Acoustic Source Localization and Discrimination in Urban Environments

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1 Acoustic Source Localization and Discriination in Urban Environents Manish Kushwaha, Xenoon Koutsouos, Peter Volgyesi and Aos Ledeczi Institute or Sotware Integrated Systes (ISIS) Departent o Electrical Engineering and Coputer Science Vanderbilt University Nashville, TN 3735, USA anish.ushwaha@vanderbilt.edu Abstract Collaborative localization and discriination o acoustic sources is an iportant proble or onitoring urban environents. Acoustic source localization typically is perored using either signal-based approaches that rely on transission o raw acoustic data and are not suitable or resource-constrained wireless sensor networs or eature-based ethods that result in degraded accuracy, especially or ultiple targets. In this paper, we present a eature-based localization and discriination approach or ultiple acoustic sources using wireless sensor networs that uses beaor and power spectral density data ro each sensor. Our approach utilizes a graphical odel or estiating the position o the sources as well as their undaental and doinant haronic requencies. We present siulation and experiental results that show iproveent in the localization accuracy and target discriination. Our experiental results are obtained using otes equipped with icrophone arrays and an onboard FPGA or coputing the beaor and the power spectral density. 1. Keywords: Acoustic source localization, wireless sensor networs, Bayesian estiation, eature-level usion. 1 Introduction Acoustic source localization is an iportant proble in any diverse applications such as ilitary surveillance and reconnaissance, underwater acoustics, seisic reote sensing, counications, and environental and wildlie habitat onitoring. Recently, ore innovative applications such as sart video-conerencing, ultiodal sensor usion and target tracing have been proposed to utilize ultiodal source localization. In wireless sensor networs (WSNs), collaborative source localization is needed, where the objective is to estiate the positions o ultiple sources by usion o observations ro ultiple sensors. There are two 1 This wor is partially supported by ARO MURI W911NF broad classes o ethods or collaborative source localization. The irst class o approaches, where the estiation is done by usion o the sapled signals, is called signal-based, orsignal-level usion ethods. The second class o approaches, where signal eatures are extracted at each sensor and estiation is done by usion o the extracted eatures collected ro all the sensors, is called eature-based, oreature-level usion ethods. In this paper, we present a eature-level usion ethod or collaborative source localization o ultiple acoustic sources in WSNs. We use icrophone arrays as sensors that copute beaors and estiate power spectral density (PSD) as the signal eatures. The advantage o using the beaor over signal energy is that the beaor captures the angular variation o the signal energy, which results in better localization resolution. The use o PSD as another signal eature allows us to identiy ultiple sources under our haronic signal assuption. The target tracing application in 1] deonstrated that the counication bandwidth available in sensor networs is suicient to support wireless transissions o such eatures. Several signal-based ethods using a icrophone array or source localization have been proposed ]. These approaches use tie delay o arrival (TDOA) or direction o arrival (DOA) estiation, beaoring, 3] and axiu lielihood estiation 4]. The signal-based ethods are not suited or WSNs because they require transission o the raw signal. On the other hand, the eature-based ethods are appropriate or WSNs due to its lower bandwidth and power requireents. An exaple o the eature-based ethod is energy-based localization (EBL), where signal energy is taen as the eature. EBL has been solved using various least squares 5, 6] and axiu lielihood 7] orulations. EBL suers ro poor localization resolution or ultiple targets, where the resolution is deined as the ability o the localization algorith to discriinate two closely spaced targets. Localization algoriths based on least squares operate on a strict Gaussian noise assuption and are

