1-8-7 DOA-HMM ʹͮ͘جҠಈԻݯͷྼܾఆϒϥΠϯυԻݯ ∗ ˑඉ࠸ޱɼߴफయݰɼதଜ༑ɼُԬ߂ (౦େใཧ) 1 पղΛ༻͍ΔͱɼΈࠐΈࠞ߹Λۙࣅతʹॠ ͡Ίʹ ࣌ࠞ߹Ͱද͢͜ͱ͕Ͱ͖Δɻ͜ͷ؍ଌ৴߸Ϟσϧʹ ຊߘͰɼҠಈԻݯΛରͱͨ͠ྼܾఆϒϥΠϯυ ԻݯͷΛѻ͏ɻϒϥΠϯυԻݯ (Blind Source Separation; BSS) ͱɼԻ͔ݯΒ؍ଌ৴߸· Ͱͷୡಛੑ͕ະͰ͋Δ߹ʹɼෳͷԻ͕ࠞ ߹ͨ͠৴߸͔ΒݩͷԻ৴߸Λ͢Δٕज़Ͱ͋Δɻ ྫ͑ɼձٞʹ͓͍ͯෳͷԻ৴߸ͷࠞͬͨ͡Ի σʔλ͔ΒձٞΛࣗಈ࡞ͨ͠ΓɼϩϘοτʹपғ ͷԻڥΛೝࣝ͢ΔػೳΛඋ͑ͤ͞Δ༻్ͷԠ༻ ͕ظ͞Ε͍ͯΔɻ BSS Ͱ؍ଌ৴߸͔ΒԻݯ৴߸ͱͦͷࠞ߹աఔΛ ਪఆ͢Δඞཁ͕͋ΔͨΊɼ௨ৗԻݯͦͷࠞ߹աఔ ʹରͯ͠ԿΒ͔ͷԾఆΛஔ͖ɼͦͷԾఆʹΑΓཱͯΒ ΕΔن४ΛͱʹະมΛਪఆ͢Δ࠷దԽͱ ͯ͠ఆࣜԽ͞ΕΔɻྫ͑ɼBSS ʹ͓͍ͯ؍ଌ৴߸ ͕ԻݯΑΓଟ͍༏ܾఆͰɼԻݯ৴߸ؒͷಠ ཱੑΛԾఆͯ͢͠Δಠཱੳ (Independent Component Analysis; ICA) ͕༗༻Ͱ͋Δ͜ͱ͕Β Ε͓ͯΓɼԻݯ৴߸ؒͷಠཱੑΛ࠷େԽ͢ΔΑ͏ʹ ϑΟϧλΛਪఆ͢Δ͜ͱ͕తͱͳΔ [1]ɻ͔͠͠ɼ ICA Ͱ؍ଌ৴߸͕ԻݯΑΓগͳ͍ྼܾఆ Λѻ͏͜ͱͰ͖ͣɼ͜ͷ߹ಠཱੑΑΓ͞Β ʹ͍ڧԾఆ͕ඞཁͰ͋Δɻ ԻΛରͱͨ͠ྼܾఆ BSS ͰɼԻͷ࣌ؒप ͷεύʔεੑΛར༻ͨ͠Ξϓϩʔν͕༗ޮ Ͱ͋Δ͜ͱ͕ΒΕ͍ͯΔ [2–9]ɻԻͷεύʔεੑ ͱɼԻ৴߸ͷ࣌ؒप͕΄ͱΜͲͷ࣌ؒ पʹ͓͍ͯ΄΅ 0 ͱͳΔੑ࣭Ͱ͋Δɻ͜ͷੑ ࣭ʹΑΓɼෳͷԻ͕ಉ࣌ʹൃ͞Εͨঢ়Ͱگɼ ֤Իͷ༏ͳ࣌ؒप͕ͱ΄ʹ͍ޓΜͲॏ ͳΓ߹Θͳ͍ͱԾఆͰ͖Δ߹͕ଟ͍ɻΑͬͯɼνϟ ωϧؒͷҐ૬ৼ෯ͷҧ͍Λखֻ͔Γͱ֤ͯ࣌͠ ؒपͰͲͷԻ࠷͕ݯ༏Β͍͔͠ΛਪఆͰ ͖ΕɼతͷԻ৴߸ͷΈΛ௨աͤ͞Δ࣌ؒप ϚεΫΛઃ͢ܭΔ͜ͱͰ৴߸ΛಘΔ͜ͱ͕Ͱ ͖Δɻ Ҏ্ͷԻͷεύʔεੑΛ؍ଌ৴߸ͷϞσϧʹ ΈࠐΉͨΊʹɼ؍ଌ৴߸ͷϞσϧΛ࣌ؒपྖ ҬͰఆࣜԽ͢Δඞཁ͕͋Δɻ௨ৗɼ֤ϚΠΫϩϑΥϯ ͷ؍ଌ৴߸Իݯ৴߸ͷ࣌ؒΕΛؚΉΈࠐΈࠞ ߹Ͱද͞ΕΔ͕ɼԻ͔ݯΒϚΠΫϩϑΥϯ·ͰͷΠϯ ύϧεԠʹରͯ͠ेʹ͍࣌ؒ૭Λͭ࣌ؒ ∗ ͮ͘جBSS पྖҬ BSS ͱݺΕɼ࣌ؒྖҬͷ BSS ʹରͯ͠ԋࢉྔͷগͳ͍ΞϧΰϦζϜΛ࣮Ͱݱ ͖ΔɼԻͷεύʔεੑΛΈࠐΊΔͳͲಛ ͕͋ΔҰํͰɼप͝ͱʹͨ͠৴߸ΛԻݯ ͝ͱʹάϧʔϐϯά͢Δύʔϛϡςʔγϣϯ߹ͱݺ ͿΛղܾ͢Δඞཁ͕͋Δɻ ຊڀݚͷతɼ֤Ի͕ݯҠಈͨ͠߹ʹԻݯ ҐஔΛ͠ͳ͕ΒదʹԻݯΛߦ͑Δख๏Λ ࣮͢ݱΔ͜ͱͰ͋ΔɻզʑҎલɼԻݯ౸དྷํΛ ࢄͷજࡏมͱѻ͍ɼͦͷࠞ߹ϞσϧʹΑΓ֤Իݯ ͷεςΞϦϯάϕΫτϧΛ֬ϞσϧԽ͠ɼ؍ଌ৴߸ ͷੜϞσϧʹΈࠐΉ͜ͱͰύϥϝʔλਪΛ௨ ͯ͠ύʔϛϡςʔγϣϯ߹ͱपྖҬ BSS Λಉ ࣌ʹߦ͏ΞϓϩʔνΛఏҊͨ͠ [8] (ͳ͓ɼ΄΅ಉ࣌ ʹظେ௩ΒʹΑͬͯྨࣅͨ͠Ξϓϩʔν͕ఏҊ͞ Ε͍ͯΔ [9])ɻຊߘͰ͜ΕΛ֦ு͠ɼ࣌ؒมԽ͢Δ ֤ԻݯͷεςΞϦϯάϕΫτϧΛɼࢄԽ͞Ε֤ͨ֯ Λঢ়ଶͱ͢ΔӅΕϚϧίϑϞσϧ (Hidden Markov Model; HMM) ʹΑΓ֬ϞσϧԽ͠ɼ؍ଌ৴߸ͷੜ ϞσϧʹΈࠐΈɼύϥϝʔλਪΛ௨ͯ͠ύʔ ϛϡςʔγϣϯ߹ɼ֤ҠಈԻݯͷ౸དྷํɼप ྖҬ BSS Λಉ࣌ʹߦ͏ख๏ΛఏҊ͢Δɻ 2 ؍ଌϞσϧ I ݸͷԻ͔ݯΒ౸དྷ͢Δ৴߸Λ M ݸͷϚΠΫϩ ϑΥϯͰ؍ଌ͢Δ߹Λߟ͑ɼm ൪ͷϚΠΫϩϑΥ ϯͰ؍ଌ͞ΕΔ৴߸ͷ࣌ؒपΛ ym (ωk , tl )ɼ i ൪ͷԻݯ৴߸ͷ࣌ؒपΛ si (ωk , tl ) ͱ ͠ɼy(ωk , tl ) = (y1 (ωk , tl ), . . . , yM (ωk , tl ))T ∈ CM , s(ωk , tl ) = (s1 (ωk , tl ), . . . , yI (ωk , tl ))T ∈ CI ͱ͢Δɻ ͨͩ͠ɼ1 ≤ k ≤ K, 1 ≤ l ≤ L ࣌ؒपྖҬʹ ͓͍ͯͦΕͧΕप͓Αͼ࣌ؒʹରԠ͢ΔΠϯσο ΫεͰ͋Δɻઌʹड़ͨ௨Γɼ࣌ؒपྖҬʹ͓͍ ͯ؍ଌ৴߸ y(ωk , tl ) ۙࣅతʹ y(ωk , tl ) = I X ai (ωk )si (ωk , tl ) + n(ωk , tl ) (1) i=1 ͷΑ͏ʹ s1 , . . . , sI ͷॠ࣌ࠞ߹ͷͰܗද͢͜ͱ͕Ͱ ͖Δɻ͜͜Ͱɼai (ωk ) Ի ݯi ͷεςΞϦϯά (ํ ) ϕΫτϧΛද͠ɼ͜ΕΛฒͨߦྻ A(ωk ) = Underdetermined blind separation of moving sound sources based on DOA-HMM. by HIGUCHI Takuya, TAKAMUNE Norihiro, NAKAMURA Tomohiko, KAMEOKA Hirokazu (Graduate School of Information Science and Technology, The University of Tokyo) 日本音響学会講演論文集 - 23 - 2013年9月 (a1 (ωk ), . . . , aI (ωk )) ∈ CM ×I Λࠞ߹ߦྻͱͿݺɻ n(ω, t) എࡶܠԻϑϨʔϜΛ͑Δڹͳ ͲͰ͋ΔɻԻͷεύʔεੑΛԾఆ͠ɼ֤࣌ؒप (ωk , tl ) ʹ͓͍ͯΞΫςΟϒͰ͋ΔԻݯͷΠϯσο ΫεΛ zk,l ∈ {1, . . . , I} ͱද͢ͱɼࣜ (1) y(ωk , tl ) = azk,l (ωk )s(ωk , tl ) + n(ωk , tl ) (2) Δɻͦ͜ͰɼԻ ݯi ͷ౸དྷํ θi ͕طͷͱ͖ɼai,k h(θi , ωk ) Λฏͨ͠ͱۉෳૉਖ਼نΑΓੜ͞Ε ΔͱԾఆ͢Δɻ͔͠͠વͳ͕Β౸དྷํ θi ࣮ࡍ ʹ؍ଌ͢Δ͜ͱ͕Ͱ͖ͳ͍ͨΊɼ͜ΕΛજࡏม ͢ʹͱ͜͢ͳݟΔͱɼai,k ͷੜϞσϧ DOA Λજ ࡏมͱͨࠞ͠߹ϞσϧͱͳΔɻ͜ΕΛ 3.1 અͷੜ ϞσϧʹΈࠐΈɼੜϞσϧશମͷύϥϝʔλਪ Λߦ͏͜ͱɼύʔϛϡςʔγϣϯ߹ɼ֤Իݯͷ ͷΑ͏ʹॻ͖ͤΔɻ͜ͷ؍ଌϞσϧ͓͍ͯɼ֤ ࣌ؒपʹ͓͍ͯ zk,l ൪ͷԻݯҎ֎ͷ ͯ͢ 0 ͱԾఆ͞Εͨ͜ͱʹͳΔɻै֤ͬͯ࣌ؒप ͰԻݯΛද͢ม zk,l ͷΈͰेͰ͋Γɼ ͜ͷͨΊ্ࣜͰ si (ωk , tl ) ͷΠϯσοΫε i Λল͍ ͍ͯΔɻ͢ͳΘͪ s(ωk , tl ) ֤࣌ؒपʹ͓͍ ͯΞΫςΟϒͳ͍ͣΕ͔ͷԻݯͷΛද͢มͱ ͳΔɻҎࢴޙ໘ͷεϖʔεͷઅͷͨΊɼωk ͱ tl Λ Լ͖ఴ͑ࣈ k, l Ͱද͢هΔ͜ͱʹ͢Δɻ DOA ਪఆɼप͝ͱͷԻݯΛڠௐతʹߦ͏͜ ͱʹ૬͢Δ [8]ɻ ·ͣɼϑ1 , . . . , ϑD (ͯ͢ఆ) ͔ΒͳΔ D ݸͷ DOA ީิͷू߹Λ༻ҙ͢Δɻྫ͑ 180 Λ D ͨ֯͠ ϑd = (d − 1)π/D, (d = 1, . . . , D) ͷू߹ Λߟ͑Δɻ֤Իݯͷ DOA ͕͜ͷ DOA ީิͷத͔ Βܾఆ͞ΕΔͱԾఆ͢ΔͱɼԻ ݯi ͷ౸དྷํ θi ͕ ੜ͞ΕΔϓϩηεҎԼͷΑ͏ʹهड़Ͱ͖Δɻ ci |ρi ∼ Categorical(ci ; ρi ) 3 (5) ੜϞσϧ θ i = ϑc i 3.1 (6) ؍ଌ৴߸ͷੜϓϩηε ؍ଌϞσϧΛͱʹɼ؍ଌ৴߸͕ੜ͞ΕΔϓϩ ηεΛੜϞσϧʹΑΓهड़͢Δɻ (n) ·ͣɼࡶԻ nk,l ͕ɼฏ ͕ۉ0ɼڞࢄ͕ Σk ͷෳૉਖ਼نʹै͏ͱԾఆ͢Δͱɼ͠ a1:I,k = {a1,k , . . . , aI,k } ,sk,l ͓Αͼ zk,l ͕طͰ͋Εɼࣜ (2) ΑΓ yk,l (n) yk,l |a1:I,k,l , sk,l , zk,l ∼ NC (azk,l ,k sk,l , Σk ) (3) P yd = 1 ͱ͢Δ ͱɼCategorical(x; y) ∝ yx Ͱ͋Δɻ·ͨɼρi = (ρi,1 , . . . , ρi,D ) Ͱ͋Δɻci ∈ {1, . . . , D} i ൪ͷ ԻͲʹݯͷ DOA ީิׂ͕ΓͯΒΕΔ͔Λද͢ ΠϯδέʔλมͰ͋Γɼ্ࣜ͜Ε͕ࢄ (֤ ͕֬ ρi,1 , . . . , ρi,D ) ͔Βੜ͞ΕΔ͜ͱΛҙຯ͠ ͍ͯΔɻ͜ͷϓϩηεʹΑΓ֤Իݯͷ DOA ͕ܾఆ͞ Εɼୡपಛੑ ai,k ͨͩ͠ɼy = (y1 , . . . , yD ), d (a) ʹΑΓੜ͞ΕΔɻ͜͜Ͱɼzk,l Λࢄͷજࡏมͱ ai,k |ci ∼ NC (ai,k ; h(ϑci , ωk ), Σk ) ͤͳݟɼyk,l ͷ֬ࠞ߹ਖ਼نͱͳΔ [6,7]ɻ ઘΒɼ͜ͷ֬Ϟσϧʹ͖ͮجɼExpectation- ʹΑΓੜ͞ΕΔɻ Maximization (EM) ΞϧΰϦζϜʹΑΓ࠷ͷ࣌ؒप ϚεΫΛਪఆ͢ΔΞϓϩʔνΛఏҊ͍ͯ͠Δ [6]ɻ 3.3 (7) DOA-HMM Ի͕ݯҠಈ͢Δ߹ɼ࣌ࠁ͝ͱʹεςΞϦϯάϕ 3.2 ࠞ߹ DOA Ϟσϧ [8] Ϋτϧ͕มԽͯ͠͠·͏ͨΊɼҠಈԻݯΛѻ͑ΔΑ ຊઅͰ·ͣԻݯҐஔ͕ݻఆͷ߹Λߟ͑ɼ࣍અ ͰԻ͕ݯҠಈ͢Δ߹Λߟ͑Δɻ͜Ε·Ͱ֤Իݯͷ ͏ʹ͢ΔͨΊʹ ai,k Λ࣌ࠁ l ʹґଘ͢Δม ai,k,l ʹ֦ு͢Δඞཁ͕͋Δɻ͜ͷͱ͖ɼࣜ (2) ୡपಛੑ ai,k ΛपΠϯσοΫε k ͝ͱʹ yk,l = azk,l ,k,l sk,l + nk,l (8) ಠཱͳมͰ͋Δ͔ͷΑ͏ʹѻ͍͕ͬͯͨɼ֤͠Ի ͕ݯ୯Ұํ͔Βฏ໘ͱͯ͠౸དྷ͢ΔͱԾఆͰ͖ ͱॻ͖ͤΔɻ ΔͳΒɼྫ͑ϚΠΫϩϑΥϯ͕ 2 ͷ߹ɼୡ ͜͜Ͱɼ3.2 અͷࣗવͳ֦ுͱͯ͠ɼ֤Իݯͷ DOA पಛੑ ai,k ɼ౸དྷํ (Direction-of-Arrival; ΠϯσοΫε ci Λ࣌ࠁ l ʹґଘ͢Δม ci,l ʹ֦ு DOA)θ ͷؔͱͯ͠ ͠ɼci,1 , . . . , ci,L Λঢ়ଶ ͨ͠ͱྻܥHMM ʹΑΓες h(θ, ω) = " 1 eωB cos θ/C # ΞϦϯάϕΫτϧ ྻܥai,k,1 , . . . , ai,k,L Λ֬Ϟσϧ (4) Խ͢Δ͜ͱΛߟ͑Δɻ͜ͷͱ͖ɼԻ ݯi ͷ࣌ࠁ l ʹ͓ ͚Δ DOAθi,l ͷੜϓϩηεɼ ͱͯ͠ཅʹද͞ΕΔɻͨͩ͠ɼ0 ≤ θ ≤ 2π ɼB ΛϚΠ ΫϩϑΥϯͷִؒ (m)ɼC ΛԻ (m/s) ͱ͢Δɻ࣮ࡍ ʹڹ࣌ؒपྖҬͷॠ࣌ࠞ߹ۙࣅͳͲʹΑ ci,l |ci,l−1 ∼ Categorical(ci,l ; ρci,l−1 ) θi,l = ϑci,l (9) (10) Γɼai,k ্هͷཧ͔ࣜΒҳ͢Δ͜ͱ͕༧͞Ε 日本音響学会講演論文集 - 24 - 2013年9月 ᥦἲ ᚑ᮶ἲ 1, . . . , D ͷભҠ֬Λද͠ɼρd,d′ Λཁૉͱ͢Δ D × D ߦྻ ρ = (ρd,d′ )D×D ΛભҠߦྻͱ͍͏ɻ࣮ࡍͷҠ ಈԻݯɼे͍࣌ؒͷؒʹେ͖͘౸དྷํΛม ͑ΔՄೳੑ͍ͱߟ͑ΒΕΔͷͰɼྡ͢Δঢ়ଶ ͷભҠ֬ΛߴΊʹઃఆ͢Εྑ͍ɻ Ҏ্ͷεςΞϦϯάϕΫτϧྻܥͷ֬ϞσϧΛ 3.1 અͷϞσϧ (ͷ࣌ม൛) ʹΈࠐΈɼશମͷύϥ ϝʔλਪ (ޙड़) Λ௨ͯ͠ύʔϛϡςʔγϣϯ߹ɼ ҠಈԻݯͷैɼप͝ͱͷԻݯΛಉ࣌ʹߦ ͓͏ͱ͍͏ͷ͕ఏҊख๏ͷཁͰ͋Δɻ 4 มਪΞϧΰϦζϜ ؍ଌ৴߸ Y = y1:K,1:L ͕༩͑ΒΕͨͱͰɼҎ ্ͷੜϞσϧͷύϥϝʔλ A = a1:I,1:K,1:L , S = s1:K,1:L , Z = Z1:K,1:L , C = c1:K,1:L ͷࣄޙ p(A, S, Z, C|Y ) ΛٻΊ͍ͨɻ͜ͷࣄޙΛղੳత ʹಘΔ͜ͱ͍͕͠ɼมਪ๏ʹࣅ͖ۙͮج Λ෮ʹࢉܭΑΓಘΔ͜ͱ͕Ͱ͖ΔɻҎԼͰɼρ, (n) (a) Σ1:K , Σ1:K ࣮ݧతʹఆΊΔఆͱ͢Δɻ มਪࣄޙ p(A, S, Z, C|Y ) ͱɼ Z Z · · · q(A, S, Z, C)dA · · · dC = 1 (11) Λ ຬ ͨ ͢ ඇ ෛ ͷ ม ؔ q(A, S, Z, C) ͱ ͷ ؒ ͷ Kullback-Leibler μΠόʔδΣϯε p(A, S, Z, C|Y ) F[q] = log q(A, S, Z, C) q(A,S,Z,C) (12) Λ q ʹؔͯ͠࠷খԽ͢Δ͜ͱ͕తͱͳΔɻͨͩ͠ R hf (x)iq(x) q(x)f (x)dx Λද͢ɻແɼF[q] p = q ͷͱ͖࠷খͱͳΔ͕ɼq ʹؔͯ͠ q(A, S, Z, C) = q(A)q(S)q(Z)q(C) (13) ͱͳΔΑ͏ͳΫϥεΛߟ͑ɼF[q] Λ q(A), q(S), q(Z), q(C) ʹ͍ͭͯަ࠷ʹޓখԽ͢ΔεςοϓΛ܁Γ ฦ͢͜ͱͰɼ֘ΫϥεͷதͰ p(A, S, Z, C|Y ) Λ࠷ྑۙ͘ࣅ͢ΔΛಘΑ͏ͱ͍͏ͷ͕มਪ ๏ͷجຊతͳߟ͑ํͰ͋Δɻ ಋग़লུ͢Δ͕ɼࣜ (12) Λࣜ (11) ͷ߆ଋͷԼͰ ࠷খԽ͢Δ֤ q ղੳతʹҎԼͷ·ٻͯ͠ͱܗΔɻ Y