PASSIVE ACOUSTIC TRACKING OF CETACEANS USING CHIRPLET TRANSFORM

Farzad FarhadZadeh, Hamidreza Amindavar

Amirkabir University of Technology, Department of Electrical Engineering, Tehran, Iranfarhadzadeh@aut.ac. ir, hamidami@aut.ac. ir

ABSTRACT

To study the behavior of marine mammals, dolphins, whales,and porpoises, etc., unobtrusively without influencing their be-havior, a passive acoustic tracking system is used to accuratelyestimate the location and track of such animals. We introducea new method to track underwater animals. We utilize chirplettransform to estimate differential delays-Dopplers between pairsof sensors of an array from the received acoustic signal, and useextended Kalman filter (EKF) for tracking. Since the acous-tic signals from these animals are inherently non-stationary, thetime-frequency processing of the received wavefront is required.The performance of our method is illustrated on real data, wherea whale song is contaminated with simulated underwater noisein different signal-to-noise ratios.

I. INTRODUCTION

Many scientists focusing on environmental protection pursue theecology of cetaceans, but, little is known about their behavior es-pecially during their diving because the methods to observe themare limited at present. For example, the simplest way of observa-tion is watching their behavior from a boat. It is necessary for hu-mans to get close to cetaceans, i.e., dolphins, porpoises and whales,for observation while they are staying near the surface. In order tostudy their movement often data loggers are attached to their body,however, this is not a feasible approach since most of the times thedata loggers can not be recovered. A modern approach involves anautonomous underwater vehicle (AUV) as the data logger platform[1, 2], by detecting and listening to whistles and clicks tracking canbe initiated [3]. From signal processing stand point, detecting andtracking echo-locating cetaceans is not an easy task, due to the verycomplicated environment. Underwater mammal sounds can be con-sidered to comprise acoustic events of interest superimposed on abackground underwater sound environment, termed as backgroundnoise. In the search for signals, we have some a priori knowledgethat allows us to focus attention on certain frequency bands, but oth-erwise the nature of signals is ill-defined, and they are perhaps bestthought of as transient features of potential interest. In particular, wedo not have access to obvious models for, nor any reference libraryof, the signals that we wish to detect. The purpose of this paper isto provide a passive approach that could avoid the by-catch of echo-locating cetaceans, i.e., dolphins, porpoises and whales. To this end,the track of these animals are essential, by observing them they aremade aware of the trawl by various means such as active pingersor transponders, or the trawl itself. On the other hand, by in large,researchers and practitioners alike have considerable evidence thatsome species of marine mammals can suffer harm from active sonaroperations [4]. Therefore, it is humane to consider the state of well-being of marine mammals nearby prior to active sonar operations.We describe a tracking scheme for echo-locating cetaceans. We use

chirplet transform to generate images of differential delay-Dopplersonar returns from cetaceans. Our primary interest here is simplyin tracking, and we restrict ourselves solely to that objective. Ouravailable data relate to underwater sounds of different types of echo-locating cetaceans in addition to ever-presence of background noise.They consist of selected extracts from lengthy recordings taken inreal life conditions in the ocean, using a hydrophone array placedseveral meters beneath sea level. The recording apparatus sampledthe sound at 4 kHz, the sampling rate is over twice the highest fre-quency of the signals that we potentially wish to identify, so theremay be aliasing problems, evidently, a salient feature of the marinemammals' sound is the possible spread of frequencies across a widerange of frequencies biased toward the upper end of the frequencyrange up to 20 kHz, this is a major aliasing source in the data. Anal-ysis of such underwater marine mammals is especially cumbersomedue to a large amount of background interference where the struc-ture of this noise is potentially non-Gaussian. Historically, severalapproaches have been used for signal tracking in underwater, eitherby working directly with the raw sound or by using some transfor-mation of it. Many of the various methods for the tracking of sig-nals make use of the Fourier transform. Although this transformis extremely useful and well established, it does have drawbacks-principal difficulties in analyzing short-term transient sound behav-ior. In addition, alternatives to the short time Fourier transform withbetter time-frequency localization have been suggested; for exam-ple, the Wigner distribution and its variants. Our justification forwishing to use chirplet transformation is simply that signals withvery short time duration are frequently those of most interest in ourparticular underwater sound data generated by an underwater mam-mal. The resolution of the chirplet transformation has local adap-tivity, and this potentially enables us to zoom in on irregularitiesand characterize them more specifically than is possible with Fouriertransformations. Conventional tracking systems employ active tags,due to the limited range of the mobile sound source, this approachtypically requires a tracking vessel, this tagging is not practical un-der all environmental circumstances. Hence, we track the animalspassively by their acoustic signatures, in so doing we are faced withnon-stationary signals in a non-stationary environment. The ap-propriate information as to their position is extracted via differen-tial delay-Doppler processing. Therefore, a passive tracking systemis equipped by a reliable tracking algorithm is capable of trackingcetacean echo-location sounds in the vicinity of a trawl. In a long runof operation, the system is capable of sensing and storing a multitudeof environmental information regarding the animals endangered bythe trawls, the information such as movement patterns, stock distri-bution, habitat preferences. In addition, extracting the differentialdelay-Doppler is not a simple problem and some researchers haveproposed some algorithms which are complicated [9]. In this pa-per, we introduce a simple new method to extract proper informa-tion from received signals. In this method, we use received signals