2 not extensible to ultiple sources; while those based on axiu lielihood are not extensible to tracing applications where data association across tie becoes an issue. A Bayesian approach or source localization can handle non-gaussianity and ultiple sources, both stationary and oving. Several approaches based on graphical odels 8] and Bayesian estiation 9, 10] have been proposed or ultiple target localization and tracing. A graphical odel based approach or audiovisual object tracing is presented in 8] that cobines the audio and video data. A Bayesian approach or tracing the DOA o ultiple targets using a passive sensor array is presented in 9]. Another Bayesian approach or ultiple target detection and tracing or unnown nuber o targets, and a particle ilter-based algoriths are proposed in 10]. An alternative to Bayesian statistics is Finite Set Statistics (FISST), which treats the ultitarget state and ultiple observations as inite sets. An approxiate ultitarget tracing approach based on FISST, called the Probability Hypothesis Density (PHD) ilter, is proposed in 11]. We solve the localization proble using a graphical odel that is generalization o Bayesian estiation. Graphical odels provide a copact representation o joint probability density and acilitate the actorization o joint density into conditional densities 1]. Graphical odels require generative odels that describe the observed data in ters o the observation process and the hidden state variables. We present generative odels or beaor and PSD data. The proble is divided into two steps as source separation and source localization. The idea is to separate the sources in requency doain using the received PSD ro the sensors, and then use the separated sources or localization. We propose a axiu lielihood (ML) estiation ethod or source separation and Bayesian estiation or localization. We present siulation results or ultiple source localization in a grid sensor networ. Our algorith is able to achieve an average o 5 c localization error or three targets, 8 c or two targets, and less than 5 c or single target in a sensor networ o our sensors. We are able to distinguish between two targets as close as 50 c using our algorith. Our results show that as the separation between targets increases, our algorith is able to achieve higher localization accuracy, coparable to single target localization. Finally, we present results or an outdoor experiental setup with icaz sensor nodes and real acoustic sources. The rest o the paper is organized as ollows. In Section, we present the acoustic source odel and the acoustic sensor odel. Section 3 describes the graphical odel. Sections 4 and 5 describe the source separation and source localization, respectively. In Section 6, we present the Gibbs sapler and the initialization strategy. We present results or various siulation scenarios in Section 7, and the outdoor experient setup and results in Section 8. We conclude in Section 9. Source & Sensor Models Consider a wireless sensor networ o K acoustic sensors in a planar ield. Each acoustic sensor is a icrophone array with N ic icrophones each. Consider M ar-ield stationary acoustic sources coplanar with the sensor networ. The acoustic waveront incident on the sensors is assued to be planar or ar-ield sources. Each sensor receives the signal and runs siple signal processing algoriths to copute the beaor and acoustic PSD. The goal o this wor is to estiate the D position o all the sources given the beaor and the PSD ro all sensors. Acoustic Source Model The ain assuptions ade in this paper or acoustic sources are that they are (1) stationary point sources, () eitting stationary signals, (3) the source signals are haronic, and (4) the cross-correlation between two source signals is negligible copared to the signal autocorrelations. Haronic signals consist o a undaental requency, also called the irst haronic, and other higher-order haronic requencies that are ultiples o the undaental requency. The energy o the signal is contained in these haronic requencies only. The haronic source assuption is satisied by a wide variety o acoustic sources 13]. In general, any acoustic signal originating due to the vibrations ro rotating achinery will have an haronic structure. The state or the th acoustic source is given by, (1) the position, x () = x (),y ()] T, () the undaental requency, ω (), and (3) the energies in the haronic ] T requencies, ψ () = ψ () 1,ψ (),,ψ () H,whereH is the nuber o haronic requencies. Acoustic Sensor Model The intensity o an acoustic signal eitted oni-directionally ro a point sound source attenuates at a rate that is inversely proportional to the distance ro the source 7]. The discrete signal received at the p th icrophone is given by r p n] = =1 d 0 x p x () s() n τ () p ]+w p n] (1) or saples n =1,,L,whereLis the length o the acoustic signal, M is the nuber o sources, w p n] is white Gaussian easureent noise such that w p n] N (0,σw ), s() n] is the intensity o the th source easured at a reerence distance d 0 ro that source, and τ p () is the propagation delay o the acoustic signal ro the th source to the p th icrophone. The icrophone and source positions are denoted by x p and x (), respectively. We deine the ultiplicative ter in

