A Spatiotemporal Approah Passive Sound Soure Loalization Pasi Pertilä, Mikko Parviainen, Teemu Korhonen and Ari Visa Institute of Signal Proessing Tampere University of Tehnology, P.O.Box 553, FIN-330, Tampere, Finland Tel: +358-3-35-4798, Fax +358-3-35-4989 E-mail: {pasi.pertila, mikko.p.parviainen, teemu.korhonen, ari.visa }@tut.fi Abstrat The delay between the event and the observation is a fundamental problem in aousti loalization. This fat is aounted for in the presented loalization approah as an additional stage in the applied model. This work onentrates on passive aousti soure loalization from a spatiotemporal viewpoint. The diretion of arrival () estimates are measured over time at spatially separated sensor stations, e.g. mirophone arrays. The estimates are ombined produe soure likelihood in suh a manner that the propagation delays are ompensated. This paper fouses on inorporating the propagation delay model rather than studying the properties of the loalization algorithm itself. The propagation delay orretion is substantial in large area surveillane. I. Introdution In reent years, the need for passive loalization has inreased in surveillane appliations of airports, harbors and industrial omplexes. Aousti loalization an be applied in poor visibility onditions suh as foggy weather and darkness. The term soure loalization embraes determining the diretion and distane of a sound soure relative the observer. The goal of loalization is find out the soure position in a hosen oordinate system. Soure loalization has been widely researhed over the past deades. Still no general and straightforward solutions exist. Loalization methods an be roughly divided in far and near field methods. The far field methods assume that the observed wavefront is planar. Wavefront urvature is assumed in the near field approah. Loalization methods an also be divided in passive and ative methods. The passive methods loalize the sound soure only with the signals emitted by the soure, whereas the ative methods produe the measured energy. This work fouses on passive loalization, but the disussion is also relevant for ative methods. A lass of near field loalization methods are based on time differene of arrival (T) information between mirophones. T between mirophones is the measured differene between signal arrival times the mirophones. T measurement inside a sensor station does not provide information about the signal propagation time the sensor station. However, the soure loation an be determined based on T information [], [2]. T based methods are summarized in [3]. This lass of near field methods loalize a sound soure the intersetion of hyperboli surfaes defined by T information. In this disussion propagation delay refers the propagation time between a soure and a sensor station. methods assume the far field situation [3], [4], [5]. The propagation diretion of a plane wave is alulated and the opposing ver is onsidered the soure diretion estimate. Soure loalization an be performed by ombining the measurements from separate stations [6], [7], [8], [9]. To minimize the required ommuniation bandwidth and omputations, the measurements from a network of sensor stations should be ombined. The interest in this work is in utilizing information in loalization. Initial loation estimate an be used obtain propagation delay information, whih in turn an be used searh orreted values [6]. The initial loation is alulated from the newest measurements of eah array via triangulation. The final loation estimate is alulated from the orreted values and is proposed for moving sound soures. If the sound soure signal is transient the newest estimates may be inorret whih results in a poor initial loation. The iterative orretion attempt may then produe an erroneous estimate of the loation, even if all the arrays detet the signal. Diret loalization methods ombine s without propagation delays alulate the soure loation [7]. Dommermuth presented a loalization sheme that searhes the spae along a single observation line find the maximum likelihood soure loation with propagation delay orretions for eah sensor station [9]. Fig. illustrates a model for sound soure loalization used in the presented approah. The fous in this work is in studying the effet of stage 5, that is, applying the propagation delay information the sound soure loation estimation. This paper is organized as follows. In Setion 2 the spae-time nature of aousti event observation is disussed. Setion 3 overs a soure likelihood estimation proedure for loalization. Loalization with estimars
τ N+2 τ N+ τ N τ, I x p p2 rs in transmitted signal of orret estimates ates using 2 stations. Stage 5 disabled Stage 5 enabled multipliation far 2 2 2 4 2 6 2 8 2 0 2 2 2 4 τ τ5 τ4 τ3 τ2 τ τ0.0. Emission stage 2. Propagation t t 2 t i 3. Reeiver stage Sensor station Sensor station 2 Sensor station i Any estimar 4. Ver Conversion k ( t ) Cartesian Ver k 2 ( t ) Cartesian Ver k i ( t ) Cartesian Ver 5. Spatiotemporal proessing A) Generation of spatiotemporal representation of aousti events B) t t 2 Propagation time delay alulation Sensor station loations p,2,, N t i Hypothetial soure position r s Soure likelihood information l ( r s) 6. Soure loalization Algorithm for soure loation estimation Soure loation estimate r^s Fig.. Sound soure loalization model is onsidered. Simulation results are displayed in Setion 4. Setion 5 and 6 onlude the disussion. A. Loalization Model Overview Let us present the model briefly (Fig. ). In stage an ative omnidiretional sound soure emits waves in an isotropi environment. Stage 2 models the propagation delay when the wavefront travels wards the spatially separated sensor stations. In a far field situation the propagation delay an range from a fration of a seond several seonds, and thus it should be onsidered. In stage 3 the sound waves are reeived by the network of sensor stations. The diretion of the sound soure is alulated in eah station. An individual sensor station an be, for instane, a