Source localization in noisy and uncertain ocean environments

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Source localization in noisy and uncertain ocean environmentsLaurie T. Fialkowski, Michael D. Collins, and John S. PerkinsNaval Research Laboratory, Washington, DC 20375

W. A. KupermanScripps Institution of Oceanography, La Jolla, California 92093

~Received 15 April 1996; accepted for publication 20 November 1996!

Interference from noise and uncertainties in the environmental parameters are arguably the two mostserious limitations in matched-field processing~MFP!. Among the techniques that have beendeveloped for handling these difficulties are the noise-canceling processor@M. D. Collins, N. C.Makris, and L. T. Fialkowski, ‘‘Noise cancellation and source localization,’’ J. Acoust. Soc. Am.96, 1773–1776~1994!# and focalization@M. D. Collins and W. A. Kuperman, ‘‘Focalization:Environmental focusing and source localization,’’ J. Acoust. Soc. Am.90, 1410–1422~1991!#. Thenoise-canceling processor is a generalization of the Bartlett processor that is based on matching thecovariance matrix of the data with replica covariance matrices of the signal and the noise.Simulations are presented to illustrate the performance of the noise-canceling processor when thereare errors in the noise replica. Focalization is a generalization of MFP in which environmentalparameters are included along with source parameters in the search space. An implementation ofthis approach that is suitable for applications is developed and tested. The noise-canceling processorand focalization are used to simulate the localization of a source buried in noise in an uncertainenvironment. ©1997 Acoustical Society of America.@S0001-4966~97!03206-2#

PACS numbers: 43.60.Gk@JLK#

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INTRODUCTION

Matched-field processing~MFP! is the inverse problemof localizing an acoustic source in the ocean by compardata with solutions of the wave equation.1,2 MFP is veryeffective under ideal conditions because each propagapath contains information about the source location. Sideparture from ideal conditions tends to be the rule ratthan the exception, MFP has been an active area of resefor nearly two decades.3,4 Since ocean environments acomplex, there are several difficulties that arise in MFP tare not encountered in other signal-processing probl~such as beamforming!. MFP techniques have been designto handle difficulties such as environmental mismatch5–8

~uncertainties in the environmental parameters!, interferencefrom ambient noise and jammers,9,10 source motion,11–17andmultiple sources.17

In this paper, we implement and test MFP techniqueslocalizing a source buried in ambient noise, a source inuncertain environment, and a source buried in noise inuncertain environment. In Sec. I, we describe an implemtation of focalization8 that is suitable for applications. In SeII, we describe an implementation of the noise-cancelprocessor10 that is suitable for applications and derive a spcial noise-canceling processor that is useful for many apcations. In Sec. III, we investigate the performance ofnoise-canceling processor as a function of signal-to-noisetio ~SNR!, environmental mismatch, and noise misma~uncertainties in the noise covariance!, and apply the noisecanceling processor and focalization to localize a sourceied in noise in an uncertain environment.

3539 J. Acoust. Soc. Am. 101 (6), June 1997 0001-4966/97/101

ribution subject to ASA license or copyright; see http://acousticalsociety.org

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I. FOCALIZATION

Environmental uncertainty~or mismatch! results in erro-neous replica fields and is a serious difficulty in MFP.18–21

This problem is common because ocean environmentslarge and dynamic. Relatively small uncertainties can renMFP techniques useless even when other factors~such as theSNR! are favorable. An obvious approach for overcomimismatch is to measure the environmental parameters arately. This approach is usually impractical because thegions of interest are relatively large. Even small regions cbe difficult to characterize when bottom interaction is signcant because sediment parameters are difficult to obtain.other approach for overcoming mismatch is to develop Mtechniques that are relatively tolerant of uncertainties.5

When uncertainties are large, it is necessary to incluboth environmental and source parameters~and possiblyother parameters, such as corrections to the locations oreceivers! in the search space and perform focalization.8 Fo-calization involves adjusting the environmental parametuntil the source location comes into focus in the ambigusurface. Since the purpose of the original investigationfocalization was simply to test feasibility, the original implementations were designed to be efficient and capture thesential characteristics of the problem with little concernapplicability to data. Focalization proved to be not only fesible but also robust at determining source position dueparameter hierarchy in which source parameters outrankvironmental parameters. Focalization parameter searcheten recover the source position without converging tocorrect environmental parameters. This can be an advanif the main goal is to localize the source. The promisiresults of the feasibility test motivated us to design an impmentation that is suitable for applications.

