Real-time Super-resolution Sound Source Localization for Robots

Transcription

1 22 IEEE/RSJ International Conference on Intelligent Robots and Systes October 7-2, 22. Vilaoura, Algarve, Portugal Real-tie Super-resolution Sound Source Localization for Robots Keisuke Nakaura, Kazuhiro Nakadai, and Gökhan Ince Abstract Sound Source Localization (SSL is an essential function for robot audition and yields the location and nuber of sound sources, which are utilized for post-processes such as sound source separation. SSL for a robot in a real environent ainly requires noise-robustness, high resolution and real-tie processing. A technique using icrophone array processing, that is, ultiple Signal Classification based on Standard Eigen- Value Decoposition (SEVD-USIC is coonly used for localization. We iproved its robustness against noise with high power by incorporating Generalized EigenValue Decoposition (GEVD. However, GEVD-based USIC (GEVD-USIC has ainly two issues: the resolution of pre-easured Transfer Functions (TFs deterines the resolution of SSL, 2 its coputational cost is expensive for real-tie processing. For the first issue, we propose a TF interpolation ethod integrating tiedoain-based and frequency-doain-based interpolation. The interpolation achieves super-resolution SSL, whose resolution is higher than that of the pre-easured TFs. For the second issue, we propose two ethods, USIC based on Generalized Singular Value Decoposition (GSVD-USIC, and Hierarchical SSL (H-SSL. GSVD-USIC drastically reduces the coputational cost while aintaining noise-robustness in localization. H-SSL also reduces the coputational cost by introducing a hierarchical search algorith instead of using greedy search in localization. These techniques are integrated into an SSL syste using a robot ebedded icrophone array. The experiental result showed: the proposed interpolation achieved approxiately degree resolution although we have only TFs at 3 degree intervals, GSVD-USIC attained 46.4% and 4.6% of the coputational cost copared to SEVD- USIC and GEVD-USIC, respectively, H-SSL reduces 59.2% coputational cost in localization of a single sound source. I. INTRODUCTION Since a robot should work in a real environent, robot audition is essential for huan-robot interaction. Sound Source Localization (SSL in robot audition tells us the location and nuber of sound sources, which are utilized for other robot audition functions such as sound source separation. Since SSL affects the perforance of a whole robot audition syste drastically, it has been studied widely. Since robots should work in real-tie and localize sound sources in a noisy environent, SSL for robots ainly requires: noise-robustness, high-resolution, and real-tie processing. To solve the first proble, we previously extended ultiple Signal Classification (USIC based on Standard EigenValue Decoposition (SEVD-USIC [] by incorporating Generalized EigenValue Decoposition (GEVD, called GEVD-USIC [2]. The ethod successfully realized localization of target sources under noise with high power. K. Nakaura, K. Nakadai, and Gökhan Ince are with the Honda Research Institute Japan Co., Ltd., 8- Honcho, Wako, Saitaa, 35-4, Japan. {keisuke, nakadai, gokhan.ince}@jp.honda-ri.co Although GEVD-USIC has such an advantage in noiserobustness, it has ainly two issues: The resolution of pre-easured Transfer Functions (TFs between a directional sound source and icrophones decides that of SSL. 2 USIC algoriths are coputationally expensive for subspace decoposition