beamformer system [5]. In fat, the sensor network an onsist of any type of aousti sensor stations that produe values. Note that some methods may be based on T in stage 3. The T onept should not be mixed with the propagation delay between the soure and the sensor station formed in stage 2 and onsidered in stage 5. Possible oherene of signals between sensor stations an be used estimate the propagation time differenes and utilized in soure loalization [0]. In the presented approah oherene between sensor stations is not assumed and therefore the propagation time differenes between sensor stations an not be measured. When the distane between the sensors inreases [3] the oherene between the sensors dereases. Eah sensor station produes a estimate at every measurement time interval. The stages 4 and 5 in Fig. are optional. Loalization is possible using diretly the output of stage 3 as in [7]. In some systems the soure diretion is given in Cartesian form as in [4]. Instead of horizontal and elevation angle there is a unit ver of equivalent information. This work fouses on stage 5 where the measured s are spatially and temporally ombined. The ombination of spatial information for soure loalization has been studied by Aarabi in []. Aarabi s artile onentrates on loalization in near field, and the propagation delay in room sale is relatively small. The presented approah is similar that of Dommermuth s [9] but represents the aousti events in a spaetime oordinate system, also known as Minkowski spae. This spatiotemporal approah inludes the propagation delays and therefore utilizes appropriate past estimates for eah sensor station. It must be noted that the presented approah is not an algorithm for solving the soure loation, but rather a method for ombining spatially and temporally separate measurements produe a soure likelihood distribution. The final stage of the soure loalization is stage 6, where the likelihood distribution is searhed for possible sound soure. In this paper, an exhaustive searh algorithm is used in stage 6 evaluate the signifiane of stage 5. II. The Spatiotemporal Approah The observation of aousti events an be depited with spae-time diagrams [2], whih are often used illustrate the eletromagneti propagation model. A twodimensional ase is presented in Fig. 2. The horizontal and vertial axis represent the spatial oordinate and time, respetively. An event is generated in the figure at time at point r s. The information of the event travels all diretions at a onstant speed. The large dots represent the oordinates of the information at disrete time instants. The dots form a triangle when onneted along the line of propagation. This triangle depits the spae-time oordinates of the event information. The sensor stations reeiving information are loated at p and p 2. The information in the studied ase is the diretion of the arriving wavefront. The reeption time of an event depends on the loation of the event and reeivers. The losest sensor station p reeives the
2 2 2 4.0 τ time emission reeption p r s p 2 spae Fig. 2. Spae-time representation of an aousti event. The axis are spatial oordinate x and time τ. A sound soure loated at r s emits sound waves at time. The sound waves propagate from the soure along arrows at a onstant speed. The waves reah sensor stations at p and p 2 at different time instants and, respetively. The soure an be loalized only when both sensor stations have reeived the information (at time ). This applies all methods. information first at time. The other sensor station p 2 reeives the same information at time. After this the event an be loalized in theory. Note that the event is generated at time but before time no information is available the sensors due propagation delay. If the sensors produe information every disrete time instant, the first station outputs the orret value at time and the seond station p 2 produes the orret value at time. The event loalization via triangulation fails, if the propagation delay is not onsidered, i.e. only the newest values are used. In the spatiotemporal approah, the appropriate values are used for loalization. This means that the propagation delay of the soure emission is inluded in the estimation proedure. The apex angle of the triangle in Fig. 2 broadens as the propagation speed in the medium inreases. In some eletromagneti appliations there is no need ompensate the propagation speed, beause the effet of propagation delay an be onsidered insignifiant. This orresponds a situation where the apex angle of the triangle is so broad that the triangle approahes a horizontal line. Indeed, if no propagation delay assumption is made, information travels impliitly at infinite speed. III. Sound Soure Loalization It is assumed that the reeived wavefront approximates a plane wave at the sensor stations, thus fulfilling the far field assumption disussed above. This enables the estimation of soure diretion at eah station. Any method produing estimates an be used. It is then assumed that the sound waves have traveled the sensor stations at onstant speed in an isotropi aousti environment. A ase with sensor stations produing single estimates is studied and shown how the approah an be applied. A estimate (e.g. azimuth and elevation) produed by any method at disrete time t an be mapped τ x Cartesian ver k i (t) = [ k x(i) (t), k y(i) (t), k z(i) (t) ] T, as in stage 4 in Fig.. A measurement ver k i points the opposite diretion of the propagating wavefront. The sensor stations are loated at p i, i =,..., N, where N is the number of stations. The ase N = is omitted. The time between two adjaent estimates is termed K and the distane between the estimates is K, see Fig. 3. The value of K affets the resolution of Minkowski spae. The resolution also depends on the station loations. Propagation delays from the estimated soure loation sensor station i are quantized values used index the vers: [ ] [ ] rs p i ri t i = Q = Q, () where Q( ) is the quantization operar with a quantization