Development of moving sound source localization system

Transcription

1 Eletroni Journal «Tehnial Aoustis» , 11 Doh-Hyoung Kim 1, Youngjin Park 2 Korea Advaned Institute o Siene and Tehnology, ME3076, 373-1, Guseong-Dong, Yuseong-Gu, Daejon, , Republi o Korea Development o moving sound soure loalization system Reeived , published orresponding author, dh_kim@kaist.a.kr 2 yjpark@kaist.a.kr This paper proposes a novel approah o moving sound soure loalization using adaptive time delay estimation (TDE) algorithm and ative-positioning o mirophone arrays. Using the adaptive TDE that ontinuously estimates the time dierenes between the aptured signals in the mirophones sensors, the ativepositioning ontroller keeps trak o the soure diretion by rotating arrays mehanially. Theoretial analysis and omputer simulations o the onvergene harateristis o the proposed TDE algorithm are presented. The ativepositioning array guarantees the highest delay-position sensitivity with smaller number o mirophones than the ixed arrays. The overall perormane is shown by using an experimental prototype system. 1. INTRODUCTION Sound soure loalization is to estimate the loation o sound soures using the measurements o the aousti signals by mirophone arrays [1]. Moving sound soure loalization [2 5] has several additional diiulties beause the signals aptured are nonstationary. The proposed method employs an expliit adaptive time delay estimation (EATDE) algorithm [6 10] and ative array positioning. EATDE methods expliitly parameterize an adaptive delay estimate to minimize some kind o delay-error untions. It has the ability o traking time-varying delay parameter very ast without a prior knowledge o the statistial harateristis o signals [8]. However, it may onverge to inorret delay estimation when the delay-searh range or the signal bandwidth is wide [6]. In this paper, a modiied EATDE using wavelet transorm is proposed to avoid suh loal onvergene phenomenon. The algorithm uses Haar wavelet [11] transorm o ross-orrelations o aptured signals instead o its simple gradient. We also present an ative positioning method o mirophone array. One o the disadvantages o a soure loalization using delay inormation is that the sensitivity o position estimation depends on the relative positions o mirophones and a sound soure sine the relationship between the delay and positions is nonlinear [1]. An ative positioning ontroller an trak the optimal array diretion aording to the soure movement using a eedbak loop o delay estimator and motor-driven mirophone array. The harateristis o the proposed system are investigated through theoretial analysis, omputer simulations and the experiment results using a prototype experimental system.

2 2 o ADAPTIVE TIME DELAY ESTIMATION Time delay estimation (TDE) between signals reeived at two spatially separated sensors an be mathematially modeled as x() t = s() t + w() t, yt () = st ( d) + w() t, where st () is the soure signal, w() t and w () t 1 2 are the orrupting white noises, d0 is the time dierene between the reeived signals [12]. It is assumed that st (), w() t, w () t 1 2 are mutually unorrelated, zero-mean, stationary proesses. The task is to estimate and trak the time delay d0. The existing adaptive TDE methods are divided into two general ategories: the impliitly-adaptive methods [13 15] and the expliitly-adaptive methods [6 10]. The impliitly-adaptive method uses adaptive ilters or modeling the ross-orrelations or delays between the reeived signals. The delay is estimated as the loation o the maximum. Alternatively, in the expliitly-adaptive time delay estimation (EATDE) method, the delay d is expliitly parameterized and adapted to minimize a delay-error untion gdn ( [ ]) as dn [ + 1] = dn [ ] + µ gdn) ( [ ], (2) where µ is an adaptation size. The adaptation iterates until d onverges to true delay stands or an integer time index, a positive step-size. The delay-error untion based on gradient o the ross-orrelations o signals and a steepest-desent method is generally used. EATDE is simple, omputationally eiient, and suitable or time-varying delay appliations like moving platorms. The onventional EATDE algorithms assume that the true delay and delay estimate d are limited to ensure that the orrelations would have only one maximum d 0 at d =. This assumption is not valid when the atual delay searh range is wider than the unimodal region, whih is a part o main lobe o the ross-orrelation where the slope o let part o a maximum is positive, and the slope o right part is negative, hene, a gradient searh method an onverge to a global maximum. The searh range o delay estimation is determined by the distane between two sensors while the unimodal region is determined by the signal bandwidth. I two sensors are plaed too wide with respet to the signal bandwidth, the orrelations would have multiple loal maxima in the searh range. Thereore, a gradient searh based optimization method annot onverge to these loal maxima. A sample rossorrelation untion is shown in Fig. 1. The global maximum or true delay is at d 0 (1). n d 0 = 0, but onventional EATDEs using simple gradient searh method annot onverge to zero i the initial delay estimate is outside the onvergene range ( 0.5, 0.5). d 0