3 Equation (1) as the attenuation actor, λ () p = d 0 / x p x (). λ () p,givenby, source 1 source 60 both sources Beaoring is a signal processing algorith or DOA estiation o a signal source. In a typical delayand-su single source beaorer, the D sensing region is discretized into directions, or beas as α = i π Q, where i =0,,Q 1andQ is the nuber o beas. The beaorer coputes the energy o the reconstructed signal at each bea direction. This is acheived by delaying and suing the indiviual icrophone signals. The bea energy is given by angle (degree) (a) B(α) = L n=1 Nic p=1 r p n + t pq (α)]] () PSD (db) where α is the bea angle, r p ] is the received signal at the p th icrophone, q is the index o a reerence icrophone, and t pq (α) is the relative tie delay or the p th icrophone with respect to the reerence icrophone q, givenby,t pq (α) =d pq cos(α β pq ) s /C, whered pq and β pq are the distance and angle between the p th and q th icrophones, and s and C are signal sapling rate and speed o sound, respectively. Bea energies are coputed or each o the beas, and are collectively called the beaor. The bea with axiu energy indicates the DOA o the acoustic source. In case o ultiple sources, there ight be ultiple peas where the axiu pea would indicate the DOA o the highest energy source. Figure 1(a) shows a beaor or two acoustic sources. Advances in sensor networ hardware and and FPGA integration has allowed us to ipleent real-tie beaoring on icaz sensor otes 1]. Acoustic PSD estiation is the estiation o the spectru o the received acoustic signal, which describes how the power o the signal is distributed with requency. We estiate the PSD as the agnitude o the discrete Fourier transor (DFT) o the signal. The PSD estiate can be written as requency (Hz) (b) Figure 1: (a) Acoustic Beaors; The beaors or single sources clearly show peas at the source location but the beaor when both sources are present does not show two peas. (b) Power spectral density (PSD); The highest PSD values are shown as epty circles. The PSD is copactly represented as pairs o the highest PSD values and corresponding requencies. 3 Graphical Model Overview Source separation and localization o ultiple sources is perored using the graphical odel shown in Figure. The nodes with clear bacgrounds denote hidden K θ x λ ω ψ K M P (ω) =Y (ω) Y (ω) (3) B P where Y (ω) = FFT(r, N FFT ) is the discrete Fourier transor o the signal rn], N FFT is the length o the transor, and Y (ω) is the coplex conjugate o the transor. For real-valued signals, the PSD is real and syetric, hence we need to store only hal o the spectral density. In our ipleentation, we represent the spectral densities as the requency power pairs, (ω j,ψ j ), or the N PSD requencies with the highest power values. Figure 1(b) shows an acoustic PSD estiate or a received signal when two haronic sources are present. Figure : Graphical odel (plate notation is used to represent the repetition o rando variables). state variables; x (),ω (),ψ () denote source position, undaental requency and haronic energies or the th source, respectively. The nodes with shaded bacgrounds denote observed variables; B and P denote the beaor and the PSD received at th sensor, respectively. Finally, the nodes with dotted outlines denote unctions o rando variables, or auxiliary rando

4 variables, that capture the unctional dependence o the observed variables on the hidden variables. These variables will be utilized in the generative odels or the observed variables. The two auxiliary variables shown in the graphical odel are the angle θ () and the attenuation actor λ (). We peror ultiple source localization in two steps. First, we use the PSD data only to separate the sources. Source separation, in our proble, reers to separating the PSDs o the sources. For haronic sources, estiation o undaental requencies is suicient or source separation, because all the doinant requencies in the signal are ultiples o the undaental requency. A ML estiation ethod is used or undaental requency estiation. The ML estiate is independent o the source location, which is intuitive because the doinant requencies in the source signal are independent o the source location, as long as the source and sensor are stationary. We will support this intuition in next section via derivation o ML solution. In second step, we use the beaor data and the separated source PSDs to localize all sources. We chose to peror ultiple source localization in two steps instead o joint estiation because o the ollowing two reasons, (1) estiation in two steps has lower coputational coplexity than joint estiation, and () during the siulations, we realized that the lielihood sensitivity or source separation and localization are dierent. In Monte Carlo context, joint estiation ight cause slower convergence, and ay require a large nuber o saples. Moreover, as entioned earlier, the ML estiate or source undaental requencies is independent o the source locations. 