3539(6)/3539/7/$10.00 © 1997 Acoustical Society of America

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FIG. 1. Results for example A, which tests the sensitivity of the noicanceling processor to SNR and mismatch in the noise and source repThe asterisks indicate combinations of mismatch and SNR for whichnoise-canceling and Bartlett processors provide an estimate of the slocation that lies within 600 m in range and 6 m in depth of the true sourelocation. The mismatch parameter is the sound speed at the ocean su

3540 J. Acoust. Soc. Am., Vol. 101, No. 6, June 1997


Focalization involves a parameter space, cost functand optimization algorithm. The most common MFP prolems that have been considered involve two unknown pareters, the range and depth of the source. Focalization p

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FIG. 2. Results for example B, which involves an SNR of220 dB, a mov-ing source, and data-based noise canceling. The source is atr57 km whenthe noise replica is obtained. The source is atr58 km andr59 km whenthe data samples are obtained. Red corresponds to the most likely slocations. Blue corresponds to the least likely source locations. The Baprocessor~top! contains peaks near the ocean surface because the surgenerated noise dominates the signal from the source atr58 km. The noise-canceling ambiguity surfaces corresponding tor58 km ~middle! and r59 km ~bottom! contain two distinct peaks corresponding to the soupositions.

3540Fialkowski et al.: Source localization


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FIG. 3. Results for example C, which involves plane-wave beamforming with a towed array for a source buried by 10 dB in noise generated by theThe Bartlett processor, which appears in the top row for two cases, is dominated by the tow ship signal. The noise-canceling processor appears inrow. When the source is atu5245 deg~left column!, the noise-canceling processor clearly resolves the source bearing. When the source movesu5215 deg tou5230 deg~right column!, data-based noise canceling clearly resolves both source bearings.

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lems involve these parameters plus the focusing paramethat describe the environment and other aspects of the plem. The dimension of the parameter space may be mmized by exploiting the parameter hierarchy and includonly key environmental parameters. The coordinate rotaapproach of Ref. 22 can be used to identify the key paraeters. The sharp peaks in parameter landscapes assowith high-resolution processors make them ineffective cfunctions for focalization. We use low-resolution processbecause of their simplicity and robustness. OptimizationMFP problems is often based on exhaustively searchingcost function. Since this approach is not practical for focization problems that involve high-dimensional paramespaces, we apply simulated annealing23–25 to search the fo-cusing subspace. To avoid difficulties associated withextremely multi-modal nature of the cost function in rangdepth slices of the parameter space, we exhaustively sethe source coordinates for every sample of the focusing



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rameters. This approach is practical because the sourcespace is of low dimension.

II. THE NOISE-CANCELING PROCESSOR

In this section we describe the noise-canceling procsor, a practical approach for applying it under conditions tfrequently arise in practice, and a special noise-canceprocessor for a special case. The data are assumed tdominated byn temporally uncorrelated processes so thatm3m covariance matrixK is of the form

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their entries into unit vectors of dimensionm2, and definethe cost function,

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where the unit vectoru corresponds toK, the unit vectoruj corresponds toKj , and the energy levelsej are unknown.Theuj are either modeled or estimated from data.

We defineA to be them23n matrix whosej th columnis uj so that Eq.~2! becomes

E5uu2Aeu2, ~3!

wheree contains the entriesej . The minimum ofE occursfor

e5~A*A!21A* u. ~4!

Substituting this solution into Eq.~3!, we obtain

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E5u*Qu, ~5!

where Q5A(A*A)21A* . For the casen51, the noise-canceling processorB reduces to the Bartlett processor. Aestimate for the source location and other parameters istained by maximizingB. For this MFP problem,K corre-sponds to the data and theKj correspond to the replicas.

FIG. 4. The focalization parameter search for example D, which involvesource buried by 10 dB in ambient noise and three sound speed paramThe range and depth of the source are recovered. Although the environtal parameters are not recovered, there is a strong correlation betweefirst two sound speed parameters. The dashed lines indicate the true peter values.



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Since it is difficult to model noise covariance matricescomplex environments, it may be necessary to use datathe replica noise covariance matrix in practice. We referthis approach as data-based noise canceling. In some cthe measured noise covariance matrix may be corruptedthe signal. This difficulty can be overcome by exploitinsource motion. For the casen52, Eq. ~2! is of the form,

E5uuN1uS2e1~uN8 1uS8!2e2u2u2, ~6!

