Passive Localization using Mode Filtering.pdf - The University of ...

Maximum-likelihood passivelocalization using mode filtering Melvin J. Hinich

Applied Research Laboratories, TheUniversity ofTexas atAustin, Austin, Texas78713 Edmund J. Sullivana) SACL4NT Undersea Research Centre,VialeSanBartoiomeo 400, 19026LaSpezia;Italy

(Received13June1988;accepted forpublication15August1988) The maximum-likelihood estimatorfor passive rangeanddepthestimationof an acousticpoint sourcein a shallow-water waveguide is presented. The datafroma verticalarrayof hydrophones arepassed througha modalfilter,theoutputof whichisthesetof complex modalamplitudes associated withthenormal-mode modelof acoustic propagation. The range

anddepthestimates arethenfoundbya maximum-likelihood estimation procedure thatuses thesemodalamplitudes asinputs.Thistechnique iscompared to thematched-field procedure andisshownto havebettersignal-to-noise andsidelobe behavior for a givenscenario. Results aregivenforbothsynthetic andrealdata.Theresultswiththerealdatademonstrate the importance of themode-filtering property ofthemaximum-likelihood estimator presented in this work.

PACS numbers:43.60.Gk, 43.30.Jx, 43.30.Wi

INTRODUCTION

The ideaof includingenvironmental informationwithin the sonarsignalprocessing schemehasbeenput forth on severaloccasions. In thecaseof shallow-waterpassivelocalization, the problemhas becometractabledue to the existenceof sophisticated propagationmodelscoupledwith the adventof moderncomputertechnology. In 1973,Hinich1 usedthe normal-modemodelof propagationto developthe maximum-likelihoodestimatorfor the depth of a point sourceusingthe datafrom a verticalarray of hydrophones. This wasprobablythe firsttime that a sophisticated propagation model was used for source localization.Later,

Bucker 2 proposed a scheme that hasbecomeknownas "matched-field processing." Here,a searchismadeoverforward solutionsof the propagation model,whereeachsolution assumesa particularsourcelocation.The estimation process consists of comparingthesesolutions,eachof which constitutesa predictionof the fieldreceivedon the measurement array, to the measuredfield. Bucker'smethodof mak-

ing thiscomparison effectivelyconsists of formingthe inner productbetweenthe measuredand predictedvectorof array outputs.The squaredmagnitudeof this estimatoris then

plottedon a range-depthmap wherethe coordinates of the maximumconstitutethe estimateof the rangeanddepthof the source.Variousversionsof thisapproachhavebeenput

forth.3'4More recently,directinversiontechniques have beeninvestigated. 5-7Theseapproaches arebased onnormalmode theory, which allows a set of linear equationsin the

modalamplitudesto bewritten that canbedirectlyinverted. Theseamplitudescontainthe rangeand depthinformation that must then be extractedas a secondstep.This second stepcan of coursebe cartledout by a forwardsearchjust as in the matched-fieldmethod;the differencebeing that the direct inversionapproachallowsmode filtering,sincethe modalamplitudesare solvedfor directly. •')Presently at:NavalUnderwater Systems Center,Code0IV, Newport,RI

matched beamformer, i.e., a beamformer that differs from a

standardplane-wave beamformer in thatit matchestheconfiguration of the field peculiar to the particular acoustic propagationconditions. •- It shouldbepointedout that althoughthematched-field techniquescan involve prohibitively large computation times,sincetheymustreeomputethe fieldfor eachassumed sourcelocation,theyofferthe luxuryof allowingpropagation modelsof any desireddegreeof complexity,suchas range-dependent models,whereasthedirect-inversion techniquesarebasedon thelinearityof themodalequations and thus are basicallylimited to the range-independent case. However,sincethe direct inversiontechniquesessentially constitutea modal filter, they allow solutionsto be carried out usingasmanyor asfew modesasdesired.This canbe an

importantadvantagesincenumericalstudieshave shown that errorsin the assumedvalueof the soundvelocityprofile assumedfor the model can impact the modesin diverse

ways,depending onthenatureof theerror?9 In this article we wish to addressthe questionof the estimatoritself.In particular,we showthat, giventhe normal-modemodelof propagation,the maximum-likelihood estimatorof the rangeand depth of the sourcefollowsdirect-

ly. The inversionof the modalequationsleadsdirectlyto a maximumlikelihoodestimatorof the rangeand depth.This

basically constitutes a generalization of theworkof Hinich• in which the maximum-likelihood estimatorof the depth only is treated.In See.I the maximum-likelihoodestimator

is derived.In Sec.II a numericalexampleis presentedin whichthe performanceof the maximum-likelihood estimator is evaluated,for a particularscenario,for severalvalues of the signal-to-noise ratio (SNR). Also a comparisonis made between the maximum-likelihood

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In' both the matched-fieldand direct inversionapproaches, the scenariousually,but not necessarily, consists of a verticalarray of hydrophones that samplesthe vertical structureof the field.The applicationof the modelcanthen be viewed as being equivalentto the introductionof a

J. Acoust.Soc.Am. 85 (1). January1989

0001-4966/89/010214-06500.80

estimator and the

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ownloaded 16 Jul 2010 to 146.6.201.36. Redistribution subject to ASA license or copyright; see http://asadl.org/journals/doc/ASALIB-home/info/terms.js

matched-field estimator. In thelastpartofSee.II theexperimentalresults arepresented. Section III contains a general discussion oftheresults alongwithcomments onsomeofthe theoretical aspects of thetechnique. I. MAXIMUM-LIKELIHOOD

y = [y(Zl)ty(Z2),...,.¾(Z•/) ] T, e= [e•,e• .....e•]r, fi= b

...., IZi(Zo)--,Z2(zo) •ik,r +iO ffik•r +iO

eik •r+iO •T

ESTIMATOR

The scenariofor the problemis as follows.An acoustic pointsource,locatedat depthZobelowthesurface,isradiating acousticenergyat circularfrequency•0. The sourceis

(6) (7)

'l '

(8)

and the m, n elementof Z is givenby Zm(Z,); l