4 Source Separation An ML estiation ethod is presented or source separation. We begin by presenting the generative odel and lielihood unction or PSD data. We also present a result showing that the lielihood unction at ML estiate o haronic energies is independent o source positions. Generative Model or PSD Data. sources, the PSD can be given by P () s (ω) = H h=1 For haronic ψ () h δ(ω hω () ) (4) where =1,,M are source indices, ω is the requency, ω () is the undaental requency, ψ () h is the energy in the h th haronic, H is the nuber o haronics, and δ( ) is the Dirac delta unction. Using Equation (4), we derive a generative odel or the PSD data received at a sensor node. Following proposition states the generative odel or the PSD data. Proposition 1. For an arbitrary nuber o acoustic source signals, the power spectral density o the signal received at a sensor is given by P(ω) = =1 n=1 λ () λ (n) ( P () s cos(φ () (ω) Φ (n) (ω)) (ω)p (n) (ω) s ) 1 (5) where M is the nuber o sources, λ () is the attenuation actor, and Φ () (ω) is the phase spectral density given by, Φ () (ω) =φ () x () x s ω/c, where φ () is the phase o the source signal, x () and x s are the positions o the source and the sensor, respectively. The proo or the proposition is given in 14]. Since we do not aintain the phase o the signal in the source odel (see Section ), we assue all the phases to be norally distributed with equal ean. The expected value o the cosine o the dierence o two norally distributed angles is one, i.e. Ecos(Φ i Φ j )] = 1. Using this, Equation (5) becoes M ( ] 1/ P(ω) = λ () P (ω)) () (6) =1 Data Lielihood. Using Equation (6), the negative log-lielihood or PSD data at the th sensor is deined as l (Ω, Ψ, X) = 1 σp P (ω j ) P (ω j ) ω j where Ω = ψ () = ω (1) ψ () 1 ψ () H ] T ω (M), Ψ = ψ (1) ψ (M)] T, ] T,andX = x (1) x (M)] T. Proposition. Lielihood or PSD data at ML estiate o haronic energies is a unction o source undaental requencies only and is independent o source positions. Matheatically, l (Ω, Ψ ML, X) =l (Ω, X) =l (Ω ) (7) Proo. The axiu lielihood estiate o Ω, Ψ, X] T can be obtained by iniizing the lielihood, l (Ω, Ψ, X)/ ψ () h = 0. This leads to P (hω () )=P (hω () )= where ψ (j) h j = I the requency hω () { > 0 i hj = hω () 0 otherwise. j λ (j) ψ(j) /ω (j) h j 1/ Z (8) is shared by M sources (or the

5 nuber o nonzero ψ (j) h j is M ), then Equation (8) becoes M P (hω () )= λ (j) 1/ ψ(j) h j (9) I we assue the energy contribution o all the sources to be sae, i.e. λ (j) 1/ ψ(j) h j = ψh,orj =1,,M,we have P (hω () )= ( M ) ψh = M ψh = M () λ rearranging Equation (10), we have j ψ () h (10) ψ () ML P (hω () ) h = M λ () (11) Substituting the ML estiate or the energies (Equation (11)) in the negative log-lielihood (Equation (7)), we have a odiied negative log-lielihood l (Ω, ˆΨ ML, X) =l (Ω, X) = P (ω j ) P(ω j ) ω j H + P (ω j ) P(ω j ) ω j H where H is the haronic set, which is the set o all haronic requencies or all sources, H = T ω (), ω (), ]. The value o generative odel P is zero at the requencies not in the haronic set, while it is exactly equal to the observed PSD at the requencies in the haronic set. Hence l (Ω, X) = (P (ω j )) (1) ω j H Equation (1) is the negative log-lielihood with the constraint o Equation (11) iposed. Equation (1) iplies that the odiied lielihood at the ML estiate o energies is independent o the source locations l (Ω, Ψ ML, X) =l (Ω, X) =l (Ω ) Hence, according to proposition, source separation can be perored independent o source localization. The ull negative log-lielihood or all sensors, l (Ω )is deined as l (Ω )= 1 K l K (Ω ) =1 Thus, the ML estiation o the undaental requencies can be obtained by iniizing l (Ω ) ˆΩ ML =argin Ω l (Ω ) (13) Since an exact ML estiation ethod or Equation (13) is not available we will use a Monte Carlo ethod described in Section 6 or estiation. 