step of K. The hypothetial soure position is noted as r s and station--soure ver as r i = r s p i. Equation () represents stage 5B, see Fig.. Note that the hypothetial soure position r s determines the quantized propagation time delays ( t i ) for eah sensor station. Several riteria exist for determining soure loation estimate based only on values. Hawkes and Nehorai utilize the weighted sum of the minimum squared distanes between the hypothetial soure position and the lines determined by eah estimate [7]. In this paper, the riterion is the angle deviation between the estimate k i and the station--soure ver r i. The objetive is find a point in spae that minimizes the sum of these angle deviations. The spae-time approah is that an appropriately hosen estimate k(t + t) is used from eah sensor station instead of the most reent one k(t + t last ), where t represents a disrete time instant and t last is the time passed after t. The angle deviation minimization an be formulated as a likelihood funtion of soure loation r s at disrete time t: N N l(r s ) = k i (t + t i ) r i = e i, (2) i= where e i [, ] is the result of the dot produt and ( ) is the unit ver of ( ). Propagation delays t i are defined in (). The likelihood funtion of (2) is a sum of e i and is depited as stage 5A in Fig.. Geometrially, the smaller the sum of angle deviations (i.e. greater the sum of dot produts) between measured s and station--soure vers, the greater the likelihood. Grid based or iterative searh methods an be used in the estimation of (2), with appropriate instability onsiderations. A grid based exhaustive searh method is given in Algorithm. The initial requirement is that enough sensor data has been reeived and sred for extrating the required values. If there is not enough data available i=
2 8 2 0 2 2 2 4 τ τ.0 p k p 2 r e e 2 r 2 k 2 K r s r N e N Fig. 3. Soure loation probability alulation. The likelihood of sound soure loated at r s is evaluated by summing e,..., e N. p i denotes loation of sensor station i. Note that propagation delays have be taken in aount. The distane between two adjaent estimates is K. in line 7 of the algorithm, the system an wait for the sensor station reeive more data. IV. Results k N p N τ τ Ratio of orret estimates.0 Corret observations at right oordinates using 2 stations. Stage 5 disabled Stage 5 enabled 2 2 2 4 2 6 2 8 2 0 2 2 2 4 000 m 000 m size area multipliation far Fig. 4. The effets of using orret propagation delays with reduing area size are displayed. Mean and standard deviation of normalized values of orret soure loation estimate ratios are presented. The size of the area dereases along x-axis, and the amount of grid ells was fixed. Two sensor stations used in loalization were uniformly distributed over the area. The signifiane of the propagation delay is greater with large area sizes. The input signal this system onsisted of sequential bloks of length T and was of form: The effets of inluding orret propagation delays between spatially separated sensor stations were studied. The proposed riterion for sound soure likelihood estimation was simulated for a stationary soure. The soure was not audible at all time instants. In real world this may be due low SNR onditions, or a property of the soure. The purpose was find out the behavior of likelihood estimation, when signal propagation delays are onsidered in the estimation proess. Two ways of handling temporal information were evaluated. In the first approah, propagation delays were omitted, therefore the speed of sound was impliitly assumed infinite, see Setion 2. This orresponds omitting stage 5 in Fig.. In the proposed method, propagation delays were obtained from () (in stage 5B), based on known propagation speed. The loation of the sound soure affets the loalization performane. Therefore the produing sensor stations were uniformly distributed over a 000 m 000 m area, evaluate the average performane. The soure was loated in the enter of the area. Algorithm Soure maximum likelihood exhaustive searh : selet time value t 2: while searh area loations r s remain do 3: likelihood l(r s ) 0 4: for station i = N do 5: station--soure ver r i r s p i 6: alulate t i using Eq. () 7: extrat appropriate measurement k i (t + t i ) 8: alulate e i using Eq. (2) 9: l(r s ) l(r s ) + e i 0: end for : end while 2: ˆr s max rs l(r s ) { rs, t mod T < t S i (t) = pure v U(p i, σ 2, (3) I), t mod T t pure where i =,..., N, U( ) denotes uniform distribution with zero mean and ovariane matrix of σ 2 I. In Fig., S i (t) is the output of stage 4. Note that proper k i an be derived from r s in (3). Eah blok was divided in a pure signal part, length t pure and pure noise part, length T t pure. The signals were delayed depending on the distane from the soure. The sound field was assumed isotropi. The noise signal, S i (t) = v, was independent between the stations. The speed of sound was fixed 343 m/s. Time between two adjaent non-overlapping windows, termed K (see Fig. 3), was 0.02 s, the tal length of all signal and noise bloks was set 20 s and blok length was assigned a value of s, see (3). The simulations onsisted of 000 repetitions. The area was divided in equal size ells. A grid with 20 m 20 m ell size was used for soure likelihood estimation. The loalization estimate was orret if the global maximum of the grid was deteted in the soure loation. This inluded also false detetions, where the soure was not present but the system still reported a detetion due noise. The methods were ompared with different parameters. The hosen parameter set orresponds realisti onditions when propagation delay orretion beomes signifiant. In Fig. 4, the proportion of the pure signal in one blok was fixed 50 % with a network of two sensor stations. The size of the simulation area dereases along x-axis, whih indiates the area in m 2 (original area multiplied by the far). The smallest area size far /2 4 orresponds approximately a 4 m 4 m room. The amount of grid ells was fixed 2500.
