progress in sar ship detection and wake analysis

PROGRESS IN SAR SHIP DETECTION AND WAKE ANALYSISJ.K.E. TunaleyLondon Research and Development Corporation,114 Margaret Anne Drive,Ottawa, Ontario K0A 1L01-613-839-7943

http://www.london-research-and-development.com/

www.london-research-and-development.com

OUTLINEK-distributionNew simple asymptotic approach for large threshold valuesParameter estimation difficulties Implications for ship detectionShip WakesStudy started at RMC, Kingston using RADARSAT-2 images, AIS, plus other information.Findings and implications for MDA See Web site for papers


K-DistributionShips are bright blobs in SAR imagesNeed statistics of clutter background for CFARK-D excellent description of radar clutterBasis is modulated complex Gaussian clutterPhysical / statistical basis incompleteModulating distribution assumed gammaModified Bessel functions of 2nd kind.Computational complexityApproximation for tail values needed


K-D APPROXIMATIONLow PFA: interested in tail of distributionRepresent pdf as an integralUse steepest descentsAccurate to better than 0.1% (PFA = 10-9)Not sensitive to statistics of modulationImplies that K-D has sound physical basisBasic code can be implemented in < 18 lines of C# or C++.


THRESHOLD COMPARISON


PARAMETER ESTIMATIONNeed to estimate mean and order parameterNumber of looks is givenCan estimate optimal performanceUses Fisher information (Cramer Rao)Parameter variance depends on number of independent samples, NNeed to consider biasNote: Parameters need not be integer


OPTIMUM MEAN INTENSITYCramer Rao Bound#Samples N = 256L = 1L = 4L = 10SpikyRayleigh


Chart1

0.26467696520.22316963840.2082291406

0.19211579170.15934435980.1479019946

0.15997337120.13134916890.1212993886

0.14198828920.11481983170.1055121439

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0.10750342780.08001193490.0718674513

0.08733059650.07654655450.0684653197

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0.06347642540.03360283310.0229107473

0.06312785960.03244774950.0213954124

0.03202172110.0208229141

Nu

Standard Deviation Mu

Basis Nu

LN256

1munucrossSDs

numeanE(logLike)Fisher mununumudeterminantinv i11inv i22inv i12raw muFisher muraw nuFisher nucalc mucalc nu

0.11.00320-0.002360.0557667920.512791940.011232731.143806386217.93379735180.0487554456-0.0098204820.2646623680.26467696520.0137996360.01380039710.28641098090.1293689612

0.21.00309-0.014980.105836124.238776930.000071860.44861569879.44857021890.2359171119-0.00016018160.19211579060.19211579170.03035706190.03035706210.20728904940.1984313483

0.31.00249-0.016100.15341841.809808020.037564860.2762467326.55141875060.5553672938-0.13598300230.15956634330.15997337120.0464583480.04657685580.17305466380.2622655203

0.41.00203-0.014940.198222091.116581540.070617580.21634428395.16113261610.9162344686-0.32641296880.14037959720.14198828920.05914728250.05982508580.15309310890.3253843881

0.51.00187-0.014020.239727720.788155150.090511680.18075027294.36046450921.3262924374-0.50075542650.12765002080.1305107830.0704002430.07197798160.13975424860.3893729936

0.61.00204-0.014090.277722560.578302060.099085190.15078965373.83515742551.8417879027-0.65710867810.11859720050.12239723730.08218690910.08482030410.1301041250.4549725266

0.71.00267-0.015640.312267460.428534240.099934190.12383045633.46065299882.5217339037-0.80702432160.11184502010.11626769020.09547446940.09924980130.12274756330.5225855941

0.81.00420-0.020050.343585990.318680260.096146010.10025001743.178854913.4272910764-0.95906227760.10662579790.11143339710.1107139730.1157059020.11692679330.5924525297

0.91.00913-0.034830.371976430.237926070.089911720.08041877272.95858867184.6254924985-1.11804392120.10247603330.10750342780.12813241210.13441848860.11219093350.6647265063

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81.00000-0.000000010.822044720.000126060.001649160.00010090721.24926629768146.5394561921-16.34332863250.0689338120.06985661375.56661731255.64113638820.069877124312.8598211496

161.0000000.897333550.000009990.000291920.00000887911.1251083451101060.807354685-32.8770398510.06597859520.066294452819.774124911519.86878906050.066291260743.4885042281

321.0000000.943810920.000000740.000045650.00000069631.0627051191355395.53526011-65.5574171410.06433355020.064429743772.654774214972.76340982670.0644235254158.4187488904

641.0000000.970324460.000000050.000006530.00000004851.031489686420017593.4594279-134.71255304650.06344852460.0634764254279.5084971875279.63140819820.06346905602.9469296713

1001.000000.000000.980531240.000000010.00000180.00000000981.0201924238100033054.234531-183.63463628360.0631174290.0631278596625625.10328594850.06312190591445.1611069358

4

0.10.22316963840.0763347378

0.20.15934435980.1167690027

0.30.13134916890.1539088356

0.40.11481983170.1904205871

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0.60.0954703270.26478293

0.70.08917403730.3032951198

0.80.08414320010.3429066928

0.90.08001193490.3837016969

11.00000-0.000370.711619480.504947630.10268610.34878613481.44772850662.0402745668-0.29440992560.07408940440.07520099390.08795425380.08927386250.07654655450.4257346591