5 Source Localization Source localization is perored by Bayesian estiation in the graphical odel shown in Figure, and taing the axiu a-posteriori (MAP) estiate o the source positions. The posterior, p(x B) o the source positions at the ML estiates or source undaental requencies and haronic energies given the beaor data, is ollowing p(x B) ˆΩ ML p(b X, ˆΩ ML, ˆΨ ML )p(x) (14) where p(b X,, ˆΨ ML ) is the lielihood unction or beaor data. The lielihood unction requires a generative odel or the beaor data. In this section, we begin by presenting the generative odel and three results pertaining to the generative odel. Finally, we present the lielihood and MAP estiation. Generative Model or Beaor. We start by developing a generative odel or a beaor or a twoicrophone array, single-source case. We will show that the beaor or an arbitrary icrophone array and an arbitrary nuber o sources can be coposed ro the siple two-icrophone array, single-source case. Proposition 3. Consider a icrophone pair separated by distance d and the angle between the x-axis and the line joining the icrophones is β. For an acoustic source at angle θ and range r with power spectral density P (ω), the beaor B at the icrophone pair is given by B(α) =λ (R ss (0) + R ss (κ α )) + R η (0) (15) where R ss (τ) =FFT 1 (P (ω)) or τ, + ] is the autocorrelation o the source signal, R ss (0) is the signal energy, R η (0) is the noise energy, λ is the attenuation actor, and κ α = d(cos(α β) cos(θ β)) s /C, where α 0, π] is the bea angle, s and C are sapling requency and speed o sound, respectively. The proo or the proposition is given in 14]. For an arbitrary icrophone-array, the generative odel can be extended using the odel in Equation (15). Proposition 4. For an arbitrary icrophone-array o N ic icrophones, the beaor is expressed in ters

6 o pairwise beaors as The MCMC algoriths are ore eicient in highdiensions than Monte Carlo (MC) ethods, also B(α) = B i,j (α) N ic (N ic )(R η (0)+λ R ss (0)) called particle ilters, due to the act that the saples in (i,j) pa MC ethods are drawn independently while in saples (16) where pa is the set o all icrophone pairs, R ss (0) is the signal energy, R η (0) is the noise energy, λ is the attenuation actor, and B i,j is beaor or the icrophone pair (i, j) (Equation (15)). in MCMC are drawn ro a Marov chain. The Gibbs sapler wors on the idea that while the joint probability density is too coplex to draw saples ro directly, the univariate conditional densities the density when all but one o the rando variables are assigned ixed values are easier to saple. The proo or the proposition is given in 14]. For The choice o algorith to saple ro the univariate density deterines the speed and convergence o an arbitrary nuber o acoustic source, the generative odel can be extended using the odel in Equation the Gibbs sapler. We selected slice sapling 15] or (16). its robustness in paraeters such as step size and applicability toward non-log-concave densities, which is the Proposition 5. For an arbitrary nuber o uncorrelated acoustic sources M, the beaor is expressed in case in our proble. ters o single source beaors as The lielihood in Equation (13) and the posterior density in Equation (19) are sapled using the Gibbs sapler to the estiate the ML estiate and MAP B(α) = B (α) N ic (M 1)R η (0) (17) estiate, respectively. =1 where R η (0) is the noise energy and B is the beaor or th acoustic source (Equation (16)). The proo or the proposition is given in 14]. A general or o generative odel or beaor or arbitrary icrophone array and arbitrary nuber o sources can be obtained by substituting Equations (15) and (16) into Equation (17), which gives ollowing B(α) = =1 λ () + N ic M =1 (i,j) P R () ss (κ α) λ () R () ss (0) + N icr η (0) (18) Data Lielihood. Using Equation (18), the negative log-lielihood or beaor data is given as ln p(b X) =l (X) = 1 σb B (α) B (α) The MAP estiate o the source positions is given by ˆX MAP =argaxp(x B) (19) X Again, since an exact estiation ethod or Equation (19) is not available we will use the Monte Carlo ethod described in Section 6 or MAP estiation. 6 Bayesian Estiation Due to the non-linearity o the observation odel and non-gaussianity o the probability densities, the use o exact ethods or state estiation is not possible. We use Marov Chain Monte Carlo (MCMC) sapling algoriths, speciically Gibbs sapling and slice sapling 15] or approxiate state estiation. α Initialization Strategy. A good initialization o the state will ensure aster convergence o the Gibbs sapler. For source separation, the undaental requencies, Ω are initialized by doing a coarse resolution search to iniize the lielihood in Equation (13). During the source localization step, the source positions are initialized using one o the ollowing ethods, (1) the least-squares ethod or a single target, siilar to one described in 6], or () the weighted-average o the sensor positions. Finally, the haronic energies are initialized according to Equation (11). 