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FIG. 5. Noise-canceling ambiguity surfaces encountered during the foization parameter search for example D~from top to bottom: iterations 3, 26and 195!. Red corresponds to the most likely source locations. Blue cosponds to the least likely source locations. The crosses mark the locatiothe peaks.



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whereu5uN1uS andu15uN8 1uS8 are data samples obtainewhen the source is at different locations,uN anduN8 are thecontributions of the noise,uS anduS8 are the contributions othe signal, andu2 is the source replica.

Assuming that the minimum ofE occurs whene1>1and uN8 >uN so that the noise terms in~6! approximatelycancel, we obtain

min E>minuuS2uS82e2u2u2. ~7!

If not for the minus sign in front ofuS8 , the right side of Eq.~7! would be equivalent to the Bartlett processor appliedthe datau5uS1uS8 corresponding to two sources. The minsign does not make a significant difference if the soumoves far enough so thatuS anduS8 are uncorrelated. In thiscase, the ambiguity surface is similar to the Bartlett ambiity surface for two sources. The ambiguous peak due tocorrupting signal can be rejected by requiring thate2.0.Stationarity is a key assumption in data-based noise caning, which breaks down when the noise covariance varapidly ~e.g., when the noise is dominated by nearby surfships that are moving!.

The noise-canceling processor is applicable when anall of theKj depend on the unknown parameters. For maproblems of interest, one of theKj depends on the unknowparameters~the variable replica! and the otherKj are inde-pendent of the unknown parameters~the fixed replicas!. Wederive a special noise-canceling processor for this caseinterchanging the roles of the data and the variable replicthat the variable replica is matched with a combination ofdata and the fixed replicas~for the general case, the datamatched with a combination of the variable and fixed repcas!. We letpp* correspond to the variable replica, wherepcontains the replica complex pressures on the array. Inchanging the roles of the data and the fixed replica in Eq.~5!and using the definitions ofA andu, we obtain the specianoise-canceling processor,

Bs5uQsbu, ~8!

whereQs5(A*A)21/2 and thej th entry ofb is p*Kjp.For the casen51, Bs reduces to the Bartlett processo

EvaluatingBs involves the evaluation ofn Bartlett proces-sors and requires slightly more thann times the computa-tional effort that is required to evaluate the Bartlett procsor. The matrixQs is independent of the variable replica anmust be computed only once. In contrast, the matrixQ in Eq.~5! depends on the variable replica and must be computedevery sample point in the ambiguity surface. Another advtage ofBs is that the ambiguity function is normalized witrespect to the replica so thatBs>1 always indicates a goomatch. SinceB is normalized with respect to the data,B>1 does not necessarily indicate a good match whenSNR is low.

III. TEST PROBLEMS

In this section we apply the noise-canceling procesand focalization to test problems involving simulated daWe work in cylindrical coordinates, where the ranger is thehorizontal distance from an array of receivers,u is the bear-ing, andz is the depth below the ocean surface. For simp



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ity, we consider range-independent examples and use idized models of noise mismatch. We model surface-genernoise using the approach of Ref. 26. We solve the examusing the general noise-canceling processor given by Eq.~5!.

The purpose of example A is to test the performancethe noise-canceling processor when there are errors inestimates of the noise covariance matrix and the envirmental parameters. The 25-Hz source is located ar513 km andz5150 m. We takem513 for the vertical ar-ray, with the j th receiver placed atz5(215130j ) m. Thesound speed is 1500 m/s in the 400-m-deep water columnthe sediment, the sound speed is 1700 m/s, the densi1.5 g/cm3, and the attenuation is 0.5 dB/l. To simulate en-vironmental mismatch, we treat the sound speed in the wcolumn as a linear function of depth, with the value at tsurface unknown and the value at the bottom assumed t1500 m/s. All of the other environmental parameterstreated as known. We also use this mismatch parametrizato simulate noise mismatch. Although noise mismatch wobe due to factors such as finite sampling and fluctuationpractice, the actual form of the mismatch model is probanot critical for the sake of testing.