21.00000-0.000001.222905080.078792550.0655790.09205520440.855927163413.2844751984-0.71238775050.05651759110.05782270730.22265755680.22779921260.05846339670.9185586535

41.00000-0.000001.882444570.009581640.02931580.01717749010.5578020984109.5878713024-1.70664048690.0455532030.04667884370.63849881050.65427641120.0468752.3082731641

81.00000-0.000002.549700910.000938540.008871980.00231428430.40554222961101.7233063448-3.8335740090.03914131370.03980137352.04011018492.07451359730.03983608996.6872079375

161.000000.000003.096924150.000082070.002004080.00025014820.328085473712380.3561212511-8.01156983310.03551523830.03579921626.89902630156.95419054230.035801372621.7735504684

321.000000.000003.479478550.000006550.000366720.00002265610.2891053503153577.994668412-16.18636855940.03350602710.033605323624.420770786424.4931427480.033602833177.1516364052

641.000000.000003.716383470.000000480.000057750.00000178050.26958280332087235.57073744-32.43418102120.03242050370.032450852590.210979560990.29542595390.0324477495288.6186930883

1001.000000.000003.811986520.000000090.000016620.00000034280.262541794811120064.2530553-48.48271810930.03201137580.0320242703208.3333333333208.41725213740.0320217211686.9948712509

10

0.10.20822914060.0626080316

0.20.14790199460.0955771939

0.30.12129938860.1257145203

0.40.10551214390.1552080715

0.50.09478594310.1848174583

0.60.08690272340.2148910929

0.70.08080233820.245612971

0.80.07590598630.2770887616

0.90.07186745130.3093824379

11.00000-0.000316530.84991640.579239880.06425250.48817708981.18653638631.7410001776-0.13161719660.0677941020.06808015690.08212034970.08246685360.06846531970.3425340063

21.00000-0.000005511.576462330.110429580.051554260.17143023130.64416631299.1959412198-0.30073027160.04977808880.05016248260.18807770090.18953006460.05038911090.7239804744

41.00000-0.000000952.742803590.01908960.034215780.05118830380.372928942353.5826230958-0.668429650.03773832870.03816744270.45235729990.45750095240.03827327721.758098146

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161.00000-0.000000026.031073150.000302210.005572670.0017915960.16868200523366.3132008303-3.11045018330.02544970310.02566932183.59522108343.62624612250.025674494915.044328439

321.0000007.505003580.00002820.001340450.00020984430.134385354835764.6300978351-6.38783151850.02281416430.022911630111.76943089311.81971176970.022910747351.0440985815

641.0000008.5595450.000002290.000251740.0000195380.1172075829438097.633414429-12.88464494730.0213626280.021397245641.301162528441.36809012420.0213954124185.2214890341

1001.000000.000009.021520090.000000430.000078070.00000387320.11102049562329241.0036946-20.1566746340.02080847040.020824836495.311606457995.38656965570.0208229141435.1460047554

11.00020-0.002750.402793640.252608950.09997370.09175453782.75309494.3899043008-1.08957771920.09847788550.103702830.12435282350.13095061540.10825317550.7395099729

Basis Nu

64

Nu

Fisher Information (Mu)

Basis Nu-1

Nu

Standard Deviation Nu

Sheet3

Nu

Fisher Information (Nu)

Nu


Nu

SD Nu (MOM)

Nu

Standard Deviation Mu

LInverse NuN=256

1munucrossSDs

numeanE(logLike)Fisher mununumumunumunudeterminantinv11inv22inv12raw muFisher muraw nuFisher nucalc mucalc nu

11.0002-0.002750.402793640.252608950.09997370.402793640.252608950.09997370.09175453782.75309494.38990430081.08957771920.09847788550.103702830.12435282350.13095061540.10825317550.7395099729

21-0.000000980.567187520.018601940.031986660.567187520.297631040.127946640.15244226881.95241806893.72067094380.83931209520.08298826480.08733059650.11456208430.12055650490.08838834760.408646776

41-0.000000080.711619480.001528070.007984250.711619480.391185920.1277480.26205596951.49275714192.71552478440.48748364810.07408940440.07636152560.09992827950.10299280890.07654655450.266084162

81-0.000000010.822044720.000126060.001649160.822044720.516341760.105546240.41331600871.24926629761.98890123440.25536450990.0689338120.06985661370.08697839550.08814275610.06987712430.2009347055

16100.897333550.000009990.000291920.897333550.654704640.074731520.58190363871.12510834511.54206554190.12842593690.06597859520.06629445280.07724267540.07761245730.06629126070.1698769696

32100.943810920.000000740.000045650.943810920.775946240.04674560.73016138351.0627051191.29260591050.06402091520.06433355020.06442974370.07095192790.07105801740.06442352540.1547058095

64100.970324460.000000050.000006530.970324460.83886080.026746880.81325175721.03148968641.19314154740.03288880690.06344852460.06347642540.06823937920.06826938680.063469050.1472038403

