Signal Processing for Airborne Bistatic Radar

182 Pages·2012·3.3 MB·English

Signal Processing for Airborne Bistatic Radar
Kian Pin Ong
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AthesissubmittedforthedegreeofDoctorofPhilosophy.
TheUniversityofEdinburgh.
-June2003-
Abstract
The major problem encountered by an airborne bistatic radar is the suppression of bistatic
clutter. Unlikeclutterechoesforasidelookingairbornemonostaticradar,bistaticclutterechoes
arerangedependent. Usingtrainingdatafromnearbyrangegateswillresultinwideningofthe
clutternotchofSTAP(space-timeadaptiveprocessing)processor.Thiswillcausetargetreturns
from slow relative velocity aircraft to be suppressed or even go undetected. Some means of
Dopplercompensationformitigatingtheclutterrangedependencymustbecarriedout.
This thesis investigates the nature of the clutter echoes with differentradar configurations. A
novelDopplercompensationmethodusingDopplerinterpolationintheangle-Dopplerdomain
and power correction for a JDL (joint domain localized) processor is proposed. Performing
DopplercompensationintheDopplerdomain,allowsseveraldifferentDopplercompensations
to be carried out at the same time, using separate Doppler bins compensation. When using
a JDL processor, a 2-D Fourier transformation is required to transform space-time domain
training data into angular-Doppler domain. Performing Doppler compensation in the space-
time domainrequires Fourier transformationsof the Doppler compensatedtraining data to be
carried out for every training range gate. The whole process is then repeated for every range
gate under test. On the other hand, Fourier transformations of the training data are required
onlyonceforallrangegatesundertest,whenusingDopplerinterpolation. Beforecarryingout
anyDopplercompensation,thepeakclutterDopplerfrequencydifferencebetweenthetraining
rangegateandtherangegateundertest,needstobedetermined.Anovelwayofcalculatingthe
Dopplerfrequencydifferencethatisrobusttoerrorinpre-knownparametersisalsoproposed.
Reducing the computational cost of the STAP processor has always been the desire of any
reduced dimension processors such as the JDL processor. Two methods of further reducing
the computationalcost of the JDL processor are proposed. A tuned DFT algorithmallow the
size of the clutter sample covariance matrix of the JDL processor to be reduced by a factor
proportionaltothenumberof arrayelements,withoutlossesinprocessorperformance. Using
alternate Doppler bins selection allows computational cost reduction, but with performance
lossoutsidetheclutternotchregion. Differentsystemsparametersarealsousedtoevaluatethe
performance of the Doppler interpolation process and the JDL processor. Both clutter range
and Dopplerambiguity exist in radar systemsoperating in mediumpulse repetitivefrequency
mode. When suppressingrange ambiguous clutterechoes, performingDoppler compensation
fortheclutterechoesarrivingfromthenearestambiguousrangealone,appeartobesufficient.
Clutter sample covariance matrix is estimated using training data from the range or time or
both dimension. Investigationsonthenumberof range andtimetrainingdata requiredfor the
estimation process in both space-time and angular-Doppler domain are carried out. Due to
error in the Doppler compensationprocess, a method of using the minimumamount of range
training data is proposed. The number of training data required for different clutter sample
covariancematrixsizesisalsoevaluated. ForDopplerinterpolationandpowercorrectionJDL
processor,thenumberofDopplerbinsusedcanbeincreased,toreducetheamountoftraining
datarequired,whilemaintainingcertaindesirableprocessorperformancecharacteristics.
Declaration of originality
Iherebydeclarethattheresearchrecordedinthisthesisandthethesisitselfwascomposedand
originatedentirelybymyselfintheSchoolofEngineeringandElectronicsattheUniversityof
Edinburgh,exceptFigure1.5andFigure4.17.
KianPinOng
June2003
iii
Acknowledgements
Iwouldliketoextendmysincerethankstothefollowingpeoplefortheirinvaluableassistance
duringthecourseofthisPhD:
* ProfessorBernardMulgrew,mysupervisor,forhiscontinuoussupport,guidanceandin-
valuableadvice. Alsoforreadingandcheckingthisthesisduringtimewhenhisattention
isgreatlydemandedbysomanyotherpeople.
