2-10-1ଟνϟϯωϧ֊৐ӅΕϚϧίϑϞσϧʹΑΔԻ‫ݯ‬෼཭ɾԻ‫ڹ‬Πϕϯτ‫ݕ‬ग़ɾ࢒‫ڹ‬আ‫ڈ‬ɾ౸དྷํ޲ਪఆͷ౷߹తΞϓϩʔνͱͦͷੑೳධՁ ∗˕ඉ‫( ࠸୎ޱ‬౦େӃ৘ใཧ޻)ɼُԬ߂࿨ (౦େӃ৘ใཧ޻ɼNTT)1͸͡ΊʹϒϥΠϯυԻ‫ݯ‬෼཭ (Blind Source Separation; BSS) ͷ໰୊ͱ͸ɼԻ‫ݯ‬৴߸΍Ի‫͔ݯ‬ΒϚΠΫ·Ͱͷ఻ୡಛੑ͕ະ஌ͷ৔߹ʹɼෳ਺ͷԻ‫ݯ‬৴߸͕ࠞ߹͞Εͨ‫؍‬ଌ৴߸͔ΒԻ‫ݯ‬৴߸Λਪఆ͢Δ໰୊Ͱ͋ΔɽҰൠతʹɼBSS ͷ໰୊Λղͨ͘Ίʹ͸ɼԻ‫ݯ‬৴߸ʹରཱͯͯͨ͠ͳΜΒ͔ͷԾఆΛ‫࠷ʹج‬దԽ‫ج‬४Λཱͯɼ࠷దԽ໰୊Λղ͘ඞཁ͕͋ΔɽචऀΒ͸ɼԻ‫ڹ‬Πϕϯτɼ࢒‫ڹ‬ɼԻ‫ݯ‬ͷ౸དྷํ޲ͳ
Ͳ͕ BSS ͷ໰୊Λղͨ͘Ίͷख͕͔Γͱ੒Γ͏Δ͜ͱʹண໨͠ɼଟνϟϯωϧ֊৐ӅΕϚϧίϑϞσϧͱ‫Ϳݺ‬ϞσϧΛ༻͍ͯɼԻ‫ݯ‬෼཭ɼԻ‫ڹ‬Πϕϯτ‫ݕ‬ग़ɼ࢒‫ڹ‬আ‫ڈ‬ɼԻ‫ݯ‬ͷ౸དྷํ޲ਪఆΛ౷߹తʹߦ͏ख๏ΛఏҊ͖ͯͨ͠ [1, 2, 3]ɽຊߘͰ͸ɼ͞ΒͳΔ࣮‫ݧ‬Λߦ͍ɼͦͷੑೳΛৄࡉʹධՁͨ͠ɽ2ଟνϟϯωϧ֊৐ӅΕϚϧίϑϞσϧ

2.1 ৞ΈࠐΈࠞ߹ۙࣅʹΑΔ‫؍‬ଌ৴߸ͷࠞ߹ϞσϧI ‫ݸ‬ͷԻ‫͔ݯ‬Β౸དྷ͢Δ৴߸Λ M ‫ݸ‬ͷϚΠΫϩϑΥϯͰ‫؍‬ଌ͢Δ৔߹Λߟ͑Δɽࣨ಺ΠϯύϧεԠ౴௕͕࣌ؒप೾਺ల։ͷ࣌ؒ૭௕ʹରͯ͠े෼ʹ୹͍ͱ‫ݶ‬Βͣɼॠ࣌ࠞ߹ۙࣅ͕੒Γཱͨͳ͍৔߹ (࢒‫͕͋ڹ‬Δ৔߹) Λߟ͑ɼ࣌ؒप೾਺ྖҬʹ͓͚Δ৞ΈࠐΈࠞ߹ۙࣅʹΑͬͯ࣌ؒप೾਺ྖҬͷ‫؍‬ଌ৴߸Λۙࣅ͢Δɽy(ωk , tl ) ≈TI 

(q)

(q)

zi,1 , . . . , zi,L ͕Ϛϧίϑ࿈࠯ʹै͏ͱԾఆ͢Δͱɼ
(q)

(q)

(q)

zi,l |zi,l−1 ∼ Categorical(zi,l ; ρ(q)(q)

i,zi,l−1)ɼ (4)ͱॻ͚Δɽ͜͜Ͱ Categorical(x; y) = yx Ͱ͋Γɼ
(q)
(q)
(q)
ρi,q = (ρi,q,1 , . . . , ρi,q,Q ) ͸ i ൪໨ͷԻ‫͚͓ʹݯ‬Δঢ়(q)