10010.000000.980531240.000000010.00000180.9805312410.0180.980207241.02019242381.00033054230.01836346360.0631174290.06312785960.06250.06251032860.06312190590.1445161107

4determinantinv11inv22inv12raw muFisher muraw nuFisher nucalc mucalc nu

11-0.000370.711619480.504947630.10268610.711619480.504947630.10268610.34878613481.44772850662.04027456680.29440992560.07408940440.07520099390.08795425380.08927386250.07654655450.4257346591

21-0.000001.222905080.078792550.0655791.222905081.26068080.2623161.47288327070.85592716340.83027969990.17809693760.05651759110.05782270730.05566438920.05694980310.05846339670.2296396634

41-0.000001.882444570.009581640.02931581.882444572.452899840.46905284.39743745540.55780209840.42807762230.10666503040.0455532030.04667884370.03990617570.04089227570.0468750.1442670728

81-0.000002.549700910.000938540.008871982.549700913.844259840.567806729.4793083410.40554222960.26897541660.05989959390.03914131370.03980137350.03187672160.0324142750.03983608990.104487624

1610.000003.096924150.000082070.002004083.096924155.378539520.5130444816.39371429280.32808547370.18890924260.03129519470.03551523830.03579921620.02694932150.02716480680.03580137260.0850529315

3210.000003.479478550.000006550.000366723.479478556.86817280.3755212823.75664370360.28910535030.14646338910.01580700050.03350602710.03360532360.0238484090.02391908470.03360283310.0753433949

6410.000003.716383470.000000480.000057753.716383478.053063680.23654429.87231967930.26958280330.12440893480.00791850120.03242050370.03245085250.02202416490.02204478170.03244774950.0704635481

10010.000003.811986520.000000090.000016623.8119865290.166234.280256240.26254179480.11120064250.00484827180.03201137580.03202427030.02083333330.02084172520.03202172110.0686994871


11-0.000316530.84991640.579239880.06425250.84991640.579239880.06425250.48817708981.18653638631.74100017760.13161719660.0677941020.06808015690.08212034970.08246685360.06846531970.3425340063

21-0.000005511.576462330.110429580.051554261.576462331.766873280.206217042.74288370020.64416631290.57474632620.07518256790.04977808880.05016248260.04701942520.04738251620.05038911090.1809951186

41-0.000000952.742803590.01908960.034215782.742803594.88693760.5474524813.10420577550.37292894230.20930712150.04177685310.03773832870.03816744270.02827233120.02859380950.03827327720.1098811341

81-0.000000134.322403250.002695510.016646414.3224032511.040808961.0653702446.58781478310.23698920010.09277969510.0228680020.03006196580.03042596030.01880960040.01903734970.03045873230.0759461801

161-0.000000026.031073150.000302210.005572676.0310731519.805634561.42660352117.41403321030.16868200520.0513658630.0121501960.02544970310.02566932180.01404383240.01416502390.02567449490.058766908

32107.505003580.00002820.001340457.5050035829.56984321.3726208220.03769121540.13438535480.03410780920.00623811670.02281416430.02291163010.01149358490.01154268730.02291074730.0498477525

64108.5595450.000002290.000251748.55954538.419824641.03112704327.79299492560.11720758290.02611265380.00314566530.0213626280.02139724560.01008329160.01009963140.02139541240.0452200901

10010.000009.021520090.000000430.000078079.02152009430.7807387.315871380.11102049560.023292410.00201566750.02080847040.02082483640.00953116060.0095386570.02082291410.0435146005

000

000

000

000

000

000

000

000

Nu

Standard Deviation 1/Nu

000

000

000

000

000

000

000

000

Nu

SD 1/Nu (MOM)

SDs USING MOM: N = 1000OptimumPracticalL = 1 Black; L = 4 Red; L = 10 Yellow


Chart1

0.06625635290.04516939860.0417252942

0.06099730280.02881457440.0239738676

0.05211069740.02069003680.0144674504

0.04459709890.016400470.0096322217

0.03926914240.01374442590.0071669982

0.0359528290.0121022060.0058401891

0.03454188110.01115387530.0051100542

0.03162800250.01054517150.0048262211

Nu


Basis Nu

LN1000

1munucrossSDs


11.0002-0.002750.402793640.252608950.09997370.09175453782.75309494.3899043008-1.08957771920.04982630680.05246994280.06291810490.06625635290.05477225580.3741657387

21-0.000000980.567187520.018601940.031986660.00952764181.952418068959.5307351006-3.35724838090.04198910970.04418617510.23185735670.2439892110.04472135950.8270429251

41-0.000000080.711619480.001528070.007984250.00102365611.4927571419695.1743448113-7.79973836940.03748660290.03863621540.80896247240.83377115850.03872983352.1540659229

81-0.000000010.822044720.000126060.001649160.00010090721.24926629768146.5394561921-16.34332863250.03487805660.03534496142.81651033122.85421433260.03535533916.5066120216

16100.897333550.000009990.000291920.00000887911.1251083451101060.807354685-32.8770398510.0333828220.033542634710.005003753110.05290044490.033541019722.0036360632