V. Disussion Traditional loalization methods do not onsider the propagation delay. The use of propagation delay has greater signifiane with large areas ompared room sale environments, see Fig. 4. measurements are alulated from sequential windows of data samples, separated by K seonds. If the area size is small enough, the time it takes a sound wave travel aross the area is more than the time required alulate one estimate. In this ase no propagation time orretion is neessary. Then the loalization an only use the urrent value, beause () is negligible regardless of r i. This is the ase in room sale environments. In onlusion, let an important property of the presented model be pointed out. It is relatively easy inlude additional information onerning the aousti properties of the field e.g. information about aousti shadow areas and audibility onditions. This extra information an be thought as a probability value for a given point in the field, and an be inluded in the likelihood funtion (2). However, the modeling of these fars may not be trivial. VI. Conlusions The propagation delay orrupts estimates when the soure distane the sensors beomes signifiant. This paper presents a solution for dealing with this problem. A spatiotemporal approah sound soure loalization was presented. Simulation results were given illustrate the signifiane of the method. In the spatiotemporal model, the past information observed by sensor stations, or aousti arrays, is utilized in loalization of a sound soure. The initial results are promising, as the method improves loalization results of a stationary soure. The work will be extended wards real data measurements and studying the atual loalization performane. Also possibilities loalize a moving soure with the presented approah will be studied, as the urrent work foused on a stationary sound soure. Referenes [] B. Friedlander, A passive loalization algorithm and its aurany analysis, IEEE Journal of Oeani Engineering, vol. 2, no., pp. 234 245, 987. [2] J. O. Smith and J. S. Abel, The spherial interpolation method of soure loalization, IEEE Journal of Oeani Engineering, vol. 2, no., pp. 246 252, 987. [3] M. Brandstein and D. Ward, Eds., Mirophone Arrays, hapter 8, and 4, Springer-Verlag, 200. [4] J. Yli-Hietanen, K. Kalliojärvi, and J. Asla, Low-omplexity angle of arrival estimation of wideband signals using small arrays, in 8th IEEE Signal Proessing Workshop on Statistial Signal and Array Proessing (SSAP 96), 996, pp. 09 3. [5] B. D. Van Veen and K. M. Bukley, Beamforming: A Versatile Approah Spatial Filtering, IEEE ASSP Magazine, vol. 5, no. 2, pp. 4 24, 988. [6] R. Blumrih and J. Altmann, Medium-range loalisation of airraft via triangulation, Applied Aoustis, vol. 6, no., pp. 65 82, 2000. [7] M. Hawkes and A. Nehorai, Wideband Soure Loalization Using a Distributed Aousti Ver-Sensor Array, IEEE Transations on Signal Proessing, vol. 5, no. 6, pp. 479 49, 2003. [8] L. M. Kaplan, Q. Le, and P. Molnár, Maximum Likelihood Methods for Bearings-Only Target Loalization, in Proeedings of the 200 IEEE International Conferene on Aoustis, Speeh, and Signal Proessing (ICASSP 0), 200, vol. 5, pp. 300 3004. [9] F. M. Dommermuth, A simple proedure for traking fast maneuvering airraft using spatially distributed aousti sensors, J. Aoust. So. Am., vol. 4, no. 82, pp. 48 424, 987. [0] R. J. Kozik and B. M. Sadler, Distributed soure loalization with multiple sensor arrays and frequeny-seletive spatial oherene, in Proeedings of the Tenth IEEE Workshop on Statistial Signal and Array Proessing, 2000, pp. 49 423. [] P. Aarabi, The Fusion of Distributed Mirophone Arrays for Sound Loalization, EURASIP Journal on Applied Signal Proessing, vol. 4, pp. 338 347, 2003. [2] F. W. Sears and R. W. Brehme, Introdution the Theory of Relativity, hapter 3, p. 46, Addison-Wesley, 968.