and high resolution SSL. Issue stes fro the utilization of natural pre-easured TFs. The resolution of pre-easured TFs decides the resolution of SSL, and easureents of fine resolution are tie consuing. To obtain fine resolution without fine easureents, one siple solution would be a nuerical TF calculation using geoetric inforation of a icrophone array, known as a nuerical ethod which iplicitely assues that icrophones are in a free space. However, the accuracy of nuerical ethods is not sufficient because a robot-ebedded icrophone array is attached to a coplex robot surface not in a free space, which includes high-order reflections at several different aterials. Several nuerical ethods adaptable for a robot-ebedded icrophone array have high coputational cost [3-4], which are not suitable for real-tie SSL. The better solution would be interpolating pre-easured TFs to obtain TFs with any desired resolution, that is, an interpolation ethod. Since interpolation ethods include a coplex robot surface in pre-easured TFs, they are suitable for robots. Reported interpolation ethods are divided into two categories: all-points ethods and adjacentpoints ethods. The all-points ethods [5-] utilize all the known TFs to estiate a TF, which cause low estiation errors. However, their algorith still has difficulties in realtie processing. On the other hand, the adjacent-points ethods [-3] utilize only the two closest pre-easured TFs fro the estiated point. Therefore, they have advantages in ters of real-tie processing, and are suitable for robot audition. The estiation error is not sufficiently sall since the calculation relies on two adjacent TFs. Issue 2 has two ain points. First, the subspace decoposition in USIC algoriths, naely SEVD in SEVD- USIC and GEVD in GEVD-USIC, increases the coputational cost draatically and still has difficulties in real-tie operation especially in a frae-by-frae anner. Secondly, SSL for higher resolution needs ore tie to calculate a spatial spectru and search peaks of the spectru. For robot audition, we need to achieve both high resolution and realtie processing siultaneously. The purpose of this paper is to realize SSL solving these issues and apply the SSL to a robot in a real environent. For Issue, we propose TF interpolation based on the integration of Frequency- and Tie-Doain Linear Inter /2/S3. 22 IEEE 694

2 Iaginary 2 (Pre-easured O ( ψˆ (Interpolated (a Fig.. (Pre-easured Real Iaginary 2 (Pre-easured O ( ψˆ (Interpolated (b Intuitive iage of interpolation (Pre-easured Real polation (, which is based on an adjacent-points ethod in consideration of real-tie interpolation. This is the extension of a correlation atrix interpolation for TFs [4]. Naely, two interpolation ethods for estiating aplitude and phase are integrated. The integration iproves the interpolation accuracy for both aplitude and phase of TFs. By, we can generate TFs with the desired resolution and achieve super-resolution SSL, where the super-resolution represents the resolution exceeding that of pre-easured TFs. For Issue 2, we first extended GEVD-USIC [2] to utilize Generalized SingularValue Decoposition (GSVD, which is hereinafter called GSVD-USIC. The extension not only aintains the noise-robustness in GEVD-USIC but also reduces the coputational cost enorously. Secondly, we introduced Hierarchical SSL (H-SSL based on a coarse-to-fine approach [5]. It roughly localizes sound sources using the pre-easured TFs, and consequently it precisely localizes the sound source again around the