q̂(A) = NC (ai,k,l ; mi,k,l , Γi,k,l ) (14) 6,5>G%@ ͱදͤΔɻρd = (ρd,1 , . . . , ρd,D ) ঢ়ଶ d ͔Βঢ়ଶ q̂(S) = NC (sk,l ; µk,l , σk,l ) Y 㛫>V@ ͍ͯ Forward-Backward ΞϧΰϦζϜΛߦ͏͜ͱͰ q̂(C) ΛٻΊΔ͜ͱ͕Ͱ͖Δɻ Ҏ্ͷมਪΞϧΰϦζϜʹΑͬͯਪఆ͞Εͨ sk,l ͷฏۉ µk,l ʹ֬ φk.l Λ͡Δ͜ͱͰɼԻ ݯi ͷਪఆ৴߸ΛಘΔ͜ͱ͕Ͱ͖Δɻ 5 ෳҠಈԻݯͷ࣮ݧ ఏҊ๏ͷ༗ޮੑΛࣔͨ͢ΊɼҠಈԻʹݯରͯ͠Իݯ ͱ౸དྷํਪఆੑೳͷূݕΛߦͬͨɻҠಈԻͱݯ ͯ͠ҠಈԻݯσʔλϕʔε [9] ͷஉੑऀͷԻ৴߸ 2 ͭΛ (ҠಈԻ ݯAɼB)ɼݻఆԻͯ͠ͱݯԻσʔλ ϕʔε [10] ͷঁੑऀͷԻ৴߸ʹࣨΠϯύϧε ԠΛΈࠐΈՃࢉͨ͠ͷ 1 ͭΛ༻͍ɼͦΕΒΛ ਓతʹࠞ߹ͨ͠ͷΛ؍ଌ৴߸ͱͨ͠ɻؒ࣌ڹ 0 ms Ͱ͋ΔɻҠಈԻݯΛม͑Δ͜ͱͰɼ10 ௨Γͷࠞ ߹ԻσʔληοτΛ࡞͠ɼ࣮ͨ͠ݧɻඪຊԽप 16 kHz ͱͨ͠ɻ࣌ؒϑʔϦΤม( ϑϨʔϜ 64 msɼϑϨʔϜγϑτ 16 ms) ʹΑΓࢉग़͠ (n) (a) ͨɻΣk ͱ Σk ͦΕͧΕ I ɼ101.5 × I ͱͨ͠ɻ· ͨ֯ͷׂ M = 180 ͱͨ͠ɻ4 ষͷ෮Ξϧ ΰϦζϜͷ࣮ߦޙɼԻݯͷਪఆ µk,n ʹɼԻݯ i ͕࣌ؒपͰͲΕ͚ͩΞΫςΟϒΒ͍͔͠Λද ֬͢ φi,k,n Λͨ͡ͷΛɼԻ ݯi ͷਪఆ࣌ؒप ͱͨ͠ɻԻݯੑೳͷධՁج४ͱͯ͠ɼࣜ (17)ʙ(19) ʹΑΓಋग़͞ΕΔ Signal-to-InterferenceRatio (SIR) [12] Λ༻͍ͨɻSIR ͷʹࢉܭɼ3 ͭͷ Իݯͷ͏ͪҰ൪͍͞ͷԻ͕ݯऴྃ͢Δ 3.1 s · ͰΛ༻͍ͨɻ SIRi [l] = OutputSIRi [l] − InputSIRi [l] X ŝi,k,l OutputSIRi [l] = 10 log10 XkX (15) [dB] (18) si,k,l k InputSIRi [l] = 10 log10 X X (16) si′ ,k,l [dB] (19) i′ 6=i k k,l ͳ͓ɼҎ্ͷߋ৽ଇ [8] ͱಉ༷Ͱ͋Δɻ·ͨಘΒ Εͨ q̂(A) ʹΑͬͯ A ͷظΛ ͠ࢉܭρ Λ༻ 日本音響学会講演論文集 ŝi′ ,k,l (17) i′ 6=i k XX i q̂(zk,l ), q̂(zk,l = i) = φi,k,l Fig. 1 ఏҊ๏ͱैདྷ๏ʹ͓͚ΔҠಈԻ ݯA ʹର͢ Δ SIR ͷ࣌ؒมԽ k,l q̂(Z) = i,k,l Y ͨͩ͠ ŝi,k,n Ի ݯi ͷਪఆ৴߸ φi,k,n µk,n ʹ·ؚ ΕΔԻ ݯi ͷ৴߸Ͱ͋Δɻ - 25 - 2013年9月 6,5>G%@ ฿᮶ゅᗘ>UDG@ ᥦἲ ᚑ᮶ἲ ⛣ື㡢※$┿್ ⛣ື㡢※%┿್ ᅛᐃ㡢※┿್ ⛣ື㡢※$᥎ᐃ್ ⛣ື㡢※%᥎ᐃ್ ᅛᐃ㡢※᥎ᐃ್ ⛣ື㡢※$ Fig. 2 ۉ ⛣ື㡢※% ᅛᐃ㡢※ ఏҊ๏ͱैདྷ๏ʹ͓͚ΔԻͱ͝ݯͷ SIR ͷฏ 㛫>V@ Fig. 3 ֤Ի͚͓ʹݯΔ౸དྷ֯ͷਅͱਪఆ ·֤ͨ࣌ࠁͷ౸དྷ֯ͷਪఆʹɼਪఆ͞Εͨ ζϜͷ࣮ݱΛࢦͨ͠ɻԻͷ࣌ؒपͷε ౸དྷ֯ͷ͔֬Β֤࣌ࠁʹ͓͍ͯ࠷֬ ύʔεੑʹͮ͘جपྖҬͷྼܾఆ BSS ϞσϧΛ ͷߴ͍֯Λ༻͍ͨɻ ϕΠζతʹهड़͠ɼԻݯͷҠಈΛɼࢄԽͨ͠౸དྷ֯ ͞ΒʹԻݯͷҠಈΛԾఆ͠ͳ͍ैདྷ๏͕ɼҠಈԻݯ ʹରͯ͠ྑ͍ੑೳΛͨͳ͍͜ͱΛࣔͨ͢Ίɼ[8] Λঢ়ଶͱ͢ΔӅΕϚϧίϑϞσϧͱͯ͠ද͠ݱɼ ͍࣌ؒʹ͓͍ͯԻݯͷ౸དྷ͕֯େ͖͘มԽ͢Δ֬ ͷख๏Λ༻͍ͯಉ༷ͷԻݯ࣮ݧΛߦͬͨ߹ͷ খ͍͞ͱ͍͏ԾఆΛભҠ֬ͱͯ͠؍ଌ৴߸ͷ ݁ՌͱఏҊ๏ͷ݁ՌΛൺֱͨ͠ɻ Fig. 1 ʹఏҊ๏ͱैདྷ๏ʹΑΔɼ1 ͭͷ࣮ʹݧ ͓͚ΔҠಈԻ ݯA ͷ SIR ͷ࣌ؒมԽΛࣔ͢ɻैདྷ๏ ͰɼԻݯ͕͏·͘ߦ͓͑ͯΒͣɼSIR ͕ଟ͘ͷ ࣌ࠁͰ 0 ʹ͍ۙͰ͋Δ (input ͱ output Ͱ SIR ͕ վળ͞Ε͍ͯͳ͍) ͷʹରͯ͠ɼఏҊ๏Ͱଟ͘ͷ࣌ ࠁͰ SIR ͕վળ͞Ε͍ͯΔͷ͕ͯݟऔΕΔɻFig. 2 ʹ ֤Իʹͱ͝ݯσʔληοτͱ࣌ࠁͰฏۉΛͱͬͨ SIR ͷΛࣔ͢ɻ3 ͭͷԻ͍͓ͯʹͯ͢ݯɼैདྷ๏Ͱ SIR ͕͘Իݯ͕ߦ͍͑ͯͳ͍ͷʹରͯ͠ɼఏҊ ๏Ͱ SIR ͕ 10 dB ͔Β 17 dB ఔͷΛ͍ࣔͯ͠ Δͷ͕Θ͔Δɻ3 ͭͷԻ͚͓ʹݯΔ SIR ͷฏۉɼ ैདྷ๏Ͱ 1.91 dBɼఏҊ๏Ͱ 12.31 dB Ͱ͋ͬͨɻ ࣍ʹɼ1 ͭͷ࣮͚͓ʹݧΔ౸དྷ֯ਪఆͷ݁Ռ Λ Fig. 3 ʹࣔ͢ɻ࣮ࡍͷ౸དྷ֯ͱൺͯɼ1 s ۙ ͔ΒԻݯಉ࢜ͷ౸དྷ͕֯ॏͳΓɼ͔ͭԻͷऴྃ͢ Δ 3 s ۙ·Ͱɼ͓͓ΉͶਖ਼͘͠ਪఆ͞Ε͍ͯΔ͜ ͱ͕͔Δɻ࠷ॳͷ 1 s ͷؒͰ౸དྷํਪఆͷਫ਼ ͕ྑ͘ͳ͍ͷɼੜϞσϧʹΈࠐ·Εͨɼ౸དྷ֯ ͕ʹٸมԽ͠ʹ͍͘ͱ͍͏ԾఆʹΑΓɼԻͷೖͬ ͍ͯͳ͍ॳۙࠁ࣌ظͷσʔλʹରͯ͠ਪఆ͞Εͨ ౸དྷ͔֯ΒΒ͔ʹͭͳ͙Α͏ʹ౸དྷ͕֯ਪఆ ͞Εͯ͠·͏͔ΒͰ͋Δͱߟ͑ΒΕΔɻݻఆԻݯͷਪ ఆ֯ʹόΠΞε͕ͷ͍ͬͯΔͷɼཧతͳεςΞ ϦϯάϕΫτϧͱ࣮ࡍͷεςΞϦϯάϕΫτϧͱͷ ͔ࠩޡΒ͘Δਪఆ͋ͰࠩޡΔՄೳੑ͚ͩͰͳ͘ɼ[11] ͷσʔλϕʔε࡞࣌ͷϚΠΫϩϑΥϯͷ֯ࠩޡ Ͱ͋ΔՄೳੑߟ͑ΒΕΔɻ 6 ੜϞσϧʹΈࠐΈɼࠞ߹ DOA ϞσϧͱΈ߹Θ ͤΔ͜ͱͰɼԻݯͱप͝ͱɼ࣌ؒ͝ͱͷύʔ ϛϡςʔγϣϯ߹Λಉ࣌ʹ࣮ͨ͠ݱɻ͜ΕʹΑΓɼ ࣌ؒมԽ͢Δ౸དྷ֯ͷਪఆͱԻݯΛҰߦʹڍ ͑Δ͜ͱ͕ɼఏҊ๏ͷओཁͳಛͰ͋Δɻ ࢀߟจݙ [1] A. Hyvärinen, J. Karhunen, and E. Oja, Independent Component Analysis, John Wiley & Sons, 2001. [2] Ö. Yılmaz & S. Rickard, IEEE Trans. SP, 52(7), pp. 1830–1847, 2004. [3] Y. Mori et al., in Proc. IWAENC ’05, pp. 229– 232, 2005. [4] M. I. Mandel et al., in Adv. NIPS, pp. 953–960, 2006. [5] S. Araki et al., Signal Process., 87(8), pp. 1833– 1847, 2007. [6] ઘଞ, Իߨ (य़), 2-1-5, pp. 555–556ɼ2007ɽ [7] H. Sawada et al., IEEE Trans. ASLP, 19(3), pp. 516–527, 2010. [8] ُԬଞɼԻߨ (य़), 1-1-19, pp. 713–716ɼ2012ɽ [9] T. Otsuka et al., in Proc. AAAI-12 pp. 2038– 2045, 2012. [10] A. Kurematsu et al., Speech Communication, pp. 357–363, 1990. [11] S. Nakamura et al., p. 965–968, 2000. in Proc. LREC ’00, p- [12] E. Vincent et al., IEEE Trans. ASLP, pp. 1462– 1469, 2006. ͓ΘΓʹ ຊߘͰɼԻ͕ݯҠಈ͢Δ͜ͱͰࠞ߹աఔ͕มԽ ͢Δ߹ʹ͓͍ͯ҆ఆͯ͠ಈ࡞͢Δ BSS ΞϧΰϦ 日本音響学会講演論文集 - 26 - 2013年9月
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