DopplerdR = O; % no Doppler or beam dispersion correctionR_slip(k) = R_slipl + dR;k=k+l;
endnd
I = l:DP;
~ean_R_slip = mean(R_slip) ; % Range Slip in meters, scaled for range
S(b) = mean_R_slip;
,S Sl~m(b) = sum(RS( :));—
lear Ml, clear M2, clear Ml new, clear M2 new, clear C, clear C2lear Suml, clear Sum2, clea~ S_l, clear S–2
nd
or a = l:SOF;RS(N-SOF+a)= RS(N-SOF+a-l) +(RS(N-SOF+a-l) –RS(N–SOF+a-2));RS_Sum(N-SOF+a) = RS Sum(N-SOF+a-1) + RS(N-SOF+a);—
nd
=l:N;.ange_Slip = RS(b);S_Suml = RS_Sum(b);
RS_Suml = rng_trka(d, S, P, DP, N,
Generate smooth version of RS Sum—
2 = RS Suml;—
2(1) = R2(1);2(2) = (R2(l)+R2(2)+R2(3))/3;2(3) = (R2(1)+R2(2) +R2(3)+R2(4 )+R22(4) = (R2(1)+R2(2) +R2(3)+R2(4 )+R2or e = 5:N-4
R2(e) = (R2(e-4)+R2 (e-’nd2(N-3) = (R2(N-6)+R2 (N-52(N-2) = (R2(N-4)+R2 (N-32(N-1) = (R2(N-2)+R2 (N-12(N) = R2(N);
DRSS, SOF);
using 9 point filter
5))/5;5)+R2(6)+R2(7))/7;
R2(e–l) +R2(e)+R2(e+l)+R2 (e+2)+R2(e+3) +R2(e+4)) /9;)+R2(e-2)-
+R2(N-4)+R2 (N–3)+R2 (N-2) +R2(N-1)+R2 (N))/7;+R2(N-2) +R2(N-1)+R2 (N))/5;+R2(N))/3;
Generate continuous version of RS Sum, from b samples to P samples,using 2 point linear interpolatio~ betweeen b samples.
1 = [0,R2];
or b = l:Nm(b) = (Rl(b+l) - Rl(bfor k = ((b-l)*(DP/SOF
RS_Sum2 (k) = Rl(b)end
nd
= l:N;
ata out = RS Sum2;— —
---__— ___________________
)/(Dp/SOF);)+l:b*(DP/SOF) ;m(b)*(k-(b-l)*(DP/SOF) );
.---------------.---------------------------e-----------------
~unction [data out] = autofocus (d int, S, P, Va, PRI, R, lambda, Ll, L2, CRSS) ;— —
i Auto focus John Kirk 22 March 1999—
j Auto focus the data via a Map Drift algorithm. Use two iterations.i Eliminate estimated static focus because of Doppler tracker.
;_________________________________________________________________________________
j First Iteration. Setup first half batch of data and compress first half batch; in cross range dimension with an FFT.~isp( [’Cross Range Autofocus – First Iteration’])
!ocus_d = d int;—
;=1:s;)1 = 1;1.2= p;
)4 = 1 + (P/2) - 1;) = 1:P4;
d = fft(focus d(s,p),P/2,2);;Or g = 1:s –
Al(g,:) = fftshift(Al (g,:));:nd~1 = abs(Al) ;‘hold = (1/16)’max(max(Al));
L1 = max(Al, Thold)-Thold;
% No estmated focus if using Doppler tracker
% Raw I,Q data is d(s,p)
% Shift left and right halves
% Pick threshold value% T’hold image
Set up the second batch data
)5 = P/2 + 1;‘6 = P5 + (p/2) -I;~ = p5:p6;
Compress the second batch of data in cross range dimension with an FFT.
,2 = fft(focus_d(s,p),P/2,2); % Raw I,Q data is d(s,p)“or g = 1:s
A2(g,:) = fftshift(A2 (g,:)); % Shift left and right halves,nd,2 = abs(A2);‘hold = (1/16)+max(max(A2)); % Pick threshold value,2 = max(A2, Thold)-Thold; % T’hold image
Compute the cross range slip between the two images. Cross correlate the two maps incross range, range line by range line. First take out the mean of the two images.