We constructed the noise-canceling and Bartlett procsors for various values of the SNR and the mismatch pareter and searched for the location of the main peak in eacthe ambiguity surfaces. Mismatch errors were simulatedusing the mismatch parameters to generate replicas. Wesidered cases in which the error is confined to the noiselica and cases in which there are errors in both the noisesource replicas. The performance of the processors is iltrated in Fig. 1, which indicates the SNR and mismatch vues for which the main peak is within 600 m in range andm in depth of the true source location. The Bartlett procesbreaks down when the mismatch exceeds about 5 m/s oSNR falls below about25 dB. When there are errors in thnoise replica, the noise-canceling processor is successfumuch lower SNR, even when the mismatch is significaThe noise-canceling processor also performs well when thare errors in both the noise and the source replicas.results of example A suggest that the errors in measunoise covariance matrices will be tolerable in many case

The purpose of example B is to illustrate data-basnoise canceling. This example involves the environment,ray, and frequency of example A, a moving source az525 m, covariance matrices corresponding to three soupositions, and an SNR of220 dB. The first covariance matrix, which is used as a replica for the noise, was obtainwhen the source was atr57 km. The other covariance matrices, which are treated as the data, were obtained whensource was atr58 km and r59 km. Noise-canceling andBartlett ambiguity surfaces appear in Fig. 2 for exampleThe source peak is obscured by the noise in the Barambiguity surface. Since the noise replica is contaminateda source signal, there are two prominent peaks in the nocanceling ambiguity surfaces. Although the estimate forsource location is ambiguous in the individual noiscanceling ambiguity surfaces, the initial and final positioof the source are easy to deduce from the combination ofambiguity surfaces.



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The purpose of example C is to illustrate the applicatof the noise-canceling processor to plane-wave beamformproblems. This example involves a 50-Hz source andenvironment of example A, with the exception that the wacolumn is 500 m deep. We takem515 for the towed hori-zontal line array atz515 m, with thej th receiver placed ar5(75115j ) m. Tow ship noise corresponding to an SNof 210 dB is modeled using a point source atr50 andz55 m. Mismatch in the tow ship noise is modeled by assuing that the sediment sound speed is 1700 m/s for theand 1850 m/s for the replica. We apply the noise-canceprocessor to estimate the bearing of a distant source, wproduces a signal that is approximated by a plane wacross the array. Results for example C appear in Fig. 3 fcase involving a source atu5245 deg and a case involvina source that moves fromu5215 deg tou5230 deg~thebearing change may be regarded as true motion or the eof varying the heading of the tow ship!. The plane-wavesignal is buried in the noise in the Bartlett processor for bcases. The bearing of the plane-wave signal is clearlysolved for the fixed source. Data-based noise canceclearly resolves the bearings of both plane-wave sourcesthe other case.

The purpose of example D is to illustrate the perfomance of focalization with the noise-canceling processThis example involves the environment, array, sourcequency, and source location of example A. We assumeSNR of210 dB and include mismatch in the noise covaance corresponding to a sound speed of 1505 m/s atocean surface. As the results in Fig. 1 indicate, the nocanceling processor is successful and the Bartlett procefails for this combination of SNR and noise mismatch whthe environmental parameters are known exactly. We paretrize the environment in terms of a constant sound speethe sediment and a linearly varying sound speed in the wcolumn defined by the values atz50 and z5400 m. Thedensity and attenuation in the sediment are assumed tknown. The water column sound speeds are assumed tbetween 1480 m/s and 1520 m/s. The sediment sound sis assumed to lie between 1650 m/s and 1750 m/s. The nreplica is not varied during the search.

The focalization parameter search for example D islustrated in Fig. 4. The energy decreases in the typicaregular fashion of simulated annealing. The estimates forsource range and depth converge to the correct valuessampling other locations that correspond to relatively lenergy. Although the estimates for the environmental pareters do not converge, the water column parameters focorrelated paths. This behavior suggests that the efficiencthe search could be improved using the coordinate rotaapproach of Ref. 22. Some of the noise-canceling ambigsurfaces appear in Fig. 5. The parameter search attempbring the source into focus at two false locations beforetling on the correct location.

IV. CONCLUSION

Techniques for localizing a source in noisy and unctain environments have been tested using simulations.noise-canceling processor outperforms the Bartlett proce



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when there is mismatch in the noise and the environmThe noise-canceling processor was tested for plane-wbeamforming for a source buried in tow ship noise. Dabased noise canceling is effective when the noise repliccontaminated by a source. An implementation of focalizatbased on the covariance matrix is suitable for applicatioFocalization was implemented using the noise-canceling pcessor to localize a source buried in noise in an uncerenvironment. There is a need to perform further tests ofcalization and noise canceling using data.

ACKNOWLEDGMENT

This work was supported by the Office of Naval Rsearch.

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Source localization in noisy and uncertain ocean environments