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from cetaceans' sounds for tracking by having some preconceptionabout underwater sounds. We know that an underwater sound is anon-stationary signal and can be estimated by some chirplets, it iswell understood that chirp is one of the most important functions inthe nature [5]. Many natural phenomena, for instance, the whales'whistles could be approximated by a group of chirp functions. Inthis paper the received signal is approximated by a weighted sumof chirplets [6] parameterized by the location in time, location infrequency, chirp rate and the chirp duration. Such four-parameterchirplet approximation offers more efficient representations ofmanysignals of interest than the representations obtained using short timeFourier transform, Gabor transform, wavelet transform, and waveletpackets, the literature on this subject is vast, naming a few [6, 7, 8].Wavefronts at each sensor of the array are approximated by param-eterized chirplet transform, and then differential delay and Dopplerare estimated by subtracting the location of frequency and time in thesame chirplets, finally extracted information is used to track animalsby EKF. This paper is organized as follows, in section 2, a discus-sion about estimation of differential doppler and delay is presented,in section 3, we discuss tracking by EKF, and in section 4, we pro-vide the simulations and results, and some concluding remarks at theend.

II. ESTIMATING DIFFERENTIAL-DELAY ANDDIFFERENTIAL-DOPPLER

In this section we estimate differential delay-Doppler that exist be-tween signals received from sensors of an array by the means ofchirplet transform. If w(k) is a narrowband signal transmitted by amammal at a range Ri (k) and moving with a constant velocity, seeFig. 1, then the signal received at the ith sensor is presented as [9]

Si(k) = W( T-i)eji + vi(k) (1)

where Ti, and di denote the delay and Doppler shift and vi (k) rep-resents zero-mean sensor noise. Our objective is to estimate the dif-ferential delay-Doppler parameters at a pair of sensors, i.e. A-rij =-ri- rj and Azdij = di-dj. Also for a received signal by an ithsensor Si (k), we have the following representation [6].

q

Si (k) = Z aieiPs(k; tp, wp, cp, dp) + Vk (k) (2)p=1

where tpwp, and cp are real numbers and dp is a positive real num-ber. The parameters tp, wp, cP and dp represent, respectively, loca-tion in time, location in frequency, chirp rate, and the duration of thechirped signal, respectively, and vi (k) is the receiver noise and/orthe statistical modeling mismatch. s(.) is defined as

s(k; tp,wp, cp, dp) = (v2_Fd)-2exp[ ( tP)2+ j c (k t)2 +jw(k -tp)]. (3)

2d 2

Therefor, we have received signals Si(k) {i = 1, ... N}, at eachsensor of N-element array. Then, we approximate the received sig-nals by weighted sum of chirplets. In our experiments, we assumethat q, the number of chirplets, do not vary with i, an easily justifi-able assumption if the observation time of the observation space areboth constant. We have N group that each group has q-chirplets de-scribed by {ap, Op, tp, wp, cP and dp} that are illustrated in Fig. 1.In the next step, we extract the most similar chirplets for the pairs ofsensors that each sensor has a group of q-chirplets. For instance, theith and jth sensors are selected as a pair of sensor. The important

group# 1

Sil,S1,2

_Sl,q _

group#2

S2,1S2,2

S2,q J

group#3

S3,1S3,2

L 83,q _

sensori ti sensor2 12 sensor3

01 02 03

Ri(k) R2(k) R3(k)

Source moving with velocity v

Fig. 1. A set-up for signal measurement.

issue in the most similar chirplets is to extract two most importantproperties of chirplets, chirp rate and duration, are fixed. In the for-going instance, mth and nth chirplets are selected from ijth pair ofsensors respectively. Therefor, we can extract similar chirplets withthese properties, and finally differential-delay and Doppler can beestimated by subtracting the location in time, (i.e. ATij = tm- tn,tmi is selected from ith group and tnj from jth group of chirplets),and the location in frequency; i.e., Adij = wmi- Wj ,w'j is se-lected from ith group and wnj from jth group of chirplets, of theselected chirplets. Where Iti,p, wi,p, c di,p IN =1 are the esti-mated chirplet parameters. Our algorithm consists of the followingsteps.