* My2(cid:0)(cid:2)(cid:1) supervisorProfessorSteveMcLaughlinforhissupportandguidance,aswellas
forhisconstructivecommentsonthewritingforthisthesis.
* BAESystemsEdinburghforprovidingfundingandsupportforthiswork.
* MyparentsfortheirfinancialandemotionalsupportduringmyPhD,withoutthem,com-
pletionofthisworkwouldnotbepossible.
* My brother - Ben Ong, sisters: Hui Pin Ong and Mariette Ong, and brothers-in-law:
SamFooandJefferyTan foralwaysbetheretogivemesupportandadvice. Constantly
receiving photographs and stories about my nieces: Glenda Foo, Callista Foo and Ava
Tan,neverfailstowarmmyheart.
* MycolleaguesandacademicstaffsintheformerSignalsandSystemGroup,nowknown
asInstituteofDigitalCommunicationsfortheirassistanceinonewayoranotherduring
thelastthreeyears. SpecialthankstoDr. MartinLuna-Rivera,MichaelBennettandMoti
Tabuloforprovidingadvice,readingandcorrectingthisthesis.
* The staff of the Institute of Digital Communications, particularly Dr. John Thompson,
Dr. DaveLaurensonandDr. JimmyDripps,whohaveatsomestageoranotherprovided
valuableassistance.
* David Stewart, MichaelGordon, Chris Rudd and Bryan Tierney for their instantaneous
computersupportandtolerancetowardsmyhighcomputingusage.
* MyfriendsfromCanadianRendez-Vous2002,forkeepsendingtheirencouragementand
thoughtsfromaroundtheworld.
iv
Acknowledgements
* JamieChan,forherloveandsupportduringthefirst2(cid:0) yearsofthisdegree.
(cid:1)
* Victoria Di(cid:3)(cid:2)guez and others who have one time or another lived in Kitchener House,
makingitsuchaninterestingplacetolivein.
* Special thanks to J(cid:5)(cid:4) rgen Kruse, EADS, Bremen, Germany for the kind permission to
reproduceFigure1.5.
v
Contents
Declarationoforiginality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii
Acknowledgements . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iv
Contents . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vi
Listoffigures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ix
Listoftables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xii
Acronymsandabbreviations . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii
Nomenclature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
1 Introduction 1
1.1 RADAR . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Motivationofthiswork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 4
1.2.1 AntennaRCS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.2 LowProbabilityofIntercept . . . . . . . . . . . . . . . . . . . . . . . 5
1.2.3 Radarabsorbingmaterial(RAM) . . . . . . . . . . . . . . . . . . . . 6
1.2.4 Surfacefacetshaping . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.3 Aimsofthiswork . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
1.4 Assumptions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 9
1.5 ThesisorganisationandOriginalcontributionstoknowledge . . . . . . . . . . 10
2 Clutternature ofairbornebistaticradar 13
2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
2.2 Anairbornemonostaticradar . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
2.2.1 Sidelookingarrayconfiguration . . . . . . . . . . . . . . . . . . . . . 16
2.2.2 Forwardlookingarrayconfiguration . . . . . . . . . . . . . . . . . . . 20
2.3 Anairbornebistaticradar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22
2.3.1 TransmitterandReceiverAligned . . . . . . . . . . . . . . . . . . . . 23
2.3.2 TransmitterandReceiveronParallelFlightPaths . . . . . . . . . . . . 25
2.3.3 TransmitterandReceiveronOrthogonalFlightPaths . . . . . . . . . . 26
2.4 SpaceTimeAdaptiveProcessing(STAP). . . . . . . . . . . . . . . . . . . . . 32
2.4.1 EffectsonSTAPprocessorcausedbyclutterDopplerrangedependency 38
2.5 PerformanceMetric . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
2.5.1 ImprovementFactor . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.5.2 Improvementfactorloss(IFloss) . . . . . . . . . . . . . . . . . . . . 40