32100.943810920.000000740.000045650.00000069631.0627051191355395.53526011-65.5574171410.03255048780.032599158336.760731104736.81569685960.03259601280.1542512909

64100.970324460.000000050.000006530.00000004851.031489686420017593.4594279-134.71255304650.03210269630.0321168131141.4213562373141.48354483620.0321130814305.0696969546

10010.000000.980531240.000000010.00000180.00000000981.0201924238100033054.234531-183.63463628360.03193517370.0319404512316.2277660168316.28002503250.0319374388731.2001094092

4

11-0.000370.711619480.504947630.10268610.34878613481.44772850662.0402745668-0.29440992560.03748660290.03804902770.04450172350.04516939860.03872983350.2154065923

21-0.000001.222905080.078792550.0655790.09205520440.855927163413.2844751984-0.71238775050.02859589050.02925623290.11265680290.11525829770.02958039890.4647580015

41-0.000001.882444570.009581640.02931580.01717749010.5578020984109.5878713024-1.70664048690.02304830020.02361783430.32305768390.33104058860.02371708251.1679041057

81-0.000002.549700910.000938540.008871980.00231428430.40554222961101.7233063448-3.8335740090.01980411230.02013807911.03222317791.04963008070.02015564443.3834893232

1610.000003.096924150.000082070.002004080.00025014820.328085473712380.3561212511-8.01156983310.01796944710.01811312993.490661883.51857302340.018114220911.0166419566

3210.000003.479478550.000006550.000366720.00002265610.2891053503153577.994668412-16.18636855940.01695285780.017003098312.356041264312.39265890230.017001838139.0359833999

6410.000003.716383470.000000480.000057750.00000178050.26958280332087235.57073744-32.43418102120.01640362150.016418976945.643546458845.68627332950.0164174069146.0307912736

10010.000003.811986520.000000090.000016620.00000034280.262541794811120064.2530553-48.48271810930.01619661730.0162031415105.4092553389105.45171526840.0162018517347.5949654411

10

11-0.000316530.84991640.579239880.06425250.48817708981.18653638631.7410001776-0.13161719660.03430140390.03444613750.04154997550.04172529420.03464101620.1733100217

21-0.000005511.576462330.110429580.051554260.17143023130.64416631299.1959412198-0.30073027160.02518594210.02538043170.09516062590.09589547030.02549509760.3663083649

41-0.000000952.742803590.01908960.034215780.05118830380.372928942353.5826230958-0.668429650.01909425180.01931136820.22887670140.23147920660.01936491670.8895351186

81-0.000000134.322403250.002695510.016646410.01137397820.2369892001380.0256310463-1.46355212580.01521028530.01539445360.6090872750.61646218950.0154110352.4592681838

161-0.000000026.031073150.000302210.005572670.0017915960.16868200523366.3132008303-3.11045018330.01287664440.01298776371.81905397051.83475153650.01299038117.6118949976

32107.505003580.00002820.001340450.00020984430.134385354835764.6300978351-6.38783151850.01154315560.01159246975.95491334185.98035367670.011592023125.8264980204

64108.5595450.000002290.000251740.0000195380.1172075829438097.633414429-12.88464494730.01080872980.010826245120.896918976420.9307819590.010825317593.7154843129

10010.000009.021520090.000000430.000078070.00000387320.11102049562329241.0036946-20.1566746340.01052834580.010536626448.22428221748.26221092840.0105356538220.1683983599

Basis Nu

64

Nu


Basis Nu-1

Nu


Sheet3

Nu


Nu


Nu

SD Nu (MOM)

LInverse NuN=1000

1munucrossSDs


11.0002-0.002750.402793640.252608950.09997370.402793640.252608950.09997370.09175453782.75309494.38990430081.08957771920.04982630680.05246994280.06291810490.06625635290.05477225580.3741657387

21-0.000000980.567187520.018601940.031986660.567187520.297631040.127946640.15244226881.95241806893.72067094380.83931209520.04198910970.04418617510.05796433920.06099730280.04472135950.2067607313

41-0.000000080.711619480.001528070.007984250.711619480.391185920.1277480.26205596951.49275714192.71552478440.48748364810.03748660290.03863621540.05056015450.05211069740.03872983350.1346291202

81-0.000000010.822044720.000126060.001649160.822044720.516341760.105546240.41331600871.24926629761.98890123440.25536450990.03487805660.03534496140.04400797390.04459709890.03535533910.1016658128

16100.897333550.000009990.000291920.897333550.654704640.074731520.58190363871.12510834511.54206554190.12842593690.0333828220.03354263470.03908204590.03926914240.03354101970.0859517034

32100.943810920.000000740.000045650.943810920.775946240.04674560.73016138351.0627051191.29260591050.06402091520.03255048780.03259915830.03589915150.0359528290.0325960120.078275636

64100.970324460.000000050.000006530.970324460.83886080.026746880.81325175721.03148968641.19314154740.03288880690.03210269630.03211681310.03452669830.03454188110.03211308140.0744799065

10010.000000.980531240.000000010.00000180.9805312410.0180.980207241.02019242381.00033054230.01836346360.03193517370.03194045120.03162277660.03162800250.03193743880.0731200109