7 Siulation Results The scenarios considered here involve a wireless sensor networ deployed in a grid topology. Typically, localization o an acoustic source is perored by the sensors that are close to the source because the signal-toratio (SNR) is lower or arther sensors. For this reason, we assue that even in a large sensor networ, a source will be surrounded by a sall nuber o sensors that will participate in the localization o that source. Siulation Setup and Paraeters. We consider a sall sensor networ o 4 acoustic sensors arranged in agridosize10 5, wherein each sensor can detect all the sources. We siulate the sources according the acoustic source odel (Section ), siulate the data according to the observation process (Section ), and inally chec the output o source localization against the ground truth. The perorance o the approach is easured in ters o localization error, which is deined as the root ean square (RMS) position error averaged over all the sources E = 1 M x () x () =1

7 Table 1: Paraeters used in siulations Sapling requency ( s ) 100Hz Speed o sound (C) 350 /sec Downsapling actor 5 Audio data length (tie) 1sec Maxiu haronic requency (ω ax ) 1000Hz SNR (db) 5 Nuber o beas 36 Size o Fourier transor (N FFT ) 4000 Nuber o Gibbs saple 40 We deployed a sall sensor networ o 3 icaz-based acoustic sensor nodes in an equilateral triangle o side length (15t). Figure 4(a) shows the experiental setup and the location o the sources. We collected the sensor data and ran the algorith oline. Figure 4(b) shows the localization error with source separation. The results ollow the siilar trend as that in Figure 3(c). For saller source separations, the average error reains low but the algorith is not able to disabiguate the two sources. For larger separations, the localization error decreases. where M is the nuber o source, and x () and x () are the estiated and ground truth positions or the th source, respectively. Table 1 shows the paraeters used in the algorith. Siulation Scenarios. We study three siulation scenarios. In the irst scenario, we increase the nuber o sources present in the sensing region gradually to see the eect on accuracy o detection. In the second scenario, we increase the average source SNR o two sources present in the sensing region. In the third scenario, we increase the separation between two sources present in the sensing region. Figure 3(a) shows the localization error or the irst scenario when the nuber o sources is increased ro 1 to 4. The localization error increases approxiately exponentially with the nuber o sources. Figure 3(b) shows the average localization error or the second scenario when source SNR or the two sources is increased ro 7dB to 5dB. As expected, the localization error decreases with increasing SNR and reains approxiately constant above 0dB. Figures 3(c) and 3(d) show the localization error or the third scenario when the source separation between two sources is increased ro 0.1 to 8. For sall source separations (0.1 and 0.), the localization error is o the sae order as the separation. This indicates that the two sources cannot be disabiguated at such separations. For higher source separations (above 0.5), the localization error is a sall raction o the separation. This indicates that the two sources are successully localized and disabiguated. In act, or larger source separations (above 5), the average localization error or two sources is sae as that or the single sources. 8 Outdoor Experients We ipleented the beaoring and PSD estiation described in section on an Xilinx XC3S1000 FPGA chip onboard the icaz sensor otes. Both processes run at 4Hz. Beaoring utilizes 166 sec o audio data each cycle, while the PSD estiation odule utilizes 1 sec o data with 75% overlap. The angular resolution o beaoring is 10 degrees while requency resolution o PSD estiation is 1Hz. The PSD estiation odule returns 30 PSD values. average RMS position error () (a) source separation () (b) Figure 4: (a) Outdoor experiental setup. Source 1 is ept at the sae location while source is placed at dierent locations. (b) Localization error with source separation. 9 Conclusion In this paper, we proposed a eature-based usion ethod or localization and discriination o ultiple acoustic sources in WSNs. Our approach used beaors and PSD data ro each sensor. The approach utilized a graphical odel or estiating the source positions and the undaental requencies. We subdivided the proble into source separation and source localization. We showed in siulation and outdoor experients that the approach can discriinate ultiple sources using the siple eatures collected ro the resource-constrained sensor nodes. As part o an ongoing wor, we are woring on target dynaics odels to extend the approach or ultiple source tracing. In the uture, the use o graphical odels will allow us to extend the approach to ultiodal sensors.

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