2.5.3 MeanIFloss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
2.5.4 Signal-to-interference+noisepowerratio . . . . . . . . . . . . . . . . 41
2.6 MitigatingclutterDopplerrangedependency . . . . . . . . . . . . . . . . . . 41
2.6.1 IncreasingtheDegrees-of-Freedom . . . . . . . . . . . . . . . . . . . 43
2.6.2 Variablerangedimensiontrainingdatasize . . . . . . . . . . . . . . . 43
2.6.3 MultiplePRF . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
2.6.4 Reduceddimensionprocessing . . . . . . . . . . . . . . . . . . . . . . 44
2.6.5 Derivative-basedupdating . . . . . . . . . . . . . . . . . . . . . . . . 46
2.6.6 Dopplerwarping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
vi
Contents
2.6.7 Two-dimensionalangle-Dopplercompensation(ADC) . . . . . . . . . 49
2.6.8 Scaling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
2.7 DiscussiononmitigatingclutterDopplerrangedependencyinairbornebistatic
radar . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52
2.8 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53
3 DopplerandPowercompensationforJDLprocessor 55
3.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.2 Jointdomainlocalizedprocessor . . . . . . . . . . . . . . . . . . . . . . . . . 55
3.3 ClutterDopplerfrequencydifferencebetweenrangegates. . . . . . . . . . . . 58
3.4 InterpolationofDopplerdomaindataandDopplerbinsshifting . . . . . . . . . 62
3.5 Powercorrection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
3.6 SimulationResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
3.6.1 Powercorrection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.7 Comparisonwithothercompensationmethods. . . . . . . . . . . . . . . . . . 68
3.7.1 Dopplerwarping . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
3.7.2 Two-dimensionalangle-Dopplercompensation(ADC) . . . . . . . . . 72
3.7.3 Processorperformanceatdifferentlookangles . . . . . . . . . . . . . 74
3.8 SeparateDopplerbinscompensation . . . . . . . . . . . . . . . . . . . . . . . 75
3.9 TunedDFT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
3.9.1 SimulationResults . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
3.10 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
4 Systemperformanceanalysis 87
4.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.2 Dopplerbins, (cid:0)(cid:2)(cid:1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.3 AlternateDopplerbinsselection . . . . . . . . . . . . . . . . . . . . . . . . . 89
4.4 Spatialbins, . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
(cid:3)(cid:5)(cid:4)
4.5 SizeofDFTprocessor, (cid:1) . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
(cid:6)
4.6 Errorsinestimatedparameters . . . . . . . . . . . . . . . . . . . . . . . . . . 93
4.7 Diagonalloading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
4.8 RadarAmbiguities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.8.1 Angleambiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.8.2 Rangeambiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
4.8.3 Dopplerambiguity . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.8.4 AmbiguityinMPRFairbornebistaticradar . . . . . . . . . . . . . . . 100
4.9 Samplesupportforcluttersamplecovariancematrixestimation . . . . . . . . . 102
4.9.1 DwellTime . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.9.2 SamplesrequirementforSTAPprocessor . . . . . . . . . . . . . . . . 105
4.9.3 SamplessupportforDopplerwarpingJDLprocessor(usingi.i.d.samples)110
4.9.4 Samples support for Angle-Doppler compensation (ADC) - JDL pro-
cessor(usingi.i.d. samples) . . . . . . . . . . . . . . . . . . . . . . . 112
4.9.5 SamplessupportforDopplerinterpolationprocessor(usingi.i.d.samples)113
4.9.6 SamplessupportforDopplerinterpolationprocessor(usingnon-independent
data). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 114
4.9.7 Discussiononsamplessupport . . . . . . . . . . . . . . . . . . . . . . 115