[l_mean = mean(AlJ2);[2_mean = mean(A2,2);
“or g = 1:SAl(g, :) =Al(g, :) - Ml_mean(g);A2(g, :) =A2(g, :) - M2_mean(g);
nd
“or g = 1:sC(g,:) = xcorr(Al (g,:),A2 (g, :));
nd
[ = l:P-l;
= 1:s;
‘hresh2 = 0.25*max(max(C));
= max(C, Thresh2)–Thresh2;
Now locate peak of XCORR. Restrict to just a few lzgs about center.
m = (P/2) -Ll: (P/2)+Ll; % 2*LI center lags
for fg=l:SSuml(g, :) = sum(m.*C(g,m) ,2) ;
end
Sum2 = sum(C(:,m) ,2);
UR_slip = O;k=l; % Eliminate columns below thresholdfor r=l:S
if(Sum2(r) -= O) % -= means not equeal toS_l = SumI(r);S_2 = Sum2 (r);CR_slip(k) = CRSS*((S_l./S_2)-(P/2)); % Note scale factor of CRSS%dCR = O; % no correction%CR_slip = CR slipl + dCR;.k=k+l ;
endend
URS_l = CR_slip;
nean CR slip = mean(CR_slip) ; % Cross Range Slip in meters, scaled for range——
nCRS = mean CR slip;— —
% Now compute phase correction from CRS
? = l:P;pc (p) = (4*pi/lambda)’(Va/R)*(PRI/(P/2) )*mCRS*((p-1)-(P/2)).’2;~PE_l = pC(l);iisp( [’First Iteration Autofocus QPE (rad) : ‘,num2str(QPE_l)])2PE_lst(p) = pC(p);
% Now create correction focus vector
:fv(p) = cos(pc(p)) - i*sin(pc(p)); % at question is sign of phase correction
% Now focus the data to a point with the new correct focus vector
for s=l:S;for p = P1:P2;
correct_focus_d (s,p) = cfv(p)*focus_d (s,p) ;end
~nd
~___________________________________________________________________________________
% Second Iteration. Form and image two apertures,etc. Zero files5isp( [’Cross Range Autofocus – Second Iteration’])
Sum 1=0; Sum 2=0; S_l=O; S_2=O; CR_slip=O;. —
& Compress first batch of raw data in cross range dimension with an FFT.
S=l:s;P4 = PI + (P/2) - 1;3 = P1:P4;
%1 = fft (correct focus d(s,p),P/2,2); %
for g = 1:S – –Al(g, :) = fftshift(Al (g,:)); %
~nd%1 = abs (Al);~hold = (1/16)*max(max(Al)); 06
11 = max(Al, Thold)-Thold; %
* Set up the second batch raw data
Raw I,Q data is d(s,p)
Shift left and right halves
Pick threshold valueT’hold image
?5 = P/2 + 1;?6 = P5 + (P/2) -1;o = P5:P6;
& Compress the second batch
= fft(correct focus d(s,pforg=l:S––
A2(g, :) = fftshift(A2(g, :?nd42 = abs(A2);rhold = (1/16)*max(max(A2));42 = max(A2, Thold)-Thold;
of raw data in cross range dimension with an FFT.
rP/2,2); % Raw I:Q data is d(s,p)
); % Shift left and right halves
% Pick threshold value% T’hold image
$ Compute the cross range slip between thek maps cross range line by cross range line
two images. Cross correlate the tw!. First take out the mean of the t
41_mean = mean(Al,2);12 mean = mean(A2,2);—
For g = 1:SAl(g,:) =Al (g,:) - Ml_mean(g);A2(g,:) = A2(g,:) - M2_mean(g);
?nd
For g = 1:SC(g,:) = xcorr(Al (g,:),A2 (g, :));
~nd
n = l:P–l;.= 1:s;
rhresh2 = 0.25*max(max(C));
b = max(C,Thresh2
\ Now locate peak
n = (P/2)-L2: (P/2
>—....—>–,,,
-Thresh2;
of XCORR. Restrict to just a few lags about center.
+L2 ; % center lags
For g=l:SSuml(g, :) = sum(m.*C(g,m) ,2) ;
?nd
;um2 = sum(C(:,m) ,2);
~=l; .6
~or r=l:S
I if(Sum2(r) -= O) .6
S_l = Suml(r);S_2 = Sum2(r);CR slip(k) = CRSS*((S_l./S_2)-(P/2));
I %d~R = O; %
%CR_slip = CR slipl + dCR;—k=k+l;
endsnd
;RS_2 = CR slip;
Tear.CR slip = mean(CR_slip) ; % Cross Range— —
‘oWo images.
