Reliability measure for sound source localization

Transcription

1 Reliability measure for sound soure loalization Hyejeong Jeon 1a), Seungil im 1, Lag-Yong im 1, Hee-Youn Lee 1, and Hyunsoo Yoon 2 1 Information Tehnology Laboratory, LG Eletronis Institute of Tehnology, 16 Woomyeon-dong, Seoho-gu, Seoul, , orea 2 Division of Computer Siene, Dept. of Eletri Engineering and Computer Siene, orea Advaned Institute of Siene and Tehnology, Guseong-dong, Yuseong-gu, Daejon, , orea a) hjeong@lge.om Abstrat: In this paper, we propose a method of measuring the reliability of diretion-of-arrival (DOA) estimation results. One idea for the reliability measure arises from a waterbed effet in DOA estimation. The reliability measure an be obtained from the differene between the maximum and minimum point of ross-orrelation. If the alulated reliability measure has a lower value than a predefined threshold, the estimated DOA is regarded as a wrong result and subsequently disarded. Some experiments show that the proposed method an rejet perturbed results of the estimated DOA. eywords: reliability, sound soure loalization, GCC-PHAT Classifiation: Siene and engineering for eletronis Referenes [1] M. Brandstein, and D. Ward, Mirophone Arrays : Signal Proessing Tehniques and Appliations, Springer, [2] G. lathoud, and M. Magimai.-Doss, A Setor-Based, Frequeny-Domain Approah to Detetion and Loalization of Multiple Speakers, IEEE International Conferene on Aoustis, Speeh, and Signal Proessing, vol. III, pp , Marh [3] P. Stoia, J. Li, and B. Ninness, The Waterbed Effet in Spetral Estimation, IEEE Signal Proess. Mag., vol. 21, pp , May [4] B. Ninness, The asymptoti CRLB for the spetrum of ARMA proesses, IEEE Trans. on Signal Proess., vol. 51, no. 6, June [5] M. Hayes, Statistial Digital Signal Proess. and Modeling, John Wiley & Sons, Introdution Sound soure loalization has been investigated to estimate a talker s loation and it has many appliations. The talker s spatial information is assumed to be known in the speeh enhanement algorithm by means of array proessing. 192

2 If the talker s position is known, various algorithms an be used to redue any diretional noise other than the talker s speeh. There are two main approahes to loalization [1]: the steered-beamformer approah, whih inludes various kinds of beamformers; and time-differene of arrival (TDOA) approah, whih inludes a generalized ross-orrelation (GCC). The steered-beamformer approah has the apability of enhaning a desired signal that originates from a partiular diretion. The TDOA approah uses lassial time delay estimation tehniques, suh as rossorrelation, GCC, adaptive time delay estimation, and the adaptive eigenvalue deomposition algorithm. The most ommon time delay estimation method is the GCC, whih onsists of various types suh as the unfiltered type, the maximum likelihood (ML) type, and the phase transform (PHAT) type. The GCC-PHAT is a widely used TDOA estimation method beause it works well in a realisti environment. Irrespetive of the existene of a dominant talker, the TDOA estimator always returns an estimated TDOA that orresponds to a maximum point of the ross-orrelation value. Hene, the TDOA estimation often shows a failed result. We therefore propose a method of seleting reliable TDOA estimation results. To find the aurate results, we define the reliability measure as a fator that is indued from a waterbed effet in spetral estimation. The reliability measure an be defined as the differene between the maximum and minimum of a ross-orrelation value, and it reflets the prominene of the lobe of a spatial response. 2 Waterbed effet in a DOA estimation Consider two mirophones spaed by distane d. The reeived signal is ideally assumed to be a delayed and attenuated signal of the emitted soure signal, whih arrives from a diretion of θ 0. A measured additive noise, v[n], is unorrelated with the soure signal. The sampled reeived signal at the i-th sensor, x i [n], is expressed as x 1 [n] =α 1 s[n τ 1 ]+v 1 [n] x 2 [n] =α 2 s[n τ 2 ]+v 2 [n], (1) where α i is the attenuation fator due to the propagation effets and τ i is the propagation time from the soure s[n] tothei-th mirophone. The differene in the propagation time of the two mirophones, τ 12, whih is alled the TDOA, is expressed as follow: τ 12 = τ 2 τ 1. (2) If the distane from the soure to the mirophone is muh greater than d, the wave that impinges on the mirophone may appear planar; thus, τ 12 = 0, (3) where θ 0 is the DOA and is the speed of sound. The solution of the frequeny-domain GCC-PHAT estimator is expressed as 193