1. The received signals should be approximated by the means ofq-chirplets (q is fixed, for notational simplicity).

2. After selection of pairs of sensors that belong to the array, thebest similar chirplets are extracted from pairs of sensors.

3. Differential-delay and differential-Doppler are estimated bysubtracting time-location and frequency-location of selectedchirplets.

Next, we discuss the tracking of cetaceans using the estimated dif-ferential delay-Doppler in the estimation phase.

III. EXTENDED KALMAN FILTER-BASED TRACKING

By using the Kalman prediction and update equations [11], [10], wedemonstrate the system and measurement model for tracking basedon differential delay-Doppler. We begin by assuming a linear dy-namic system model, then, the standard discrete-time Kalman stateequation takes the form

Xk+1 Fkxk+uk; (4)

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where, xk is a vector of kinematic components, Uk is the processnoise, and Fk is our (possibly) time-varying state matrix. Since ourapplication will not involve a target which is maneuvering, we adopta constant-velocity motion model. Thus, in three dimensions, xkwill contain 6 components

Xk [Px,kVx,kPy,kVy,kPz,kVz,k] (5)where p,,k and v,,k denote position, and velocity, respectively, alongthe x-axis at time k. The components for the y and z axes are definedin a similar manner. The Newtonian system matrix then assumes ablock diagonal form

FF= O FPO

-O O F(6)

where motion along each coordinate axis evolves independently ac-cording to

F [1 T]

where pi and p are the location of the ijth pair of sensors, A is thewavelength and 11 11 is the Euclidean norm. In (13), hi(Pk) is anormal vector that can be evaluated as

(14)hi (Pk) Pri -PkIPri Pkl

From (12)-(13), we see that the relationship between xk and Zk forour application is nonlinear(i.e., Z = hk (xk)). Thus, we have touse an extended Kalman filter, where the nonlinear measurementfunction hk is linearized about the one-step state prediction Xk Ik 1l.The resulting Jacobian matrix can be written as

Hk = [hk (x)A'x] X=kk -1 (15)

where A,, is the gradient operator expressed as a column vector. Us-ing the definitions of differential delay and Doppler from (12)-(13),we see that Hk will have the following form

(7)

In this case, as long as the intersample interval T is a constant,F and F do not vary with k. For this constant-velocity dynamicsystem, the process noise model Uk changes in the state due to thechanges in the underlying velocity increment sequence. We assumethat {uk } is a zero-mean white Gaussian sequence with known co-variance, E[uiu'] = Q(i -j), where a is the Kronecker deltafunction and Q is a block diagonal

Q 0 0Q = 0 Q 0

Lo 0 o,Since this is a formulation in discrete time, each random accelerationincrement acts upon the state for the sample period T. Q can beevaluated as,

(8)

Arij o OATrij o OAijHk oAd OAd Ac'3OA p___ _Hk PAdij OAdij 0PAyj OAdij OAdij OAdij

op" oV" Opy OVy Op, Ov,

(16)

where the two rows shown correspond to the differential delay-Dopplerpair from the ijth pair of sensors, and all partial derivatives are eval-uated for XkIk -1 as indicated in (15). After some algebra, the fol-lowing equations for the partial derivatives are obtained

OATij,kOp

OAZdij,k_ ni( )n(p)d2v (Pk) AJ(Pk)Dy A

(17)

(18)

(9)T3 T2

Q = 32 2(J2

2

where aou is the variance of the noise sequence modeling the veloc-ity increment process. In the measurement model, we have Zij, kas the set of measurements provided by the ijth pair of sensors attime stance k. Then, the multisensor measurement vector at timek is defined as the concatenation of all the current scans, or Zk =

{Z1,k,... ZM,, where M is the number of differential delay-Doppler involved to track the target. The measurement model forthe standard Kalman filter can then be expressed as

Zk= Hkxk + Wk (10)

where Hk is allowed to vary with time and wk is the measurementnoise sequence. The observation vector Zk for the Kalman filter willconsist of pairs of differential delay and Doppler measurements. Sowe have

Zk = {(ATJ,k, Adl,k), * *, (ATN,k, AdN,k)}

OAdij,k=

2 ( (Pr -Pk)(Prj -Pk)'&p A H,Pr Pkll

1I

HPrj- Pkll(Pr,i -Pk) (Pr,i Pk)' + 1 I)

IIP -Pkll3 IPr,i Pkll(19)

We note that in (17)-(19), the position and velocity vectors wouldbe more accurately written as Pklk,1 and vkjk-1 since they areobtained from the components of the one-step prediction Xklk1.This completes our specification of Hk. For the description of themeasurement noise sequence {Wk }, we assume it is an independentzero-mean Gaussian process with known covariance E[wiw ] =

R(i -j), where R is a block diagonal

-Ri 1...

