PROGRESS IN SAR SHIP DETECTION AND WAKE ANALYSIS
description
Transcript of PROGRESS IN SAR SHIP DETECTION AND WAKE ANALYSIS
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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/
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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
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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
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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++.
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THRESHOLD COMPARISON
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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
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OPTIMUM MEAN INTENSITYCramer Rao Bound#Samples N = 256L = 1L = 4L = 10SpikyRayleigh
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Chart1
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Fisher Information (Mu)
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Nu
Standard Deviation Nu
Sheet3
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Fisher Information (Nu)
Nu
Standard Deviation Nu
Nu
SD Nu (MOM)
Nu
Standard Deviation Mu
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000
000
000
000
000
000
000
000
Nu
Standard Deviation 1/Nu
000
000
000
000
000
000
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000
Nu
SD 1/Nu (MOM)
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SDs USING MOM: N = 1000OptimumPracticalL = 1 Black; L = 4 Red; L = 10 Yellow
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Chart1
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Nu
Standard Deviation 1/Nu
Basis Nu
LN1000
1munucrossSDs
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10
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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
Fisher Information (Mu)
Basis Nu-1
Nu
Standard Deviation Nu
Sheet3
Nu
Fisher Information (Nu)
Nu
Standard Deviation Nu
Nu
SD Nu (MOM)
LInverse NuN=1000
1munucrossSDs
numeanE(logLike)Fisher mununumumunumunudeterminantinv11inv22inv12raw muFisher muraw nuFisher nucalc mucalc nu
11.0002-0.002750.402793640.252608950.09997370.402793640.252608950.09997370.09175453782.75309494.38990430081.08957771920.04982630680.05246994280.06291810490.06625635290.05477225580.3741657387
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
4determinantinv11inv22inv12raw muFisher muraw nuFisher nucalc mucalc nu
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
10determinantinv11inv22inv12raw muFisher muraw nuFisher nucalc mucalc nu
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
Standard Deviation 1/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
numeanE(logLike)Fisher mununumudeterminantinv i11inv i22inv i12raw muFisher muraw nuFisher nucalc mucalc nu
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
Fisher Information (Mu)
Basis Nu-1
Nu
Standard Deviation Nu
Sheet3
Nu
Fisher Information (Nu)
Nu
Standard Deviation Nu
Nu
SD Nu (MOM)
LInverse NuN=1000
1munucrossSDs
numeanE(logLike)Fisher mununumumunumunudeterminantinv11inv22inv12raw muFisher muraw nuFisher nucalc mucalc nu
11.0002-0.002750.402793640.252608950.09997370.402793640.252608950.09997370.09175453782.75309494.38990430081.08957771920.04982630680.05246994280.06291810490.06625635290.05477225580.3741657387
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
4determinantinv11inv22inv12raw muFisher muraw nuFisher nucalc mucalc nu
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
10determinantinv11inv22inv12raw muFisher muraw nuFisher nucalc mucalc nu
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
Standard Deviation 1/Nu
1
2
4
8
16
32
64
100
Nu
SD 1/Nu (MOM)
-
PRACTICAL THRESHOLDL = 4N = 10000N = 100N = 1000IdealSpikyRayleigh
www.london-research-and-development.com
-
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
www.london-research-and-development.com
-
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
www.london-research-and-development.com
-
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
www.london-research-and-development.com
-
RSAT-2: QUEEN OF ALBERNIData supplied by MDA Corporation
www.london-research-and-development.com
-
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
www.london-research-and-development.com
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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)
www.london-research-and-development.com
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Q of A Wake DiameterAxialSwirlingCombined
www.london-research-and-development.com
-
Queen of Alberni Maximum Surface Flow SpeedSwirlingAxial
www.london-research-and-development.com
-
Deep Screw CaseMaximum Flow SpeedAxialSwirling
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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.
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ENDThank You All!
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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.