3 X 1 [k]x2 ˆθ =argmax [k] 2πk θ X 1 [k]x2 [k] e j =argmax θ e j( X 1 [k] X 2 [k] 2πk ), θ [ π, π]. (4) Note that the estimate ˆθ is not defined as a sample delay and is onsequently not restrited to an integer value. The DOA an be estimated by sanning all the predefined angle spae. It is mainly used in a beamformer-based DOA estimator or in a high-resolution spetral estimation-based estimator [1]. In addition, Guillaume reently proposed the SAM-SPARSE-MEAN, whih is a setor-based multisoure loalization algorithm [2]. The searhing method is known to be ineffiient beause it sans over all angles of interest. However, angular resolution is not ritial in many appliations and the searhing spae an be redued. A small mirophone array for speeh enhanement should have a large mainlobe bandwidth. Given that a soure loalizer is used as the preproessor of the beamformer, a sparse searhing spae is quite adequate. Moreover, the sanning time is not too long when the DOA estimator has a simple struture and a short proessing time. We therefore used this searhing method. The searhing method for the DOA estimation is very similar to a spetral estimation suh as a periodogram. The power spetral density estimated by a periodogram has a onstant average relative variane. This behavior is alled the waterbed effet in spetral estimation [3, 4]. Let Φ(ω) bethe power spetral density of a Gaussian white noise proess and ˆΦ(ω) bethe periodogram estimate of Φ(ω). We an then show that the variane of ˆΦ(ω) is proportional to the square of the power spetral density. The waterbed effet in DOA estimation an be redued by a similar proess in [5]. If R(θ) is the ross-orrelation value of (4), then R(θ) = X 1 [k]x2 [k] 2πk X 1 [k]x2, θ [ π, π]. (5) [k] e j In addition, a power pattern estimate of R(θ), ˆP (θ), is expressed by ˆP (θ)= 1 R(θ) 2 = 1 l=0 X 1 [k]x2 [k] X1 [l]x 2[l] X 1 [k]x2 [k] X1 [l]x 2[l] e j Furthermore, the expeted value of the power pattern is E ˆP (θ) = 1 l=0 { E e j 2π(k l) 0 e 2π(k l) j 2π(k l). (6). (7) Let the input signal be a spatially white noise proess, and note that the signal is assumed to be Gaussian white noise in the spetral estimation. For spatially white noise, the expeted value of e j 2π(k l) 0 is equal to unity when k = l only; otherwise it is equal to zero. Thus, the expeted value of the power pattern in (7) is equal to unity. That is, E ˆP (θ) =1. (8) 194

4 The seond-order moment of the power pattern estimate is E{ˆP 2 (θ) = 1 2 l=0 m=0 n=0 { E e j 2π(k l+m n) and separated by sum of two parts as follows: E{ˆP 2 (θ) = 1 2 k+m= o.w E {e j 2π(k l+m n) l+n E {e j 2π(k l+m n) 0 e 0 e 0 e 2π(k l+m n) j 2π(k l+m n) j 2π(k l+m n) j, (9). (10) The number that an be satisfy k + m = l + n is (+1)(+2)(2+3) 6 3. Hene, the Equation (10) an be simplified to E ˆP 2 (θ) = 1 [ ] ( +1)( + 2)(2 +3) 2 3. (11) 6 Thevarianeof ˆP (θ) is 2 Var{ ˆP (θ) = E ˆP 2 (θ) E ˆP (θ) = (12) By using (8) and (12), we an alulate the average relative variane of ˆP (θ) as follows: average relative variane ˆP (θ) = 1 2π π π var ˆP (θ) P 2 dθ = (θ) 6 2 (13) 3. This equation is the waterbed effet in the DOA estimation. 3 Reliability measure for the DOA estimation If a dominant soure exists, the waterbed effet should ause the mainlobe to be prominent. If there is no diretional soure, R(θ) has a flat pattern for all diretions. The reliability measure (z), whih indiates the prominene of the lobe of R(θ), is defined as z = f (R max R min ), (14) where f(x) is any monotone-inreasing funtion. We used the formula f(x) = x/ 2. Beause the reliability measure refers to the diretivity of the sound soure, we only seleted the DOA estimation results that had a high reliability value and we lustered those results. If we assume that a reliable DOA estimation result an be obtained when a dominant diretional input exists, we an onsider the following two hypotheses of reliability deision problem: 195