3 3 o 12 We propose a new EATDE algorithm whih onverges to a global maximum even in this ase. This algorithm employs the wavelet transorm o the orrelations instead o its simple gradient: dn [ + 1] = dn [ ] + µ Rdn ( [ ]). (3) Continuous wavelet transorm R( d ) o ross-orrelation r xy is deined as R( d) = rxy ( τ ) w( τ d) dτ, (4) where w(t) is a wavelet untion. 1.5 Crossorrelation and Haar wavelet untion rossorrelation wavelet =6 Tw =9 Tw =12 =15 Tw =18 r and w time lag Figure 1. Haar wavelet and ross-orrelation o baseband signal We also propose a preiltering implementation o wavelet transorm in order to redue the omputational load o transorm. This method was originally devised or Hilbert transorm in [16], but an be applied to general linear integral transorms as well. I x and y are stationary, transorm R( d ) o rxy the reversed wavelet wd ( t) : is the same as a ross-orrelation o signal y and signal x iltered by R( d) = rx y( d). (5) The ross-orrelation r x y ( d) is estimated with a one-point sample mean r x y( d) = x [ n] y[ n d/ Ts ], (6) ˆ where T s is a sampling time, x [ n ] is alulated rom a onvolution o a sampled signal x[ n ] and a wavelet preilter.

4 4 o 12 The delayed value o y is omputed by using an FIR rational delay ilter. The additional omputational burden o the proposed method to the onventional EATDE or pre-iltering is very small, with no multipliation/division, but only addition/subtration. In this researh, we hose a sampled Haar wavelet [11]: 1 i 0< n < L wn [ ] = 1 i L< n< 0, (7) 0 otherwise (inluding n = 0) where L= Tw Ts and is a support o Haar wavelet. Consider an ideal baseband signal st () with a uto requeny autoorrelation rs ( τ ) is a sin untion and the ross-orrelation r () τ is rs ( τ d 0) loss o generality, the delay d 0 In this ase, the sign o R( d ) is an be assumed zero. xy. Then the. Without < 0 i 0 < d < max( Tw, T) Rd ( ) = 0 i d = 0, (8) > 0i max( T, w T) < d < 0 where T = 1/ [17]. For instane, a ross-orrelation untion with T = 1 and Haar wavelet with T = 6, 9, 12, 15, 18 and their orresponding wavelet transorms R( d ) are presented in Fig. 1. w and Fig. 2. This numerial result illustrates above inequalities, eq. (8). Transorm o ross orrelation and its approximation 0.6 transorm approximation error 0.4 transorm and its approximation =6 =9 =12 =15 T =18 w wavelet position Figure 2. Wavelet transorms and approximations

5 5 o 12 These inequalities show that R( d ) has the similar sign-harateristis with a gradient o the ross-orrelation, and hene it an be used as a maximum searhing inormation like gradients. But the region o onvergene when wavelet is applied is wider than when the gradient is applied, as shown in eq. (8) and Fig. 2. Moreover, it an be ontrolled by the user parameter, width o wavelet. This means that the proposed algorithm statistially onverges to a true delay i we set the width wider than the delay searh range. Simulation tests were arried out to veriy this onvergene property. We ompared the proposed algorithm with a onventional gradient searh method. Ten experiments with dierent initial points d[0] rom 1 to 10 are desribed in Fig. 3. The soure signal was a baseband signal with a normalized uto requeny sampling requeny s Corrupting white noises with = / = 05. n s and the = 10 khz, so the unimodal region o orrelation was about [ 3T, 3 T ]. SNR = 20dB were added. The proposed EATDE with T = 10T and the onventional EATDE with gradient searh were ompared. As shown in the simulation results in Fig. 3, the proposed method onverged to true delay initial point d 0 = 0 w s s s or all the d[0] < Tw = 1 ms = 10 samples, while the onventional method onverged only or d [0] = 0,1,2,3, or d[0] 3T s. These indings led us to onlude that the wavelet-based EATDE provides wider onvergene range. 12 Comparison o wavelet and onventioanl EATDE wavelet with Tw=10Ts onventional 10 delay estimates (sampling time) time (se.) Figure 3. Comparison o the proposed method with onventional EATDE s = 10 khz, n = 05., T w = 1 ms, µ = 005., SNR = 10 db, d[0] = 1 10