estiated location using interpolated TFs. By this extension, H-SSL first assures the resolution of SSL with pre-easured TFs, and it can iprove using the interpolated TFs afterwards. H-SSL allows perforing super-resolution SSL in real-tie. The rest of the paper is organized as follows: Section II explains the details of TF interpolation by for Issue. Section III gives a brief introduction of SEVD-USIC and GEVD-USIC, and describes GSVD-USIC and H- SSL to solve Issue 2. Section IV shows the syste structure. Section V evaluates the techniques used in the syste, and Section VI concludes this paper. II. TRANSFER FUNCTION INTERPOLATION USING To solve the first issue discussed in Section I, is described to obtain TFs with the desired resolution for superresolution SSL. A. Related Work Here, Frequency Doain Linear Interpolation ( [6], [], [2] and Tie Doain Linear Interpolation ( [3] are explained. Let A(ψ = [A (ψ,...,a (ψ ] T C and A(ψ 2 = [A (ψ 2,...,A (ψ 2 ] T C denote preeasured TFs between a icrophone array and sound sources, in other words, steering vectors in SSL. is the nuber of icrophones, ψ and ψ 2 are directions of the preeasured TFs, and ω represents frequency. Our objective is to estiate A( ˆψ by interpolation, where ˆψ is the direction of an estiated point, which is ψ < ˆψ < ψ 2. [6] in the frequency doain interpolates a TF by:  [ψ,ψ 2 ]( ˆψ = D A (ψ + ( D A (ψ 2, ( where  [ψ,ψ 2 ]( ˆψ is an interpolated TF of the -th icrophone at ˆψ using (ψ and (ψ 2. D A R represents an interpolation factor, which is D A. In [3], ÂA [ψ,ψ 2 ]( ˆψ is obtained as follows:  [ψ,ψ 2 ]( ˆψ = (ψ 2 ( (ψ / (ψ 2 D A. (2 Fig. shows the intuitive iage of the TF interpolation by and, respectively. Both and can interpolate transfer functions between A(ψ and A(ψ 2 continuously in a short tie by the factor D A. Previously, we evaluated their interpolation errors based on aplitude and phase [4] and found that and have probles in estiating aplitude and phase, respectively. B. Frequency- and Tie-Doain Linear Interpolation With respect to the idea of the correlation atrix interpolation [4], we extended the ethod for TF interpolation. Naely, we integrated the phase interpolation result of and the aplitude interpolation result of in order to achieve the best interpolation perforance. and are integrated by the following steps: Take two interpolation results fro Eq. ( and Eq. (2. Here,  [ψ,ψ 2 ]( ˆψ in Eq. ( and Eq. (2 are redefined as  [F ψ,ψ 2 ]( ˆψ and  [T ψ,ψ 2 ]( ˆψ, respectively. 2 Decopose  [F ψ,ψ 2 ]( ˆψ and  [T ψ,ψ 2 ]( ˆψ into phase and gain.  [F ψ,ψ 2 ]( ˆψ = λ [F] exp( jωt [F] (3  [T ψ,ψ 2 ]( ˆψ = λ [T] exp( jωt [T] (4 3 Calculate  [ψ,ψ 2 ]( ˆψ as follows:  [ψ,ψ 2 ]( ˆψ = λ [T] exp( jωt [F]. (5 For SSL,  [ψ,ψ 2 ]( ˆψ in Eq. (5 will be later utilized as A(ψ in Eq. (7. Then, we can select a desired resolution in SSL depending on the resolution of D A in Eq. ( and Eq. (2. III. SSL WITH GSVD-USIC AND H-SSL To solve the second issue, this section investigates coputational cost reduction by using GSVD-USIC and H-SSL. This section first gives a brief introduction of SEVD-USIC [] and GEVD-USIC [2]. Afterwards, we describe details of GSVD-USIC and H-SSL. A. SEVD-USIC and its Extension to GEVD-USIC In advance of SSL, we need TFs (steering vectors, naely A(ψ. In Section II, we obtained A(ψ for a desired interval of ψ by easureents and interpolation. In SSL, we first copute a correlation atrix of ultichannel input acoustic signals, denoted by R( f C. SEVD-USIC [] perfors SEVD of R( f to decopose signal space into noise- and signal-subspaces as follows: R( f = E( f Λ( f E ( f (6 695