ଶ q ͔Β֤ঢ়ଶ 1, . . . , Q ΁ͷભҠ֬཰Λද͠ɼ ρi =(q)(ρi,q,q )Q×Q ͸ i ൪໨ͷԻ‫͚͓ʹݯ‬ΔભҠߦྻͰ͋Δɽ
ঢ়ଶ q Ͱ͋Δ i ൪໨ͷԻ‫ݯ‬ͷ‫ج‬ఈύϫʔεϖΫτϧΛ
wi,k,q ͱද͢ͱ͢Δͱɼ࣌ࠁ l ʹ͓͚Δ i ൪໨ͷԻ‫ݯ‬(q)৴߸ͷύϫʔεϖΫτϧ͸ zi,l ʹґଘ͠ɼsi,k,l ͷੜ੒Ϟσϧ͸ҎԼͷΑ͏ʹॻ͖ͳ͓ͤΔɽ(q)si,k,l |wi,k,1:Q , hi,l , zi,l ∼ NC (si,k,l ; 0, wi,k,z(q) hi,l ).
i,lai (ωk , tτ )si (ωk , tl − tτ ).

Tͨͩ͠ɼ y(ωk , tl ) = (y1 (ωk , tl ), . . . , yM (ωk , tl )) ∈CM ɼ ai (ωk , tτ ) = (ai,1 (ωk , tτ ), . . . , ai,M (ωk , tτ ))T ∈CM Ͱ͋Δɽ͜͜Ͱ ym (ωk , tl ) ∈ C ͸ m ൪໨ͷϚΠΫͰ‫؍‬ଌ͞Εͨ‫؍‬ଌ৴߸ͷप೾਺ ωk ɼ࣌ࠁ tl ʹ͓͚Δ࣌ؒप೾਺੒෼Ͱ͋Γɼsi (ωk , tl ) ∈ C ͸ i ൪໨ͷԻ‫ݯ‬৴߸ͷप೾਺ ωk ɼ࣌ࠁ tl ʹ͓͚Δ࣌ؒप೾਺੒
෼Ͱ͋Δɽ·ͨ ai (ωk , tτ ) ͸ i ൪໨ͷԻ‫ݯ‬৴߸ʹର͢
Δप೾਺ ωk ʹ͓͚Δ఻ୡप೾਺ಛੑͷ࣌ࠁ tτ ͷ੒෼Ͱ͋Γɼ0 ≤ τ ≤ T ͸఻ୡप೾਺ಛੑͷ࣌ؒप೾਺ྖҬʹ͓͚Δ࣌ؒΠϯσοΫεͰ͋ΔɽҎԼͰ͸ωk ɼtl ΛͦΕͧΕ k ɼl ͷఴ͑ࣈͰද͢ɽ2.2 Ի‫ڹ‬Πϕϯτʹ‫ͮ͘ج‬Ի‫ݯ‬৴߸ͷੜ੒Ϟσϧ·ͣɼԻ‫ݯ‬৴߸͕۠෼తʹఆৗͰ͋Δ͜ͱΛԾఆ
2͠ɼ֤࣌ؒप೾਺఺Ͱ si,k,l ͕ฏ‫ ۉ‬0ɼ෼ࢄ σi,k,lͷෳૉਖ਼‫ن‬෼෍ʹै͏ͱ͢ΔͱɼԻ‫ݯ‬৴߸ͷੜ੒ϓϩηε͸ɼ
2si,k,l |σi,k,l ∼ NC (si,k,l ; 0, σi,k,l)ɼ

(2)2ͱ ॻ ͖ ද ͤ Δ ɽ͜ ͜ Ͱ σi,k,l͸ प ೾ ਺ k ɼ࣌ ࠁl ʹ͓͚Δ i ൪໨ͷԻ‫ݯ‬ͷύϫʔεϖΫτϧີ౓ Λ ද ͢ɽ্ ‫ ه‬ͷ Ϟ σ ϧ ʹ Non-negative Matrix
Factorization(NMF)[4, 5] ͷԾఆΛ૊ΈࠐΉͱɼ
2
σi,k,l= wi,k hi,l ,(5)(1)

i=1 τ =0∗ͱͳΔɽ্‫ه‬ͷࣜʹΑΔଟνϟϯωϧ‫؍‬ଌ৴߸ͷੜ੒Ϟσϧ͸ɼଟνϟϯωϧ NMF[6] ͱ‫ݺ‬͹Ε͍ͯΔɽ͔͠͠ɼଟ͘ͷԻ‫ݯ‬ͷύϫʔεϖΫτϧ͸ɼແԻঢ়ଶɼԻͷ্ཱ͕ͪΓɼఆৗঢ়ଶͳͲͦͷԻ‫ݯ‬ͷঢ়ଶ(Ի‫ڹ‬Πϕϯτ) ʹԠͯ͡ҟͳΔͱߟ͑ΒΕΔͷͰɼ࣌ؒมԽ͢ΔԻ‫ݯ‬ͷঢ়ଶʹԠ֤ͯ͡Ի‫ݯ‬৴߸͕ҟͳΔύϫʔεϖΫτϧΛ࣋ͭͱԾఆ͢Δɽ࣌ࠁ l ʹ͓͚Δ i ൪໨ͷԻ‫ݯ‬ͷύϫʔεϖΫτϧͷঢ়ଶΛද͢(q)ӅΕม਺ zi,l ∈ {1, . . . , Q} Λಋೖ͠ɼঢ়ଶͷ࣌‫ྻܥ‬(3)࣍ʹɼԻ‫ݯ‬ͷԻྔʹண໨͢ΔͱɼແԻঢ়ଶͱ༗Իঢ়ଶͰ͸౰વԻྔͷେ͖ͳ஋ͷऔΓ΍͕͢͞ҟͳΔͱߟ͑ΒΕΔͷͰɼԻྔ΋·ͨԻ‫ݯ‬ͷঢ়ଶ (Ի‫ڹ‬Πϕϯτ) ʹґଘͯ͠ҟͳΔৼΔ෣͍Λ͢Δͱ͍͑Δɽͦ(j)͜Ͱɼ·ͣԻྔͷঢ়ଶΛද͢ӅΕม਺ zi,l ∈ 1, . . . , J(j)(j)Λಋೖ͠ɼঢ়ଶͷ࣌‫ ྻܥ‬zi,1 , . . . , zi,L ͕Ϛϧίϑ࿈࠯ʹै͏ͱԾఆ͢Δɽ
(j)

(j)

(j)

zi,l |zi,l−1 ∼ Categorical(zi,l ; ρ(j)(j)

i,zi,l−1).

(6)(j)

͜ͷͱ͖ɼhi,l ͕Իྔͷঢ়ଶ zi,l ∈ 1, . . . , J ʹΑͬͯҟͳΔϋΠύʔύϥϝʔλΛ࣋ͭΨϯϚ෼෍ʹै͏ͱԾఆ͢Δͱɼ(j)hi,l |zi,l ∼ Gamma(hi,l ; αz(j) βz(j) ),i,li,l(7)ͱͳΔɽ͜͜Ͱ α1:J ͱ β1:J ͸ͦΕͧΕΨϯϚ෼෍ͷ‫ܗ‬ঢ়ύϥϝʔλͱεέʔϧύϥϝʔλͰ͋Γɼ
α−1 −x/βeGamma(x; α, β) = x Γ(α)βɼͨͩ͠ Γ(·) ͸ΨϯϚα(j)ؔ਺Ͱ͋Δɽzi,l ͕ແԻঢ়ଶʹରԠ͢Δͱ͖͸ hi,l ͸খ͞ͳ஋Λͱͬͯ΄͍͠ͷͰɼখ͞ͳ஋ΛͱΔ֬཰͕ߴ͘ͳΔΑ͏ʹΨϯϚ෼෍ͷϋΠύʔύϥϝʔλΛ(j)ઃఆ͠ɼzi,l ͕༗Իঢ়ଶʹରԠ͢Δͱ͖͸Ұ༷෼෍ʹۙ͘ͳΔΑ͏ʹΨϯϚ෼෍ͷϋΠύʔύϥϝʔλΛઃఆ͢Ε͹Α͍ɽUniﬁed approach for source separation, audio event detection, dereverberation and DOA estimation basedon multichannel factorial hidden Markov model and its performance evaluation. by HIGUCHI, Takuya(The University of Tokyo), KAMEOKA Hirokazu (The University of Tokyo, NTT)