Eliminate columns below threshold
-= means not equeal to
% Note scale factor of 1 CRSS! !!no correction
Slip in meters, scaled for range
ICRS = mean CR slip;— —
~ Now compute phase correction from CRS
b=l:P;
)C(p) = (4*pi/latida) *(Va/R)*(PRI/ (P/2) )*mCRS* ((p-l )-( P/2) )."2;)PE 2 = pC(l);lis~( [’Second Iteration Autofocus QPE (rad): ‘,num2str(QpE_2)l))PE_2nd(p) = pc(p);
; Now create correction focus vector
:fv(p) = COS (PC(P)) - i*sin(pc(p)); % at question is sign of phase correction
{ Now focus the data to a point with the new correct focus vector
~or s=l:S;for p = l:P;
correct_focus_d (s,p) = cfv(p)*correct_focus_d (s,p) ;end
!nd
Now image full aperture after second iteration autofocuslisp( [’Generating Autofocus Image’])
;=1:s;)=l:P;
,5 = fft(correct_focus_d (s,p) ,P,2); % Raw I,Q data is d(s,p)[or g = 1:s
A5(g, :) = fftshift(A5 (g,:)); % Shift left and right halvestnd,5 = abs(A5);‘hold = (1/16)*max(max(A5)); % Pick threshold valueL5 = max(A5, Thold)–Thold; % T’hold image
~ata out = A5;— % Select output array
~unction [data out] = MMS mocomp (S, P, h, d, DRSS, lambda, R) ;— —
John Kirk 22 March 1999 MMS mocomp. m—
~ Generate MMS based mocomp. First range correct the data via Transform Interpolatorwith MMS RLOS. Next phase mocomp to a line, then dynamic focus to a point. (Mocompl
= Mocomp to a line.) MMS inputs of VL and Va from header file will be used to provide; mocomp to a line and to a point respectively.
_______________________________________________________________________________________
[isp([’MMS Range Interpolating’])
=1:s;)=l:P;
‘L(p) = h(lO,p); % LOS velocity in mps}RL(p) = -(h(07rp) - h(07,1)); % LOS Range Change in m‘RF = h(Ol,p); % Insert nominal value for PRF in Hz‘RI = l./PRF; % value for PRI in sec
,= h(06, p); % Radar position at each pulse from start,= h(07, l?);
= 450 - h(06,1); % Initial Range at start for 4 tgts= 40000 - h(07,1);= 4181.14;
: start = (XA2 + Y*2 + ZA2) .“0.5;:== ((450-X). ‘2 + (40000 - y).A2 + Z“2).A0.5; % Range at each pulse._predicted = Rt – R_start; % Predicted Range change
IRL = R predicted;—
ag(p) = DRL(p)/DRSS; % sample shift for.interpolator
I = fft(d, S, 1);
“or p = l:P;for s = 1:S;PS(p) = 2*pi*lag(p)*(l/S);D_shift(s,p) = D(s, p) ’exp(+i*PS(p) *s) ;% D_shift(:,p) = D(:, p)*(cos(PS (p)) – i*Sin(PS(P) ));end
nd
:_shift = ifft(D shift, S, 1);—
int MMS = d shift;— — —
= 1:s;= l:P;
j ----------------------------------------------------------------------------------
> Mocomp to a Line. Compute line of sight to a Line phase correction~isp([’MMS Mocomp to a Line’])
ielta_R(p) = VL(p) .*PRI(p) ;ielta LOS phase(p) = 4*pi*(l/latida)*delta_R (p);,OS_pFasell) = 0.0001;>3 = 2;
for p=P3:P;LOS_phase(p) = LOS_phase(p-1) - delta_LOS_phase (p);
?nd)=l:P;
Create mocomp to a line vector, mcl(p)
~cl(p) = COS(LOS phase(p) ) - i*(sin(LOS phase(p)));—
!or s=l:S;
for p = l:P;mocomp_d(s ,p) = mcl(p)*d int_MMS(s,p);—
end?nd;=1:s;?=l:P;
&--------------------------------------------------------------------------->, FOCUS dynamic 3 June 98 John Kirk\ This ~rogrhm will focus the data in CR. It will be mocomp to a line data.L, Dynamic focus is implemented with dynamic MMS input variablesiisp([’MMS Mocomp to a Point’])
7a = h(09,p); % Insert nominal value for aperture velocity in mpsix(p) = Va(p) .*PRI (p); % compuye synthetic array sample spacing ih ft
< = dx(P) *P;<dynamic = -(x/2);?3 = 2;:or p = P3:P;
x dynamic(p) = x_dynamic(p-1) + dx(p);md —
)=l:P;<CM_dynamic(p) = sqrt(RA2 + x_dynamic(p).A2) - R;=ocus_phase_dynamic (p) = 4*pi*(l/lambda) .*RCM_dynamic(p);
)P_dynamic_l = focus_phase_dynamic (l);)P dynamic P = focus phase_dynamic(P);ii~p([’Dyn~mic FOCUS–QPE (p=l) (rad): ‘,num2striisp( [’Dynamic Focus QPE (p=P) (rad): ‘,num2str
; Create dynamic focus vector
[v_dynamic(p) = cos(focus_phase_dynamic (p)) – i’
QP_dynamic_l) ])QP_dynamic_P )])
sin (fof
i Now focus the data to a point with the dynamic focus
?or s=l:S;for p = l:P;
= fv dynamic (p)’mocomp_dfocus_dynamic_mcp (s,P) _end
)nd
.