6 6 o ACTIVE MICROPHONE ARRAY CONTROL A onventional time delay based loalization algorithm omputes the soure position rom a relation o delay and the relative position o soure and sensors. The relation is nonlinear and impliit and the solution is not unique in general. For example, in two dimensional ase with two sensors as shown in igure 4, the relation is τ 1 2( l r ) 2 ( l r ) 4l r sin = + + θ, (9) where τ, 2l, r are delay, distane between the sensors, and distane o soure rom the enter o two sensors. I r >> 2l, the equation an be approximated to 2l τ sin θ (10) or π < θ < π. A sensitivity o the soure with respet to r goes to zero and the delay beomes a untion o soure angle θ only. In general 3D ase, a nonlinear optimization tehnique or minimizing the estimation errors is used and this is a heavy omputational burden or a real-time soure traking system. r θ sound soure r, θ ( ) Figure 4. A hyperbola determined by two mirophones and the TODA measured in a two-dimensional plane mirophone i mirophone j In this setion, an ative positioning method o mirophone arrays is desribed to redue the omputational burden or 3D real-time soure traking appliations. Ative positioning means to hange the physial positions o sensors using rotation mehanism, et. It also improves the estimation perormane with a smaller number o sensors. The ative positioning o mirophones makes it possible to integrate TDE and GPE more systemially and onsequently makes the loalization proess more eiient. In this researh, an ative positioning o mirophones is implemented using a mehanially steerable struture. The mirophone sensors an be rotated by motorized rotational base. The basi onept is simple. Assume that two mirophones an rotate about the enter axis o two mirophones. A soure diretion angle θ deined as the angle between the soure diretion and the line perpendiular to the line segment between two sensors at midpoint is a ontrol variable. The ontrol objetive is to drive the mirophone angle into the diretion o the sound soure.

7 7 o 12 We use the estimated delay dn ˆ[ ] to regulate the soure diretion angle θ : θ[ n+ 1] = θ [ n] µ dˆ [ n ], (11) where µ is an adaptation step size or θ. I the delay estimate ˆd is the same with the atual delay d rom the eq. (10), 2l θ[ n+ 1] θ [ n] µ sin θ[ n]. (12) This algorithm onverges to the orret soure diretion or the system is stable with the equilibrium point θ = 0 and & θ = 0. The above disrete-time dierene equation is approximated to the dierential equation & θ ksinθ, (13) where k is a positive onstant. The onvergene o this algorithm an be proved using Lyapunov stability theorem [18]. Considering the Lyapunov untion as the square o the angle V 2 = θ, (14) its derivative V& = 2θθ& = 2kθsinθ (15) is negative exept the singular point θ = π. Thereore, this irst-order nonlinear system is globally asymptotially stable. This ative-position method has the advantages that less number o mirophones are neessary beause it has virtually ininite number o sensors. Note that three sensors are required in the above 2D ase or the onventional loalization method. Additionally, the maximum estimation sensitivity is guaranteed with regardless to the soure position. From eq. (2), delay sensitivity is largest when the soure is just in ront o the mirophone ( θ = 0 ). 4. EXPERIMENTS This setion explains the experiment system and the experiment result. The experiment system onsists o three omponents: (1) mirophone array whih is steered by stepping motors, (2) mirophone sensor ampliiers and motor drivers, (3) digital signal proessing board or time delay estimation and soure position alulation. Fig. 5 shows the blok diagram o the experiment system. The mirophone array has our mirophones sensors eah o whih is plaed at eah vertex o the square o m dimension. The array is atuated by two stepping motors. The experiment was perormed in a onventional oie room with small reverberation. The soure sound is a baseband signal with uto requeny = 5 khz. Fig. 6 shows the experiment result plots. The loudspeaker is plae at the 75 angle rom the line normal at the enter o two mirophones. The dotted line denotes the angle o mirophone array and moves to the soure angle with a time onstant τ = 0.95 s. The solid line is the estimated time delay.

8 8 o 12 It irst beomes to the delay orresponding to the angle 75 one with a time onstant τ = 0.02 s and onverges to zero as the mirophone array rotates to the soure diretion. The narrow solid line denotes the delay estimation in the ase o no rotation and shown as the reerene. As a demonstration, 3-dimensional spae moving sound soure direting test was arried out. Fig. 7 shows the results o this test. A portable radio speaker was used as a sound soure. A Korean traditional mask (Hahoe-tal) was attahed to the mirophone array or emphasizing the diretion o mirophone array. This mask may ause a sound diration eet near the mirophone sensors but this is a pratial ase or the appliations suh as robot, CCTV ameras. As shown in the pitures, the soure loalization using EATDE and ative positioning works well in 3-dimensional spae test. The diretion o the array onverges to the soure diretion within about 2 s. 5. CONCLUSIONS This paper is a study to provide new expliit adaptive time delay estimation (EATDE) algorithm and an ative positioning method or sound soure loalization. EATDE method is suitable or ast traking o a time-varying delay and hene or the mobile platorm. EATDE using Haar wavelet transorm is proposed to avoid this onvergene ailure. The theoretial analysis and numerial simulations show that the proposed algorithm onverges globally to an unbiased delay estimate. The on-line wavelet sale adaptation is also proposed to ombine both the ast onvergene and small estimation error at the same time and to avoid the bias error due to seondary sound soures. This algorithm is developed or 1-dimensional audio signal, but it may also be applied to 2-dimensional image proessing. For instane, two images aptured rom a moving amera are the translated versions o eah other and the ross-orrelation o two images is a 2- dimensional peak untion. The peak inding or optimization tehnique proposed in this paper may be extended or suh ases. By ative positioning o mirophone array, alulation o position beome easy and the preision o position estimation improved beause the sensitivity o time delay with respet to the relative position is maximized. The onvergene o this method is proven theoretially and the omputer simulations are provided also. Finally, the experiment system with a steerable mirophone array whih onsists o 4 mirophones and 2 stepping motors are developed and the perormane are tested in real environment.