: *ORRM(1 1)

where (ATij,k, Adij,k) is the differential delay-Doppler measure-ment from the ijth pair of sensors at time k. Ifwe define Pk and vkas the position and velocity vectors, respectively, ofthe target at timek, then the components of Z4 are related to these state componentsby

ATij, k =IlPk Pr,i 11 _IPk Prj 11 (12)

Adi ,k 2 vk (hi (pk) _ hi (Pk)) (13)C C

(20)

and the measurement covariance corresponding to the ijth scan isdefined as

2R [ZATAjRij =

L

(21)

In our experiments, we assume that U'xTi and 2Jad do not varywith i, j. With these definitions for our system and measurementmodels, we can now express the prediction and update equations forour extended Kalman filter[1 1].

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hi (Pk) hi (Pk)

0 2072 07u

Adij

estimated differential-delay5 real differential-delay

O

65- ~ ~ v v ~ :

.10 20 40 60 80 100

5

esti,mated differential-doppler0 1/ \ - real differential-doppler

.5

E

Fig. 2. The received signal by first sensor is approximated by fivechirplets.

IV. SIMULATION AND RESULTS

In a real setting, a whale song is recorded [12] for few minutes andout of that we created a simulated itinerary. We compare the exper-imental results of the simulated motion of a whale at approximatedepth of 50 m with those from our method. We assume an array of20 sensors and inter-element spacing of 100 m towed by a ship. Inevery step the real whale's whistle is approximated by 5 chirplets,thus we have 20 quintet groups of chirplets. In Fig. 2, an approxi-mated signal by means of five chirplets is illustrated. Then the bestpair of chirplets is selected. We consider the first sensor with theother sensors ofthe array (i.e, i = 1, j = {2, .. 20}), we have 190combinations to select the pairs of sensors, and two best chirplts areselected from every pair of groups and differential delay-Doppler,A rij, Adij are estimated by subtracting their time and frequencylocations. In Fig. 4 results of estimating differential delay-Dopplerbetween 1St and 2nd sensor versus real differential delay-doppler isillustrated. Finally the estimated differential delay-doppler is givento the EKF and the target is tracked. In Fig. 4 the simulated trackedmotion of the whale is illustrated versus the real motion.

V. CONCLUSION

In this paper, we introduce a new method to track echo-locatingcetaceans using differential delay-Doppler by a towed array. Ourtracking method is based on EKF by means of chirplet transform.The simulation results based on real data collected from a whaledemonstrate the suitability of our new algorithm to track cetaceansin more realistic scenarios.

VI. REFERENCES

[1] P. Connelly, B. Woodward, D. Goodson, "Tracking a movingacoustic source in a three dimensional space," MTSIIEEE ConfProceed., Oceans, 1997.

[2] T. Ura, R. Bahl, M. Sakata, J. Kojima, T. Fukuchi., et'al,"Acoustic tracking of sperm whales using two sets of hy-drophone array," Int'l symp. on underwater technology, 2004.

[3] W. M. X. Zimmer, M. P. Johnson, A. D'Amico, P. L. Tyack,Combining data from a multisensor tag passive sonar to deter-mine the diving behavior of a sperm whale (Physeter macro-cephalus)," IEEE J of Oceanic Engineering, vol. 28, no. 1,Jan. 2003.

Fig. 3. The differential-delay and differential doppler between 1stand 2nd is estimated.

tracking by EKFE1~~ ~~~~~~~real trackl

Fig. 4. The estimated track by EKF versus real track.

[4] http:Hsolmar.nurc.nato.int/.

[5] J. Cui, W. Wong, "The adaptive chirplet transform and visualevoked potentials, IEEE Trans. on Biomedical Engineering,vol. 53, no. 7, Page(s):1378 - 1384, July 2006.

[6] J. C. O'Neill, P. Flandrin, " Chirp hunting," in Proc. IEEEInt. symp. Time-Frequency Time-Scale Anal., pp. 425428, Oct.1998.

[7] A. Bultan, "A four-parameter atomic decomposition ofchirplets," IEEE Trans. Signal Process., vol. 47, no. 3, pp.731745, Mar. 1999.

[8] R. Gribonval, "Fast ridge pursuit with multiscale dictionary ofgaussian chirps," IEEE Trans. Signal Process., vol. 49, no. 5,pp. 9941001, May 2001.

[9] A. V. Dandawate, G. B. Giannakis "Differential delay-dopplerestimation using second and higher-order ambiguity func-tions," IEE PROCEEDINGS-F, vol. 140, no. 6, Dec. 1993.

[10] S. Herman, P. Moulin, "A particle filtering approach to FM-band passive radar tracking and automatic target recognition,"IEEE Aerospace Conf Proceed., 2002.

[11] Y Bar-Shalom, X. R. Li, "Multitarget-multisensor tracking:principles and techniques." Storrs, CT: YBS Publishing, 1995.

[12] http://tfd. sourceforge.net/.

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