5 d 0 : unreliable DOA estimation result d 1 : reliable DOA estimation result z = 1 2 (R max R min ) 2 where η is the threshold for the seletion of reliable results. d 1 > < d 0 η, (15) 4 Experiments To evaluate the performane of the proposed method, we applied it to the speeh data reorded in a quiet onferene room. This onferene room, whih was suitable for a onferene with the several people, generates a normal reverberation effet. The room had various kinds of offie furniture suh as tables, hairs, a white board standing on the floor, and a projetor fixed to the eiling. The two mirophones were plaed on the table in the enter of the room, and the distane between the mirophones was set to 8 m. The sampling rate of the reorded signal was 8 khz, and the sample resolution of the signal was 16 bits. We performed the experiment of the DOA estimator for a talker s speeh from a diretion of 50. White noise and tone noise resulted from the fan of the projetor. Figure 1 (a) shows the waveform of the talker s speeh. We alulated the diretion of the talker s speeh on the basis of the GCC-PHAT, and the result is shown in Fig. 1 (b). The small irles in the figure indiate the results of the estimated DOA. Beause there were many inorret results for the estimated DOA, there was a drasti drop in the performane of the estimated DOA. We alulated the reliability values of the given speeh and applied the results to the estimated DOA. Figure 2 (a) shows the reliability measures of the given speeh, and Fig. 2 (b) shows the estimated DOA after the removal of any unreliable results. We set the threshold, η, to The x-marks indiate the eliminated values; these values were eliminated beause the reliability measure revealed that those results were perturbed. We evaluated the performane of an estimated DOA on the basis of a GCC-PHAT. One set of results based on our proposed reliability measure was ompared with another set of results derived without the proposed reliability measure. In the first experiment, the exat diretion of the soure is The disrepany between 60 and the omes from the differene, θ h, whih is aused by the talker s height. We seleted only 58 of the 106 estimated DOA values by using the threshold value of the reliability measure. As shown in Table I, the averaged diretion error was redued from to and the root mean squared (RMS) error was redued from to As a result, the DOA estimator with the reliability measure performed better than the DOA estimator without the reliability measure. This performane enhanement is due to the elimination of the perturbed results of the estimated DOA. 196

6 Fig. 1. (a) A waveform of the talker s speeh (b) DOA estimation results of GCC-PHAT. It doesn t use the reliability measure. Fig. 2. (a) The alulated reliability for Fig. 2 (a). (b) DOA estimation results of GCC-PHAT. It uses the reliability measure and eliminates unreliable estimates. Table I. The Performane of the DOA Estimator (Exat diretion = ). Method Average Standard Deviation RMS Error w/o Reliability Measure with Reliability Measure Conlusion A method of deteting a reliable DOA estimation result was proposed. The reliability measure indiates the prominene of the lobe of the ross-orrelation value, whih is used to find the DOA. The estimated DOA is regarded as a wrong result when the reliability measure has a low value than a predetermined threshold. We derived the waterbed effet in the DOA estimation and used this effet to alulate the reliability measure. Finally, we evaluated the performane of the proposed reliability measure in a fixed talker environment and a moving talker environment. 197