11-0.000370.711619480.504947630.10268610.711619480.504947630.10268610.34878613481.44772850662.04027456680.29440992560.03748660290.03804902770.04450172350.04516939860.03872983350.2154065923

21-0.000001.222905080.078792550.0655791.222905081.26068080.2623161.47288327070.85592716340.83027969990.17809693760.02859589050.02925623290.02816420070.02881457440.02958039890.1161895004

41-0.000001.882444570.009581640.02931581.882444572.452899840.46905284.39743745540.55780209840.42807762230.10666503040.02304830020.02361783430.02019110520.02069003680.02371708250.0729940066

81-0.000002.549700910.000938540.008871982.549700913.844259840.567806729.4793083410.40554222960.26897541660.05989959390.01980411230.02013807910.01612848720.016400470.02015564440.0528670207

1610.000003.096924150.000082070.002004083.096924155.378539520.5130444816.39371429280.32808547370.18890924260.03129519470.01796944710.01811312990.0136353980.01374442590.01811422090.0430337576

3210.000003.479478550.000006550.000366723.479478556.86817280.3755212823.75664370360.28910535030.14646338910.01580700050.01695285780.01700309830.01206644650.0121022060.01700183810.0381210775

6410.000003.716383470.000000480.000057753.716383478.053063680.23654429.87231967930.26958280330.12440893480.00791850120.01640362150.01641897690.0111434440.01115387530.01641740690.0356520487

10010.000003.811986520.000000090.000016623.8119865290.166234.280256240.26254179480.11120064250.00484827180.01619661730.01620314150.01054092550.01054517150.01620185170.0347594965


11-0.000316530.84991640.579239880.06425250.84991640.579239880.06425250.48817708981.18653638631.74100017760.13161719660.03430140390.03444613750.04154997550.04172529420.03464101620.1733100217

21-0.000005511.576462330.110429580.051554261.576462331.766873280.206217042.74288370020.64416631290.57474632620.07518256790.02518594210.02538043170.02379015650.02397386760.02549509760.0915770912

41-0.000000952.742803590.01908960.034215782.742803594.88693760.5474524813.10420577550.37292894230.20930712150.04177685310.01909425180.01931136820.01430479380.01446745040.01936491670.0555959449

81-0.000000134.322403250.002695510.016646414.3224032511.040808961.0653702446.58781478310.23698920010.09277969510.0228680020.01521028530.01539445360.00951698870.00963222170.0154110350.0384260654

161-0.000000026.031073150.000302210.005572676.0310731519.805634561.42660352117.41403321030.16868200520.0513658630.0121501960.01287664440.01298776370.00710567960.00716699820.01299038110.0297339648

32107.505003580.00002820.001340457.5050035829.56984321.3726208220.03769121540.13438535480.03410780920.00623811670.01154315560.01159246970.00581534510.00584018910.01159202310.0252211895

64108.5595450.000002290.000251748.55954538.419824641.03112704327.79299492560.11720758290.02611265380.00314566530.01080872980.01082624510.00510178690.00511005420.01082531750.0228797569

10010.000009.021520090.000000430.000078079.02152009430.7807387.315871380.11102049560.023292410.00201566750.01052834580.01053662640.00482242820.00482622110.01053565380.0220168398

Nu


1

2

4

8

16

32

64

100

Nu

SD 1/Nu (MOM)

Chart2

0.37416573870.21540659230.1733100217

0.20676073130.11618950040.0915770912

0.13462912020.07299400660.0555959449

0.10166581280.05286702070.0384260654

0.08595170340.04303375760.0297339648

0.0782756360.03812107750.0252211895

0.07447990650.03565204870.0228797569

0.07312001090.03475949650.0220168398

Nu

SD 1/Nu (MOM)

Basis Nu

LN1000

1munucrossSDs


11.0002-0.002750.402793640.252608950.09997370.09175453782.75309494.3899043008-1.08957771920.04982630680.05246994280.06291810490.06625635290.05477225580.3741657387

21-0.000000980.567187520.018601940.031986660.00952764181.952418068959.5307351006-3.35724838090.04198910970.04418617510.23185735670.2439892110.04472135950.8270429251

41-0.000000080.711619480.001528070.007984250.00102365611.4927571419695.1743448113-7.79973836940.03748660290.03863621540.80896247240.83377115850.03872983352.1540659229

81-0.000000010.822044720.000126060.001649160.00010090721.24926629768146.5394561921-16.34332863250.03487805660.03534496142.81651033122.85421433260.03535533916.5066120216

16100.897333550.000009990.000291920.00000887911.1251083451101060.807354685-32.8770398510.0333828220.033542634710.005003753110.05290044490.033541019722.0036360632

32100.943810920.000000740.000045650.00000069631.0627051191355395.53526011-65.5574171410.03255048780.032599158336.760731104736.81569685960.03259601280.1542512909

64100.970324460.000000050.000006530.00000004851.031489686420017593.4594279-134.71255304650.03210269630.0321168131141.4213562373141.48354483620.0321130814305.0696969546

10010.000000.980531240.000000010.00000180.00000000981.0201924238100033054.234531-183.63463628360.03193517370.0319404512316.2277660168316.28002503250.0319374388731.2001094092