3 ulti-channel input acoustic signal Short Tie Fourier Transfor : Correlation atrix for X ( f : R( f = X ( f + τr X ( f + τr T TR R τr= X ( f GSVD (SEVD of Correlation atrices : KR ( ω(, ωf, f= RE (( ω,, ff = ΛE( ω(, ωf, Ef Λ (, f E ( f Narrow-band Spatial Spectru : A A( ωψ, P( ωψ,, f Aω (, ψˆ A e ( f = = Ls Broad-band Spatial Spectru : ωh P ψ (, f = P( ωψ,, f ω ω + H L l ω= ωl SSL result ψ in the frae f r [l] ψ Noise Database N( f Correlation atrix for Noise : K( f = N( f + τk N ( f + τk T TK K τk= STF Selection for h-ssl : STF interpolation by : Aˆ l ] [ l+ ] ˆ = λ [ ψ, ψ ] [ Aω (, ψˆ = Aˆ l ] [ l ] ˆ = λ exp( jωt [ T ] [ F ] [ l ] [l] [ +] ψˆ, A ( ω, ψ, A ( ψ, A ( ψ l Decision of new search range and resolution [ l ] [ l+ ] Range : ψ ψˆ ψ for all l Ls Resolution : δψ exp( jωt [ [ ψ, ψ ] T [ ] [ F ] Fig. 3. Positive Direction Negative Direction Coordinates for SSL Fig. 2. Super-resolution SSL syste working in real-tie where Λ( f = diag(λ ( f,...,λ ( f and E( f = [e ( f,..., e ( f ] are eigenvalues and vectors, respectively. Here, e ( f is sorted in order of λ ( f (. The spatial spectru for SSL is deterined by P(ψ, f = A (ψa(ψ =L s + A (ψe ( f, (7 where L s is the nuber of sound sources considered in SSL. For the Direction of Arrival (DoA estiation, we accuulate P(ψ, f in Eq. (7 over ω as follows: k h P(ψ, f = P(ω k h k l + [k],ψ, f, (8 k=k l where k h and k l are the frequency bin indices, which represent the axiu and iniu frequency for SSL, respectively. GEVD-USIC [2] extends Eq. (6 to perfor GEVD as: K ( f R( f = E( f Λ( f E ( f, (9 where K( f is a freely designable correlation atrix and can be utilized for various purposes. For instance, when high power noise N(ω exists, K( f is designed as K( f = N(ωN ( which whitens the noise-related eigenvalues. B. GSVD-USIC Theoretically, the GEVD of K( f and R( f can be equivalently described as the following SEVD: K 2 ( f R( f K 2 ( f = E( f Λ( f E ( f. ( In [2], Eq. (9 is considered as the GEVD instead of Eq. ( since it whitens noise without calculating K 2 ( f, which has a large calculation cost. However, Eq. (9 has the following probles: The SEVD still has a large calculation cost for fraeby-frae localization working in real-tie. The eigenvectors are not utually orthogonal since K ( f R( f is not heritian, which eventually degrades the SSL perforance. To solve these probles, this paper extends Eq. (9 to utilize the following GSVD: K ( f R( f = E l ( f Λ( f E r ( f, ( where E l ( f and E r ( f are left- and right-singular vectors, respectively, which are unitary and are utually orthogonal. E l ( f is used instead of E( f in Eq. (6. The calculation cost of Eq. ( is less than that of Eq. (9, which is evaluated in Section V. We note the following aspects in GSVD-USIC. First, GSVD-USIC is equivalent to the following GEVD- USIC: R 2 e = λ K 2 e (2 This indicates that the eigenvectors are utually orthogonal, which iproves SSL perforance copared to GEVD- USIC[2]. Secondly, GSVD-USIC is equivalent to SEVD-USIC when K = I, where I C is an identity atrix. This eans that we can reduce the calculation cost of SEVD- USIC with GSVD-USIC since GSVD is less coputationally deanding than SEVD. C. H-SSL for Fast Super-resolution SSL Although we can obtain fine TFs by using, superresolution SSL is coputationally expensive. Therefore, it is not suitable for real-tie processing for robot application. To solve the issue, we introduce H-SSL. In GSVD-USIC, P(ψ, f as in Eq. (7 and P(ψ, f as in Eq. (8 are ψ-dependent processes. Naely, in these processes, finer  [ψ,ψ 2 ]( ˆψ increases the calculation cost linearly. In H-SSL, we reduced the nuber of processed TFs while aintaining the resolution by the following steps: 696

4 (a PEE : ē [ψ,ψ 2 ] (d Linearity of D A in PEE : d [ψ,ψ 2 ] Fig (b SD : ē 2[ψ,ψ 2 ] (e Linearity of D A in SD : d 2[ψ,ψ 2 ] (c SDR : ē 3[ψ,ψ 2 ] (f Linearity of D A in SDR : d 3[ψ,ψ 2 ] Interpolation error and the linearity of D A for PEE, SD, SDR using TF of a robot-ebedded icrophone array Conduct SSL with rough pre-easured TFs and search peaks of spatial spectru in Eq. (8. Let ψ [l] be the direction that has the l-th largest P(ψ, f, where l is the index of sound sources ( l L s. 2 Take two closest ψ fro ψ [l], which are denoted as ψ [l ] and ψ [l+]. Suppose ψ [l ] < ψ [l] < ψ [l+]. 3 Generate  [ψ [l ],ψ [l] ] ( ˆψ and  [ψ [l],ψ [l+] ]( ˆψ by Eq. (5 depending on a given finer resolution. 4 Conduct SSL again only with  [ψ [l ],ψ [l] ]( ˆψ and  [ψ [l],ψ [l+] ]( ˆψ, and search peaks of Eq. (8. The upper layer of the hierarchical process is for broad localization, while the lower layer provides finer localization. In this sense, SSL with H-SSL follows coarse-to-fine [5] localization, giving rough SSL results first, followed by fine SSL results. IV. SYSTE STRUCTURE Fig. 2 shows the syste structure to achieve superresolution SSL working in real-tie. All blocks explained above were ipleented to a robot located in a noral roo whose reverberation tie was.2 seconds. Fig. 3 shows the coordinate syste for ψ. We have utilized an 8- ch circular icrophone array ebedded in the robot s head and easured the TFs A(ψ at every, which were obtained by tie-stretched pulse recording. The acoustic signal was sapled with 6 khz and 6 bits. The window and shift length for frequency analysis were set to 52 and 6 saples, respectively. All the proposed functions were ipleented as odules for robot audition software HARK [6]. The syste worked in real-tie with a laptop having a 2. GHz Intel Core i7 CPU and 8GB SDRA running Linux. V. EXPERIENTAL VALIDATION A. Error of TF interpolation Using We evaluated the estiation errors of three interpolation ethods, naely,, and. We took the difference between estiated ÂA [ψ,ψ 2 ]( ˆψ and pre-easured A(ψ. ψ was fixed at, and ψ 2 = {3,6,9,2 } was used. ÂA [ψ,ψ 2 ]( ˆψ was estiated at every. We averaged the estiated errors for ω and ψ. The averaged error, ē [ψ,ψ 2 ], was calculated as: ē [ψ,ψ 2 ] = i ψ i ψ i= k h f k h k l + [ψ,ψ 2 ](ω [k], ˆψ [i], (3 k=k l where f [ψ,ψ 2 ](ω [k], ˆψ [i] is the estiation error for specific ˆψ and ω. k l and k h are defined as the sae as Eq. (8 with the frequency band 5[Hz] ω 28[Hz]. i ψ represents the nuber of ˆψ we conducted interpolation. For ˆψ, we utilized all ψ of the pre-easured A( ψ = [A (ψ,...,a (ψ] T in the range of ψ < ψ < ψ 2. We evaluated three kinds of f [ψ,ψ 2 ](ω [k], ˆψ [i] in Eq. (3. The first criterion is the suation of noralized innerproduct of all channels: ( ˆψ  [ψ,ψ f [ψ,ψ 2 ]( ˆψ = 2 ]( ˆψ ( ˆψ  [ψ,ψ 2 ]( ˆψ, (4 = which represents the Phase Estiation Error (PEE. The second criterion is the suation of Spectral Distortion (SD of all channels calculated as follows: f 2[ψ,ψ 2 ]( ˆψ = = 2log  [ψ,ψ 2 ]( ˆψ ( ˆψ, (5 which shows the aplitude estiation perforance. The third criterion is the suation of Signal-to- Distortion Ratio (SDR of all channels calculated as follows : f 3[ψ,ψ 2 ]( ˆψ = = ( ˆψ  [ψ,ψ 2 ]( ˆψ 2 ( ˆψ 2, (6 which represents the total estiation perforance. Let