4.10 Computationalcost . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 117
vii
Contents
4.11 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 118
5 Conclusion 120
5.1 Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 120
5.2 Suggestiononfutureresearchoptions . . . . . . . . . . . . . . . . . . . . . . 123
A Minimumvarianceestimator(MVE) 126
B RelativeDopplerfrequency, ,intermofthelookdirectionofthearray, 129
(cid:0)(cid:2)(cid:1) (cid:3)(cid:5)(cid:4)(cid:7)(cid:6)(cid:9)(cid:8)
C ClutterModel 131
D Dopplerfrequencydifferencebetweenrangegates 133
E Errors in pre-known parameters for calculation of Doppler frequency difference
betweenrangegates 134
F Derivationof 138
(cid:10)(cid:12)(cid:11)(cid:14)(cid:13)(cid:16)(cid:15)(cid:18)(cid:17)
G Publications 140
References 150
viii
List of figures
1.1 DifferenttypesofRadarSystems. . . . . . . . . . . . . . . . . . . . . . . . . 2
1.2 Anairbornebistaticradarsystem. . . . . . . . . . . . . . . . . . . . . . . . . 4
1.3 Fourbasiccomponentsofbackscatterfromaplanararrayantenna. . . . . . . . 5
1.4 Antennastructuralreflection. . . . . . . . . . . . . . . . . . . . . . . . . . . . 6
1.5 K-planeRCSofF117-liketarget(courtesyofEADS,Bremen). . . . . . . . . . 8
2.1 Geometryofanairbornemonostaticradar. . . . . . . . . . . . . . . . . . . . . 14
2.2 Isodopsandisorangesforanairbornemonostaticradar. . . . . . . . . . . . . . 15
2.3 Geometryofalinearairbornearray. . . . . . . . . . . . . . . . . . . . . . . . 16
2.4 Clutterspectrumofasidelookingairbornemonostaticradar. . . . . . . . . . . 17
2.5 Rangedependencyofasidelookingairbornemonostaticradar. . . . . . . . . . 18
2.6 Clutterspectrumofaforwardlookingairbornemonostaticradar. . . . . . . . . 20
2.7 Rangedependencyofaforwardlookingairbornemonostaticradar. . . . . . . . 21
2.8 Geometryofanairbornebistaticradar. . . . . . . . . . . . . . . . . . . . . . . 22
2.9 Clutterisodopsandisorangespatternwithtransmitterandreceiveraligned. . . 24
2.10 Range dependency for a transmitter ahead of receiver with a forwardlooking
array. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.11 Rangedependencyfortransmitterbehindthereceiverwithforwardlookingarray. 26
2.12 Isodopsandisorangesfor transmitterandreceiveronparallelflightpathswith
forwardlookingarray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.13 Rangedependencyfortransmitterandreceiveronparallelflightpathswithfor-
wardlookingarray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27
2.14 Isodops and isoranges for transmitter and receiver on orthogonal flight paths
withforwardlookingarray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.15 Rangedependencyfortransmitterandreceiveronorthogonalflightpathswith
forwardlookingarray. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.16 Clutterpower spectrum for transmitterandreceiver onorthogonalflight paths
withforwardlookingarrayfromrangegate27. . . . . . . . . . . . . . . . . . 29
2.17 Clutterpower spectrum for transmitterandreceiver onorthogonalflight paths
withforwardlookingarrayfromrangegate25. . . . . . . . . . . . . . . . . . 30
2.18 Clutterpower spectrum for transmitterandreceiver onorthogonalflight paths
withforwardlookingarrayfromrangegate29. . . . . . . . . . . . . . . . . . 31
2.19 MVEpowerspectrumvarieswithrangegate. . . . . . . . . . . . . . . . . . . 31
2.20 Illustrationofspatialandspectralfilteringforasidelookingairbornemonostatic
radar. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
2.21 Illustrationofsnapshotscollectedintherangedomain. . . . . . . . . . . . . . 36
2.22 Illustrationofsnapshotscollectedinthetimedomain. . . . . . . . . . . . . . . 36
2.23 STAP processor performance without compensation, using training data from
neighbourrange gates 25& 29(a) Improvementfactorplot, and(b) Improve-
mentfactorlossplot. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