4

11-0.000370.711619480.504947630.10268610.34878613481.44772850662.0402745668-0.29440992560.03748660290.03804902770.04450172350.04516939860.03872983350.2154065923

21-0.000001.222905080.078792550.0655790.09205520440.855927163413.2844751984-0.71238775050.02859589050.02925623290.11265680290.11525829770.02958039890.4647580015

41-0.000001.882444570.009581640.02931580.01717749010.5578020984109.5878713024-1.70664048690.02304830020.02361783430.32305768390.33104058860.02371708251.1679041057

81-0.000002.549700910.000938540.008871980.00231428430.40554222961101.7233063448-3.8335740090.01980411230.02013807911.03222317791.04963008070.02015564443.3834893232

1610.000003.096924150.000082070.002004080.00025014820.328085473712380.3561212511-8.01156983310.01796944710.01811312993.490661883.51857302340.018114220911.0166419566

3210.000003.479478550.000006550.000366720.00002265610.2891053503153577.994668412-16.18636855940.01695285780.017003098312.356041264312.39265890230.017001838139.0359833999

6410.000003.716383470.000000480.000057750.00000178050.26958280332087235.57073744-32.43418102120.01640362150.016418976945.643546458845.68627332950.0164174069146.0307912736

10010.000003.811986520.000000090.000016620.00000034280.262541794811120064.2530553-48.48271810930.01619661730.0162031415105.4092553389105.45171526840.0162018517347.5949654411

10

11-0.000316530.84991640.579239880.06425250.48817708981.18653638631.7410001776-0.13161719660.03430140390.03444613750.04154997550.04172529420.03464101620.1733100217

21-0.000005511.576462330.110429580.051554260.17143023130.64416631299.1959412198-0.30073027160.02518594210.02538043170.09516062590.09589547030.02549509760.3663083649

41-0.000000952.742803590.01908960.034215780.05118830380.372928942353.5826230958-0.668429650.01909425180.01931136820.22887670140.23147920660.01936491670.8895351186

81-0.000000134.322403250.002695510.016646410.01137397820.2369892001380.0256310463-1.46355212580.01521028530.01539445360.6090872750.61646218950.0154110352.4592681838

161-0.000000026.031073150.000302210.005572670.0017915960.16868200523366.3132008303-3.11045018330.01287664440.01298776371.81905397051.83475153650.01299038117.6118949976

32107.505003580.00002820.001340450.00020984430.134385354835764.6300978351-6.38783151850.01154315560.01159246975.95491334185.98035367670.011592023125.8264980204

64108.5595450.000002290.000251740.0000195380.1172075829438097.633414429-12.88464494730.01080872980.010826245120.896918976420.9307819590.010825317593.7154843129

10010.000009.021520090.000000430.000078070.00000387320.11102049562329241.0036946-20.1566746340.01052834580.010536626448.22428221748.26221092840.0105356538220.1683983599

Basis Nu

64

Nu


Basis Nu-1

Nu


Sheet3

Nu


Nu


Nu

SD Nu (MOM)

LInverse NuN=1000

1munucrossSDs


11.0002-0.002750.402793640.252608950.09997370.402793640.252608950.09997370.09175453782.75309494.38990430081.08957771920.04982630680.05246994280.06291810490.06625635290.05477225580.3741657387

21-0.000000980.567187520.018601940.031986660.567187520.297631040.127946640.15244226881.95241806893.72067094380.83931209520.04198910970.04418617510.05796433920.06099730280.04472135950.2067607313

41-0.000000080.711619480.001528070.007984250.711619480.391185920.1277480.26205596951.49275714192.71552478440.48748364810.03748660290.03863621540.05056015450.05211069740.03872983350.1346291202

81-0.000000010.822044720.000126060.001649160.822044720.516341760.105546240.41331600871.24926629761.98890123440.25536450990.03487805660.03534496140.04400797390.04459709890.03535533910.1016658128

16100.897333550.000009990.000291920.897333550.654704640.074731520.58190363871.12510834511.54206554190.12842593690.0333828220.03354263470.03908204590.03926914240.03354101970.0859517034

32100.943810920.000000740.000045650.943810920.775946240.04674560.73016138351.0627051191.29260591050.06402091520.03255048780.03259915830.03589915150.0359528290.0325960120.078275636

64100.970324460.000000050.000006530.970324460.83886080.026746880.81325175721.03148968641.19314154740.03288880690.03210269630.03211681310.03452669830.03454188110.03211308140.0744799065

10010.000000.980531240.000000010.00000180.9805312410.0180.980207241.02019242381.00033054230.01836346360.03193517370.03194045120.03162277660.03162800250.03193743880.0731200109


11-0.000370.711619480.504947630.10268610.711619480.504947630.10268610.34878613481.44772850662.04027456680.29440992560.03748660290.03804902770.04450172350.04516939860.03872983350.2154065923

21-0.000001.222905080.078792550.0655791.222905081.26068080.2623161.47288327070.85592716340.83027969990.17809693760.02859589050.02925623290.02816420070.02881457440.02958039890.1161895004

41-0.000001.882444570.009581640.02931581.882444572.452899840.46905284.39743745540.55780209840.42807762230.10666503040.02304830020.02361783430.02019110520.02069003680.02371708250.0729940066