ē [ψ,ψ 2 ], ē 2[ψ,ψ 2 ], and ē 3[ψ,ψ 2 ] denote ē [ψ,ψ 2 ] of PEE, SD, and SDR, respectively. We also evaluated the linearity of D A calculated by d [ψ,ψ 2 ] = i ψ i ψ i= ( D A[i] ˆψ [i] ψ 2 ψ ψ 2 2, (7 where D A[i] denotes D A having the sallest f [ψ,ψ 2 ](ω [k], ˆψ [i] for each ˆψ [i]. A sall d [ψ,ψ 2 ] eans D A is close to ˆψ ψ 2 ψ ψ 2, being utilized for practical interpolation. Let d [ψ,ψ 2 ], d 2[ψ,ψ 2 ], and d 3[ψ,ψ 2 ] denote d [ψ,ψ 2 ] of PEE, SD, and SDR, respectively. We have inverted the original SDR discussed in [6] since it shows the best estiation perforance with f [ψ,ψ 2 ]( ˆψ =. 697

5 Avg. Aziuth Error [deg] SSL Correct rate [%] 5 SEVD GEVD GSVD Signal to Noise Ratio [db] Fig. 5. SSL correct rate of SEVD-, GEVD-, and GSVD-USIC Fig. 4 shows the coparison of the average errors, naely ē, ē 2, and ē 3, and their linearity of D A, naely d, d 2, and d 3, respectively. The horizontal axis in all the figures shows the difference between ψ and ψ 2 for the interpolation. achieved as sall ē as and achieved as sall ē 2 as thanks to the integration. As a result, it had the sallest ē 3. Also, showed the sallest d, d 2, and d 3. Thus, has advantages in both high accuracy and intuitive paraeter deterination. B. Noise-robustness and coputational cost coparison aong SEVD-, GEVD-, GSVD-USIC In the experient, there were a target sound (white noise and a noise source (robot s fan noise away fro the icrophone array in the directions of 6 and 8, respectively. A(ψ of ψ = { 75, 7,...,8 } were used. Hence, the resolution of SSL was 5. We evaluated the relationship between Signal-to-Noise Ratio (SNR and SSL correct rate. SNR is defined as follows 2 : Calculate the average spectru of -ch input acoustic signals defined as X sa (ω. The Power Spectru Density (PSD of X sa (ω is derived as P sa (ω = k X sa (ωx wl s a ( where k wl is a window length. 2 Deterine the PSD of the noise source P na (ω by using the sae process as. 3 Calculate the SNR for each frequency bin, and we noralized the SNR of the bins between k h and k l as: ( SNR = log k h k l + k h P (ω sa [k] k=k P na (ω l [k], (8 where k h and k l are defined the sae as those in Eq. (8. The frequency range was fro 5Hz to 28Hz. The SSL correct rate was defined as the nuber of fraes whose highest peaks in Eq. (8 were in the direction of the target sound source (6 in fraes. Fig. 5 shows the result. The horizontal axis shows SNR, and the vertical axis shows the SSL correct rate. The dotted-, chained-, and solid-line show the result of SEVD-USIC, GEVD-USIC, and GSVD-USIC, respectively. GSVD-USIC shows better perforance than both GEVD- and SEVD-USIC. This eans that GSVD can obtain utually-orthogonal signal and noise subspaces. The coputational cost of each ethod was also evaluated. We conducted SSL over fraes for each ethod and easured the averaged processing tie for only Eqs. (6- (9, and (. As a result, the average processing tie for 2 This definition is the sae as that in [7]. This paper includes the result of GSVD-USIC. TABLE I FRAE PROCESSING TIE WITH/WITHOUT H-SSL source 2 sources 3 sources 4 sources w/o H-SSL 45. [s] 42.8 [s] 37.5 [s] 34.9 [s] w H-SSL 8.4 [s] 9. [s] 2.2 [s] 2.8 [s] NONE Relative Aziuth [deg] Fig. 6. DoA estiation errors SEVD-, GEVD-, and GSVD-USIC ethods was.9s, 3.6s, and 5.52s, respectively. Clearly, GSVD-USIC showed considerable iproveent in the coputational cost copared to SEVD-USIC (approxiately two ties faster. Since the frae period was s, only GSVD- USIC was able to work in real tie in a frae-by-frae