us_phase_dynamic (p));
vector
, Now compress the raw data in cross range dimension with an FFT, for each range gateiisp( [’Generating MMS Mocomp Image’])
for s = 1:S;p = l:P;m = l:P;A_focus_dynamic_mcp (s,m) = fft(focus_dynamic_mcp (s,P),P,2); % Data out of FFTA_focus_dynamic_mcp (sJm) = fftshift (A_focus_dynamic_mcp (s,m) );A_focus_dynamic_mcp (s,m) = abs(A_focus_dynamic_mcp (s,m) ); % Magnitude of FFT dataThold = (1/16)*max(max(A focus_dynamic_mcp (s,m) )); % Pick threshold valueA_focus_dynamic_mcp (s,m)–= max(A focus_dynamic_mcp (s,m) ,Thold)–Thold; % T’hold image—
end
iata_out = A_focus_dynamic_mcp;
lunction[data_out] = No mocomp(AO, S, P, VL, Va, lambda, R, PRI)—
i NO Mocomp John Kirk 22 March 1999lisp( [’Generating No_mocomp Image’])
This is a function to Doppler or phase compensate the raw I,Q data prior to forming ano mocomp image. Modified from Doppler_track.m It requires the following inputs: dataarray A.0, number of down range or time samples S, number of PRIs or pulses P, an
stimateof the cross track or LOS velocity VL, and estimate of the along track or aperturevelocity Va, the RF wavelength lambda, the estimated range R, the PRI. Both a linearand a quadratic phase correction are made, and the no mocomp image is formed.
_________________________________________________________________________________________
Mocomp to a Line. Compute line of sight to a line phase correction
= 1:s;) = l:p;
lelta R = VL*PRI;lelta–LOS phase = 4*pi’(1/lambda)*delta_R;,OS_pfiase~p) = - delta_LOS_phase*p;
Create mocomp to a line vector, mcl(p)
[cl(p) = cos(LOS_phase(p)) - i* (sin(LOS_phase(p) ));
or s=l:S; ifor p = l:P;
mocomp_A9(s, p) = mcl(p)*AO(s,p);end 1
nd=1:s;,=l:P;
.9 = mocomp_A9;
----------------------------------------------------------------------------------------
Compute static QPE and static focus the data. Same for all range.
1=1;‘2 = PI + P- 1;= P1:P2;
x = Va*PRI; 0.0 compute synthetic array sample spacing
max = P;—= dx(l)*(p_max-l);(PI) = -(x/2);3 = PI + 1;or p = P3:P2;
x(p) = X(p-l) + dx;nd=Pl :P2;
CM(p) = sqrt(R”2 + x(p) .A2) - R;tatic_focus_phase (p) = 4*pi*(l/lambda) .*RCM(p);
Create focus vector
v(p) = cos(static_focus_phase (p)) – i*sin(static focus phase(p) );— —
Now focus the data to a point with the focus vector
or s=i:s;for p = l:P;
focus_A9(s,p) = fv(p)*A9(s,p);end
nd
9 = fOCUS A9;—
------------------ —-——— ——------
& Form no mocomp static focused
-----—
image
—-- ,--- --- ---- --- --- -- -——-—-
S = 1:s;3 = l:P;
——--- —————--- --
19 = fft(A9(s, p), P,2);for g = 1:S
A9(g,:) = fftshift(A9 (g,:));?nd19 = abs(A9);!?hold = (1/16)*max(max(A9));!,9= max(A9, Thold)-Thold;
~ata out = A9:—
% Raw I,Q data is d(s,p)
% Shift left and right halves
% Pick threshold value% T’hold image
% Select output array