3.1 Anexampleoflocalisedprocessingregions. . . . . . . . . . . . . . . . . . . . 56
ix
Listoffigures
3.2 Formingofalocalisedprocessingregion. . . . . . . . . . . . . . . . . . . . . 58
3.3 ErrorinestimationofDopplerfrequencydifferencebetweenrangegates and
(cid:0)
,duetoerrorintransmittervelocity. . . . . . . . . . . . . . . . . . . . . . . . 61
(cid:1)
3.4 Illustrationoffrequencyshiftingatoneoftheangularbins. . . . . . . . . . . . 64
3.5 BlockdiagramofDopplerandpowercorrectionforJDLprocessor.. . . . . . . 67
3.6 JDLprocessorperformance(a)withimprovementfactor(b)Improvementfactor
loss. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68
3.7 Doppler interpolation processor performance with and without power correc-
tion, using (a) training data from range gate 29, (b) training data from range
gate25,and(c)trainingdatafromrangegates25&29. . . . . . . . . . . . . . 69
3.8 Dopplerinterpolationand JDLDopplerwarpingprocessors’performance, us-
ing trainingdatafrom(a)rangegate29, (b)rangegate25, and(c)rangegates
25&29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
3.9 Full dimension Doppler interpolation processor performance and STAP pro-
cessor performance with Doppler warping compensation, using training data
from(a)rangegate29,(b)rangegate25,and(c)rangegates25&29. . . . . . 72
3.10 Comparison between JDL processor performance with Doppler interpolation,
DopplerwarpingandADC,usingtrainingdatafrom(a)rangegate29,(b)range
gate25,and(c)rangegates25&29. . . . . . . . . . . . . . . . . . . . . . . . 73
3.11 JDLprocessorperformancewith =-33.48 ,using(a)Narrowbeam-4 (b)
(cid:2) (cid:1) (cid:3) (cid:3)
Widebeam-16 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
(cid:3)
3.12 IllustrationoftheseparateDopplerfrequencyshifting. . . . . . . . . . . . . . 78
3.13 JDLprocessorwithbeamwidth=16 anddifferentamountof . . . . . . 78
(cid:3) (cid:4) (cid:0)(cid:6)(cid:5)(cid:8)(cid:7)
3.14 JDLprocessorperformancewithseparatebinscompensation,using(a)Narrow
beam-4 (b)Widebeam-16 . . . . . . . . . . . . . . . . . . . . . . . . . . . 79
(cid:3) (cid:3)
3.15 OutputofDFTwithvariesangleofarrival. . . . . . . . . . . . . . . . . . . . 81
3.16 Performanceofangularbinreductionprocessorwith .. . . . . . . . . 84
(cid:2) (cid:1)(cid:10)(cid:9)(cid:12)(cid:11)(cid:13)(cid:11) (cid:3)
3.17 Performanceofangularbinreductionprocessorwith .. . . . . . . . . 85
(cid:2) (cid:1)(cid:10)(cid:9)(cid:15)(cid:14)(cid:16)(cid:11) (cid:3)
4.1 Dopplerinterpolationprocessorperformancevarieswith (cid:0) (cid:1) . . . . . . . . . . . 88
4.2 Dopplerinterpolationprocessorperformance(IFlossmean)varieswith (cid:0) (cid:1) . . . 89
4.3 DopplerinterpolationprocessorperformanceusingalternateDopplerbins. . . . 90
4.4 Dopplerinterpolationprocessorperformance(IFlossmean)varieswith ,at
(cid:3) (cid:4)
. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
(cid:2) (cid:1) (cid:9)(cid:17)(cid:14)(cid:16)(cid:11) (cid:3)(cid:19)(cid:18)
4.5 DopplercompensationwithdifferentDopplerdomainFFTsizes. . . . . . . . . 93
4.6 JDLprocessorperformance(IFlossmean)withvariousdifferenterrors. . . . . 94
4.7 IdealJDLprocessorperformancewithvariousLCNR(a)fullscale(b)zoomin. 95
4.8 Ideal JDL processor performance with various LCNR (a) uncompensated (b)
compensated. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
4.9 UnambiguousrangeversePRF. . . . . . . . . . . . . . . . . . . . . . . . . . . 98
4.10 Isodopspatternofairbornebistaticradar(a)forselectedrangegates(b)zoomed
version. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100
4.11 JDLprocessor performanceusingDopplerinterpolation,in situation with and
without range ambiguity, (a) Ideal processor, (b) Doppler Interpolation using
trainingdatafromrangegates25&29,(c)Dopplerwarpingusingtrainingdata
fromrangegates25&29. . . . . . . . . . . . . . . . . . . . . . . . . . . . . 102
4.12 Datasamplesfromoneofthetrainingrangegates.. . . . . . . . . . . . . . . . 107
x