anner. Finally, we confired that GSVD-USIC was the best ethod in ters of both noise-robustness and coputational efficiency. C. Coputational cost of H-SSL We copared the coputational cost of SSL with and without H-SSL as explained in Section III-C. Sae as Section V-B, we conducted SSL over fraes for each ethod and easured the averaged processing tie for only Eqs. (6-(8. For SSL without H-SSL, A(ψ of intervals were used for higher resolution. For H-SSL, A(ψ of intervals were used as pre-easured TFs, and we conducted to generate  [ψ,ψ 2 ]( ˆψ of intervals. Thus, these two SSLs have the sae resolution. Table I shows the average processing tie for SSL with and without H-SSL. The table includes the change of L s in Eq. (7, which affects the hierarchical process. H-SSL reduced the processing tie approxiately half regardless of L s, which shows the validity of H-SSL. D. Applicability of the proposed ethods to SSL for a robot We applied GSVD-USIC, and H-SSL to SSL by our robot-ebedded icrophone array. We evaluated our ethods by using two easures: Error of DoA estiation towards a sound source in fixed position, 2 SSL perforance towards a dynaic sound source. SSL for a Sound Source in Fixed Position: This section copares the error of DoA estiation towards a stationary sound source using different interpolation ethods. We have recorded white noise by every of ψ ( 9 ψ 9. We localized the white noise and took the average error between estiated and recorded DoA of the white noise. We assue having A(ψ at the intervals of ψ = {,5,,3,6,9,2 }. By interpolation, ÂA [ψ,ψ 2 ]( ˆψ of intervals was estiated so that we can correctly localize the sound source. 698

6 Avg. Aziuth Deletion Error Rate Error [deg] Angle[deg] 3 NONE Relative Aziuth [deg] (a DoA estiation error for dynaic SSL NONE Relative Aziuth [deg] (b Deletion error rate for dynaic SSL Frae[nu] Reference NONE (c Exaple of dynaic SSL using A(ψ at 3 intervals Fig. 7. Dynaic SSL perforance evaluation Fig. 6 shows the error coparison of DoA estiation aong the interpolation ethods discussed in Section II. The horizontal axis shows the intervals of ψ for A( ψ. The vertical axis shows the average error of DoA estiation. NONE eans that no interpolation ethod was used. We observed: had the sallest DoA estiation errors, 2 Up to the intervals of 3, aintained approxiately the sae perforance as the case at intervals, which showed the validity of in SSL. 2 SSL for a Dynaic Sound Source: We used a oving white noise source. All other conditions are the sae as those in Section V-D.. Siilar to Fig. 6, Fig. 7(a shows the error coparison between DoA estiations with and without. perfored better than NONE and it aintained SSL perforance until the intervals of 3. Fig. 7(b shows the deletion error rate in SSL. The deletion error rate was defined as the rate of fraes, which issed the DoA estiation result. perfectly localized the sound source until the intervals of 9. Fig. 7(c shows an SSL exaple using A(ψ at 3 intervals. 3 intervals were selected in consideration of the evaluation results in Figs. 6 and 7(a. The horizontal axis shows the frae index, and the vertical axis shows the DoA estiation result ψ. In addition to the SSL results, we plotted the reference trajectory recorded by an ultrasonic positioning syste [8]. The SSL with showed a better and soother trajectory than that with NONE. As a result, we were able to confir the validity of the SSL syste in both static and dynaic environents. VI. CONCLUSION This paper investigated super-resolution SSL