音源定位手法 MUSIC のベイズ拡張 - 奥乃研究室 - 京都大学

Table 1: s t−1,d 1 − s t−1,d−1 s t−1,d+1 p(s t,d = 1|s t−1,d−1:d+1 )0 (off) 0 θ 10 (off) 1 θ 21 (on) 0 θ 31 (on) 1 θ 4p(s t |s t−1 ,θ) =D41∏ ∏ ∏d=1 k=1 j=0()θ s t,dk(1 − θ k ) 1−s fk (s t−1 ,d)t,d (8) ,, f k (s t−1 ,d) 1 , d s t−1,d−1 , s t−1,d , s t−1,d+1 k f k (·,d) = 1 0 . , , d s 0,d = 0 . θ = [θ 1 ,...,θ 4 ] , (8).p(θ|α 0 ) =4∏k=1B(θ k |α 0,1 ,α 0,0 ), (9), B(·|c,d) c, d .3.1.3 VB-HMM , p(s 1:T ,θ, µ,λ|x 1:T ) .p(s 1:T ,θ, µ,λ|x 1:T ) ≈ q(s 1:T ,θ, µ,λ),= q(s 1:T )q(θ)q(µ,λ), (10)(·) 1:T , 1 T . (10) , x 1:T L(q) [Beal,2003; Bishop, 2006].∫log p(x 1:T ) =log p(x 1:T ,s 1:T ,θ, µ,λ)ds 1:T dθdµdλ ≥ L(q),L(q) =E s1:T ,θ,µ,λ [log p(x 1:T ,s 1:T ,θ, µ,λ)]−E s1:T ,θ,µ,λ [logq(s 1:T )q(θ)q(µ,λ)]. (11), E s1:T ,θ,µ,λ [·] q(s 1:T )q(θ)q(µ,λ) . (11) , .logq(s 1:T ) =E θ,µ,λ [log p(x 1:T ,s 1:T ,θ, µ,λ)]logq(θ) =E s1:T ,µ,λ [log p(x 1:T ,s 1:T ,θ, µ,λ)]logq(µ,λ) =E s1:T ,θ [log p(x 1:T ,s 1:T ,θ, µ,λ)], . q(θ) =∏ k q(θ k ) k , (12) ˆα k,1 , ˆα k,0 , q(µ,λ) = ∏ j q(µ j ,λ j ), (13), (14) , ˆβ j , ˆm j ,â j , ˆb j .ˆα k, j =α 0, j +∑〈s t,d, j f k (s t−1 ,d)〉, (12)t,dˆβ j = β 0 + w j , ˆm j = (β 0 m 0 + w j ¯x j )/(β 0 + w j ), (13)â j = a 0 + w j2 ,ˆb j = b 0 + w jS 2 j2 + β 0w j ( ¯x j − m 0 ) 2,2(β 0 + w j )(14), s t,d, j , s t,d = 0 , s t,d,0 = 1 , , s t,d =1 , s t,d,1 = 1 . (13), (14) w j = ∑ t,d 〈s t,d, j 〉, ¯x j = ∑ t,d〈s t,d, j 〉x t,dw j, S 2 j = ∑ t,d〈s t,d, j 〉(x t,d − ¯x j ) 2w j.. , 〈·〉 (10) . q(s 1:T ) , 〈s t,d, j 〉, 〈s t,d, j f k (s t−1 ,d)〉 .〈s t,d, j 〉 ∝ α(s t,d, j )β(s t,d, j ), (15)〈s t,d, j f k (s t−1 ,d)〉 ∝ ˜α(s t−1,d,k ) ˜p(s t,d |s t−1 ) ˜p(x t,d |s t,d )β(s t,d, j ),(16), α(s t,d, j ) β(s t,d, j ) .α(s t,d, j ) ∝β(s t,d, j ) =4∑k=11∑j ′ =0˜α(s t−1,d,k ) ˜p(s t,d |s t−1 ) ˜p(x t,d |s t,d ), (17)β(s t+1,d, j ′) ˜p(s t+1,d, j ′|s t,d, j ) ˜p(x t,d |s t,d ). (18) (16) , .˜p(s t,d = j|s t−1 ) ∝4∏ exp { ψ( ˆα k, j ) − ψ( ˆα k,0 + ˆα k,1 ) } f k (s t−1 ,d) , 2k=1(19){ψ(â j ) − log ˆb j − 1/˜p(x t,d |s t,d ) ∝ ∏ˆβ jexp− a }j(x t,d − ˆm j ) 2 st,d, jj22ˆb j(20) (15), (16) , j,k 1. ˜α(s t−1,d,k ) , k . (12)–(16) . , 〈s t,d, j 〉 〈s t,d, j f k (s t−1 ,d)〉 , x t,d m 0 , 0 1 .3.2 [Arulampalam et al., 2002], . , (12)–(14) . , MUSIC , . P .2 ψ(·) .p(s t |x 1:t ) ≈ w p s p t , (21)

スピーカ2.0 (m)マイクロフォンアレイ移 動 話 者180120600-60-120180120600-60-120Direction 方 向 [deg] (deg)5 10 15 20Time (sec)Direction 方 向 [deg] (deg)180120600-60-120180120600-60-120Direction 方 向 [deg] (deg)5 10 15 20Time (sec)Direction 方 向 [deg] (deg)180120600-60-120180120600-60-1205 10 15 20Time (sec)P thres =23P thres =25 P thres =27m 0 =23 m 0 =25 m 0 =27Direction 方 向 [deg] (deg)固 定 スピーカからの音 楽 音 響 信 号 ( 青 )180120600-60-1205 10 15 20時 Time 刻 (sec) [sec]34323028262422移 動 話 者 の MUSICスペクトル 上 の 軌 跡 ( 黄 , 緑 )5 10 15 20Time (sec)5 10 15 20Time (sec)5 10 15 20Time (sec)Figure 5: : Figure 6: : , . : P thres . : m 0 . : MUSIC . 180 [deg] , 2 ., w p p , s p t . w p s p t .(1) s p t .q(s p t |x t , ˆm,â, ˆb) ∝∏ds p t ∼q(s t |x t ,m,a,b), (22)1∏j=0C(x t,d ) sp t,d,1 exp(−∆ 2 d, j /2)sp t,d, j, (23), x t,d d , C(x t,d ) = 1 C(x t,d ) = 0 . , t , x t,d d , s t,d = 1 . ∆ 2 d, j = (x t,d − ˆm j ) 2 â j /ˆb j .(2) p , w p .w p ∝ ¯p(x t|st p ) ¯p(st p |s p t−1 )q(st p |x t , ˆm,â, ˆb) , (24)∫p(x t |st p , µ,λ)q(µ,λ)dµdλ,¯p(x t |st p ) =∏C(x t,d ) sp t,d,1d¯p(s p t |s p t−1 ) = ∫(25)p(st p |s p t−1,θ)q(θ)dθ. (26) (25),(26) , , VB-HMM (6),(8) . , VB-HMM . , (25) C(x t,d ) sp t,d,1 , (23) , x t,d d. , .ˆβC(x t,d ) sp j â jt,d,1St(x t,d | ˆm j ,(1 + ˆβ,2â j ) sp t,d, j,j )ˆb j¯p(x t |s p t ) =∏d¯p(s p t |s p t−1 ) = ∏d(27)(fk (s∏ ˆα k,st,d /( ˆα k,0 + ˆα k,1 )) p t−1 ,d) , (28)k, St(·|m,λ,ν) m, λ, ν Studentt-. , N max , stp N max 0 ., w p ∑ P p=1 w p = 1 . , (21) . , .4 , VB-HMM , . VB-HMM , 1 . 5 . 2 , . , 20 (sec) . . ∆T = 500 (msec),N max = 3, α 0 = [1,1], β 0 = 1, a 0 = 1, b 0 = 500. P = 500 . RT 20 = 840 (msec) . 6 . P thres = 23,25,27 , m 0 = 23,25,27 . , 0.95 . , 6 . , , . , 0.95–1.00 ,