81-0.000002.549700910.000938540.008871982.549700913.844259840.567806729.4793083410.40554222960.26897541660.05989959390.01980411230.02013807910.01612848720.016400470.02015564440.0528670207

1610.000003.096924150.000082070.002004083.096924155.378539520.5130444816.39371429280.32808547370.18890924260.03129519470.01796944710.01811312990.0136353980.01374442590.01811422090.0430337576

3210.000003.479478550.000006550.000366723.479478556.86817280.3755212823.75664370360.28910535030.14646338910.01580700050.01695285780.01700309830.01206644650.0121022060.01700183810.0381210775

6410.000003.716383470.000000480.000057753.716383478.053063680.23654429.87231967930.26958280330.12440893480.00791850120.01640362150.01641897690.0111434440.01115387530.01641740690.0356520487

10010.000003.811986520.000000090.000016623.8119865290.166234.280256240.26254179480.11120064250.00484827180.01619661730.01620314150.01054092550.01054517150.01620185170.0347594965


11-0.000316530.84991640.579239880.06425250.84991640.579239880.06425250.48817708981.18653638631.74100017760.13161719660.03430140390.03444613750.04154997550.04172529420.03464101620.1733100217

21-0.000005511.576462330.110429580.051554261.576462331.766873280.206217042.74288370020.64416631290.57474632620.07518256790.02518594210.02538043170.02379015650.02397386760.02549509760.0915770912

41-0.000000952.742803590.01908960.034215782.742803594.88693760.5474524813.10420577550.37292894230.20930712150.04177685310.01909425180.01931136820.01430479380.01446745040.01936491670.0555959449

81-0.000000134.322403250.002695510.016646414.3224032511.040808961.0653702446.58781478310.23698920010.09277969510.0228680020.01521028530.01539445360.00951698870.00963222170.0154110350.0384260654

161-0.000000026.031073150.000302210.005572676.0310731519.805634561.42660352117.41403321030.16868200520.0513658630.0121501960.01287664440.01298776370.00710567960.00716699820.01299038110.0297339648

32107.505003580.00002820.001340457.5050035829.56984321.3726208220.03769121540.13438535480.03410780920.00623811670.01154315560.01159246970.00581534510.00584018910.01159202310.0252211895

64108.5595450.000002290.000251748.55954538.419824641.03112704327.79299492560.11720758290.02611265380.00314566530.01080872980.01082624510.00510178690.00511005420.01082531750.0228797569

10010.000009.021520090.000000430.000078079.02152009430.7807387.315871380.11102049560.023292410.00201566750.01052834580.01053662640.00482242820.00482622110.01053565380.0220168398

Nu


1

2

4

8

16

32

64

100

Nu

SD 1/Nu (MOM)

PRACTICAL THRESHOLDL = 4N = 10000N = 100N = 1000IdealSpikyRayleigh


CONCLUSIONS (1)K-distribution approximation will reduce computational complexity for ship detectionMethodology adds support to use of K-distributionInsensitivity to modulating distributionMean of K-distribution can be estimated as usualParameter variance may bias detection thresholds by large factors if N < 1000Very important in spiky clutterWithout correction, PFA may increase by orders of magnitudeIf corrected, probability of ship detection is reducedAdaptive pixel block size (N) is desirable in variable clutter


SHIP WAKESTurbulent wake study with Dan Roy at RMCRADARSAT-2 imagesAISOther ship information about propulsion system (Ship owners, Internet, etc.)Analysis (60 ships) includesTwin screws/single screwLeft/right handed screws


RMC RESULTSWakes not usually visible when wind speed U > 6 m/sShip speed V is important: if U < 6 m/s && V > 5 m/s, 80% of wakes are visibleBright line on side of wake consistent with propeller flows (swirling and axial) and wind directionWakes from shallow twin screws tend to be visible


RSAT-2: QUEEN OF ALBERNIData supplied by MDA Corporation


Q of A Parameters

ParameterLength (m)139Maximum Beam (m)27.1Mean Draft (m)5.5Maximum Draft (Prop. Tip, m)5.72Block Coefficient (estimated)0.6Number of Propellers1Number of Blades4Propeller Shaft Depth (m)3Propeller Diameter (m)5Propeller TypeCPPService Speed (knots)19Propeller Speed @ 19 knots (rpm) 170Maximum Power (MW)8.83


COMBINED SWIRLING AND AXIAL WAKEConsider both linear and angular momentum in propeller wakeModify Prandtls approach to theoryEstimate fluid linear and angular momentum using standard engineering methodsApply to Queen of Alberni (BC Ferries)


Q of A Wake DiameterAxialSwirlingCombined


Queen of Alberni Maximum Surface Flow SpeedSwirlingAxial


Deep Screw CaseMaximum Flow SpeedAxialSwirling


CONCLUSIONS (2)Surface flows in the turbulent wake can be large compared with Bragg group velocityExpect significant radar wake visibility for long distancesSwirling component dominates axial flow immediately astern and especially when screws are deepWake characteristics can be used to verify shipNote:Hydrodynamic wake width is only one factor in radar wake width. Others are flow speeds, ambient wind and waves, radar effects and geometry.