working in real-tie for robots in a real environent. To achieve a fast SSL with any desired resolution, we focused on two issues, pre-defined resolution based on the resolution of easureents, and high coputational cost for conducting GEVD and high resolution SSL. To solve the, we proposed interpolation of TFs by and coputational cost reduction by GSVD-USIC and H-SSL. All the proposed functions were integrated into a superresolution SSL syste and were evaluated. The evaluation showed: showed better interpolation perforance copared to existing ethods and realized super-resolution SSL, 2 GSVD-USIC reduced the calculation cost approxiately by half and achieved better noise-robustness copared to GEVD-USIC, 3 SSL with H-SSL achieved approxiately half the calculation cost than that without H- SSL, which successfully confired the validity of the whole syste. The future work will be the extension of to 3-diensional case and real-tie 3-diensional superresolution SSL. REFERENCES [] R. Schidt, ultiple eitter location and signal paraeter estiation, IEEE Trans. Ant. Prop., vol. 34, no. 3, pp , 986. [2] K. Nakaura et al., Intelligent Sound Source Localization for Dynaic Environents, in Proc. of IEEE/RSJ IROS, pp , 29. [3] K. Yaaoto et al., An acoustic siulation for speech interface of huanoid robot, in Acoust. Soc. of Japan, pp , 29. [4] K. Nakadai et al., Applying scattering theory to robot audition syste: robust sound source localization and extraction, in Proc. of IEEE/RSJ IROS, no. 2, pp , 23. [5] L. Wang et al., Head-related transfer function interpolation through ultivariate polynoial fitting of principal coponent weights, in Acoust. Sci. & Tech., vol. 3, no. 6, pp , 29. [6] T. Nishino et al., Interpolating Head Related Transfer Functions in the edian plane, in Proc. of IEEE WASPAA, pp. 67 7, 999. [7] F. Keyrouz et al., A rational HRTF interpolation approach for fast synthesis of oving sound, in the 2th DSP and 4th SPE Workshop, pp , 26. [8] T. Ajdler et al., Plenacoustic function on the circle with application to HRTF interpolation, in Proc. of IEEE ICASSP, pp , 25. [9] C. I. Cheng et al., Spatial frequency response surfaces: an alternative visualizationtool for head-related transfer functions (HRTFs, in Proc. of IEEE ICASSP, pp , 999. [] F. P. Freeland et al., HRTF interpolation through direct angular paraeterization, in IEEE Syp. Circ. Syst., pp , 27. [] K. Watanabe et al., Interpolation of Head-Related Transfer Functions based on the Coon-Acoustical-Pole and Residue odel, in Acoust. Sci. & Tech., vol. 24, no. 5, pp , 23. [2] J. Zhang et al., A Piecewise Interpolation ethod Based on Log- Least Square Error Criterion for HRTF, in IEEE 7th Workshop on ultiedia Signal Processing, pp. 4, 25. [3]. atsuoto et al., ethod of interpolating binaural ipulse responses for oving sound iages, in Acoust. Sci. & Tech., vol. 24, no. 5, pp , 23. [4] K. Nakaura et al., Correlation atrix Interpolation in Sound Source Localization for a Robot, in Proc. of IEEE ICASSP, Prague, Czech, pp , 2. [5] D. Ringach, Look at the big picture (details will follow, Nature Neuroscience, vol. 6, no., pp. 7 8, 23. [6] K. Nakadai et al., Design and Ipleentation of Robot Audition Syste HARK, Advanced Robotics, vol. 24, pp , 29. [7] K. Nakaura et al., Intelligent Sound Source Localization and Its Application to ultiodal Huan Tracking, in Proc. of 2 IEEE/RSJ IROS, pp , 2. [8] K. Nakadai et al., Sound source tracking with directivity pattern estiation using a 64 ch icrophone array, in Proc. of 25 IEEE/RSJ IROS, pp ,