9 9 o 12 Figure 5. The overall struture o experiment system Figure 6. Time delay estimation and ative soure positioning experiment result

10 10 o 12 Figure 7. Example o sound soure traking

11 11 o 12 REFERENCES [1] Mihael S. Brandstein, Harvey F. Silverman. A pratial methodology or speeh soure loalization with mirophone arrays. Computer Speeh and Language, May [2] R. D. Short. Sting ray a sound-seeking missile. IEE Review, 35(11), , Deember [3] J. Borenstein, Y. Koren. Obstale avoidane with ultrasoni sensors. IEEE Journal o Robotis and Automation, 4(2), , [4] H. G. Okuno, K. Nakadai, K. I. Hidai, H. Mizoguhi, H. Kitano. Human-robot interation through real-time auditory and visual multiple-talker traking. Proeedings o 2001 IEEE/RSJ International Conerene on Intelligent Robots and Systems, vol.3, , [5] Yiteng Huang, J. Benesty, G. W. Elko. Passive aousti soure loalization or video amera steering. In Proeedings o IEEE International Conerene on Aoustis, Speeh, and Signal Proessing, volume 2, pages II909 II912, [6] H. Meyr. Delay-lok traking o stohasti signals. IEEE Transations on Communiations, 24(3), , Marh [7] D. Etter, S. Stearns. Adaptive estimation o time delays in sampled data systems. IEEE Transations on Aousti Speeh and Signal Proessing, 29(3), , June [8] H. Messer, Y. Bar-Ness. Closed-loop least mean square time-delay estimator. IEEE Transations on Aousti Speeh and Signal Proessing, 35(4), , April [9] H. Messer. A uniied approah to losed-loop time delay estimation systems. IEEE Transations on Aousti Speeh and Signal Proessing, 36(6), , June [10] H. C. So, P. C. Ching, Y. T. Chan. A new algorithm or expliit adaptation o time delay. IEEE Transations on Signal Proessing, 42(7), , July [11] M. Vetterli, J. Kovaević. Wavelets and subband oding. Prentie Hall, [12] C. Knapp, G. Carter. The generalized orrelation method or estimation o time delay. IEEE Transations on Aousti Speeh and Signal Proessing, 24(4), , August [13] F. A. Reed, P. L. Feintuh, N. J. Bershad. Time delay estimation using the LMS adaptive ilter stati behavior. IEEE Transations on Aousti Speeh and Signal Proessing, 29(3), , June [14] P. L. Feintuh, N. J. Bershad, F. A. Reed. Time delay estimation using the LMS adaptive ilter dynami behavior. IEEE Transations on Aousti Speeh and Signal Proessing, 29(3), , June [15] D. H. Youn, Nasir Ahmed, G. Cliord Carter. On using the LMS algorithm or time delay estimation. IEEE Transations on Aousti Speeh and Signal Proessing, 30(5), [16] Rihard C. Cabot. A note on the appliation o the Hilbert transorm to time delay estimation. IEEE Transations on Aousti Speeh and Signal Proessing, 29(3), [17] Doh-Hyoung Kim, Sound Soure Diretion Estimation or Mobile Systems. Ph.D. Thesis, Korea Advaned Institute o Siene and Tehnology, [18] Hassan K Khalil, Nonlinear Systems, 3 rd ed., Prentie Hall, 2001.

12 12 o 12 TABLE OF SYMBOLS t or (t) n or [n] s(t) w 1 (t), w 2 (t) τ or d 0 d[n] g(d[n]) ontinuous time index time step or disrete time index ontinuous soure signal orrupting noise signals real time dierene between the reeived signals delay estimation at step n delay-error untion or d[n] µ, µ positive step-size or adaptation w(t) R(d) r xy x T s L = /T s l r θ V n s Haar wavelet untion wavelet transorm o a signal with the delay wavelet untion w(t d) ross-orrelation between signal x and y signal iltered by the reversed wavelet w(t d) sampling time support o Haar wavelet normalized Haar wavelet support uto requeny o baseband signal = / normalized uto requeny distane o sensor rom the enter o two sensors distane o soure rom the enter o two sensors speed o sound soure diretion angle Lyapunov untion