ENDThank You All!


This is describes Company activities in ship detection and ship wake analysis since autumn 2008. Because of the wide scope, the results will only be summarized. Details can be found on the website; these include further summaries and papers.The overall concept is that MDA relies on AIS as the principal ship information and confirmation of AIS data (location, size, speed, propulsion) can be provided by SAR images as well as databases of ship information. Wake information is expected to be relatively low grade but should be useful in AIS verification.1.Sea clutter statistics are important for ship detection.An asymptotic calculation approach is appropriate to minimize computations and speed data delivery.Clutter statistics must be described from a limited number of pixels; this affects accuracy of parameters.Effects lead to increase in false alarms or reduction in probability of ship detection.Turbulent wake is most common wake in SAR images.Wakes have a potential for confirming (or otherwise) AIS ship identification using wake information and ship data database. Ship detection in SAR images must be accomplished against a sea clutter background. Detection thresholds must be derived from the observed clutter, which is typically variable across the image. In an operational system, the time taken to detect ships must be low to avoid staleness. The processing time for a typical SAR image (RADARSAT, Envisat) should be a fraction of a minute, in other words a few seconds.Experimentally, K-distribution is usually an excellent fit to clutter data in SAR images.It can be explained as a modulation process but the distribution of the modulation is assumed to be gamma. (Birth, death, migration stochastic process; too vague.)Modified Bessel functions of the second kind take too long to calculate.We only need values out in the tail of the distribution because false alarm rate must be about 10-9 per resolution cell.This raises questions about the validity so far out in the tail.

Code is very small with no loops (except for gamma function, which can be found efficiently).PFA is typically very small because there are about 100,000,000 pixels in an image.Integrand replaced by a simpler one with a Gaussian shape.Table shows a comparison between accurate and approximate evaluations of ship detection thresholds for single look and four-look SAR images.K-distribution is characterized by a mean and a shape or order parameter, nu and the number of looks, L.It is easy to estimate the mean accurately so that we focus on nu and derive a threshold as a multiple of the mean. Nu = 0.5 represents spiky clutter, Nu = 50.0 smoother clutter.These data were calculated by integrating the pdf down from very large values until a threshold was reached where the PFA was 10-6 or 10-9. Number of looks is given from the radar and image processing specification.It is possible to estimate optimal performance for finite number of independent samples (resolution cells or larger).Parameters need not be integers; this seems to have provided problems in the past.Spiky clutter is at left and smooth, Rayleigh type clutter on the right.When these curves are compared to those for the mean as a simple average, they are indistinguishable on the plot. (Calculate standard deviation of the mean of N samples; the standard deviation is estimated from the theoretical distribution variance.)However, the standard deviation for N = 256 is rather high compared with the mean ( = 1). Therefore for spiky clutter, it is questionable whether N = 256 is sufficient.Comparison of optimum and the practical Method Of Moments (ratio of the standard deviation of the data to the mean). MOM is quite poor for estimating nu, especially in spiky clutter at right hand side of plots. Note that when nu is large, the probability distribution is reasonably smooth and does not change very much with Nu. These plots are for N = 1000.Note that the standard deviation is for 1/Nu. This is for technical reasons.This shows the effect of a finite number of resolution cells, N, when the specified PFA is 10-9 per resolution cell. N less than 1000 results in a large increase in PFA unless the threshold is increased to compensate. The plot is for 4-look imagery. The calculations use the K-distribution approximation together with normally distributed randomization with a variance based on MOM. There is serious bias compared to the ideal infinite N curve, even with smooth clutter..Dan Roy was a MSc student at RMC jointly supervised by Prof. Joseph Buckley and myself.Information gathered by RADARSAT2, AIS, weather stations, Internet and ship owners.Focus on explaining turbulent wakes in SAR images in terms of ship size, propulsion system, ship/radar geometry and wind speed/direction.Note that velocity bunching shifts must also be taken into account.Queen of Alberni is part of BC Ferries fleet.Double ended ferry with a screw at each end to avoid turning at points of embarkation.Note bright line on port side of wake.The purple arrow is the wind vector.Wake offset is consistent with service speed of 19 knots.Data is from the Internet and discussions with BC Ferries.Note that shaft power came out to be 7.9 MW at service speed: compare with table value of 8.8 MW. This is very encouraging.Axial and swirling eddy diffusion contributes to wake broadening. In the far wake, axial diffusion dominates. Net slope is reduced from 0.25 and 0.333 to about 0.3.Group velocity of Bragg waves at C-band is about 13 cm/s. When flow speeds are comparable, the hydrodynamic wake can produce a large effect on the radar wake. Effects should be visible in calm waters when flows are as low as 2 cm/s. Note Queen of Alberni service speed 19 knots.The curves are the result of the new theory of combined axial and swirling turbulent wakes.Surface flows capable of affecting SAR image out to 10 km or more from axial component and about 1 km from transverse swirling component.When the screws are deep, the swirling component tends to predominate at small distances astern. This is for propeller tips at a depth of a few metres.

progress in sar ship detection and wake analysis

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tunaleylondon research

sar ship detection

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