日本音響学会講演論文集- 575 -

2015年3月

2.3

ࠞ߹ DOA ϞσϧʹΑΔۭؒ૬ؔߦྻͷੜ੒Ϟσϧ࣍ʹɼۭؒ૬ؔߦྻͷੜ੒ϓϩηεΛ౸དྷํ޲ʹ‫཰͍֬ͯͮج‬తʹϞσϧԽ͢Δɽ఺Ի‫ͱݯ‬ฏ໘೾౸དྷΛԾఆ͢Δͱɼۭؒ૬ؔߦྻ͸Ի‫ݯ‬ͷ౸དྷํ޲ʹ
Ԡͯ͋͡Δಛఆͷߏ଄Λ࣋ͭɽྫ͑͹ϚΠΫϩϑΥϯ
ͷ਺ M = 2 ͷ৔߹Ͱ͸ɼํ޲ θ(0 ≤ θ ≤ π) ʹ͋ΔԻ‫ݯ‬ͷۭؒ૬ؔߦྻ͸ɼҎԼͷΑ͏ʹཅʹ‫ه‬ड़Ͱ͖Δɽ
1jωB cos θ/C ]∗J (θ, ω) = jωB cos(8)θ/C [1 ee͜͜Ͱ j ͸‫਺ڏ‬୯ҐɼB [m] ͸ϚΠΫϩϑΥϯؒͷ‫ڑ‬཭ɼC [m/s] ͸Ի଎Ͱ͋Δɽi ൪໨ͷԻ‫ݯ‬ͷ౸དྷํ޲θi ͕‫ط‬஌ͷ৔߹Ͱ͸ɼ௚઀೾ʹରԠ͢Δۭؒ૬ؔߦ
ྻ͸ J (θi , ωk ) ͱ౳͘͠ͳΔ͜ͱ͕‫ظ‬଴͞ΕΔɽ͔͠͠ͳ͕Β࣮ࡍʹ͸ɼԻ‫ݯ‬ͷ౸དྷํ޲͸Ի‫ڹ‬৴߸͔Β௚઀‫؍‬ଌͰ͖ͳ͍͹͔ΓͰͳ͘ɼϑϨʔϜ಺ͷ࢒‫ڹ‬΍ϊΠζͳͲʹΑͬͯɼۭؒ૬ؔߦྻ͸ཧ૝తͳߏ଄͔
Βҳ୤͢Δ͜ͱ͕͋Δɽͦ͜Ͱ·ͣɼ[7] ͱಉ༷ʹɼθi ∈ {ϑ1 , . . . , ϑO } Λ i൪໨ͷԻ‫ݯ‬ͷ౸དྷํ޲ͱ͠ɼ֤Ի‫ݯ‬ͷ DOA ͕͜ͷDOA ީิ஋ͷத͔Βܾఆ͞ΕΔͱԾఆ͢Δ͜ͱͰɼԻ‫ ݯ‬i ͷ౸དྷํ޲ θi ͕ੜ੒͞ΕΔϓϩηεΛҎԼͷΑ͏ʹ‫ه‬ड़͢Δɻ(o)(o)(o)(o)

zi |ρi ∼ Categorical(zi ; ρi ),θi = ϑz(o) .
(o)(o)(o)Z (o) = z1:I ͸ӅΕม਺ͱ͢ΔɽҎԼͰ͸ ρ(q) ɼρ(j) ɼρ(o) ͸࣮‫ݧ‬తʹఆΊΒΕͨఆ਺ͱ͢Δɽิॿม਺ͷू߹Λ Λ ͱ͢Δͱɼ໨తؔ਺ L(Θ) = log p(Θ|Y ) ʹର͢Δิॿؔ਺ L+ (Θ, Λ) ͸ҎԼͷΑ͏ʹઃ‫͖Ͱܭ‬Δɽ
L(Θ) ≥L+ (Θ, Λ)1   (q)=−λq,i,l−τ2k,l i,q,τtr(y k,l y k,l H Ri,k,l,q,τ C −1i,k Ri,k,l,q,τ )wi,k,q hi,l−τ+ tr(U −1k,l C i,k )wi,k,q hi,l−τ+(o)(o)∼ WC (C i,k,0 ; γ, J ϑ (o) ,k + I).
z(11)iͨ ͩ ͠WC (X; γ, Y )∝|X|(γ−M )/2 exp(− 12 tr(XY −1 )) Ͱ ͋ Γɼγ ͸γ ≥ M + 1 Λຬͨ͢ϋΠύʔύϥϝʔλͰ͋Δɽ͜͜Ͱ͸ɼ‫ྻߦٯ‬ԋࢉΛՄೳʹ͢ΔͨΊʹɼۙࣅతʹ J ϑ (o) ,k ʹඍখ஋ Λ༻͍ͯ୯Ґߦྻ I Λ଍ziͯ͋͠Δɽ‫ ؍‬ଌ ৴ ߸ ͷ ࠷ ऴ త ͳ ੜ ੒ Ϟ σ ϧ ͸ a1:I,k,0:T ɼ(q)w1:I,k,1:Q ɼ h1:I,l−T :l ɼz1:I,l−T :l ͕‫ط‬஌ͷ৚݅ԼͰɼ
ࣜ (4)ɼࣜ (6)ɼࣜ (7)ɼࣜ (10)ɼࣜ (11) ͱ߹ΘͤͯҎԼͷΑ͏ʹॻ͖௚ͤΔɽ(q)

y k,l |a1:I,k,0:T , w1:I,k,1:Q , h1:I,l−T :l , z1:I,l−T :l∼ NC (y k,l ; 0,C i,k,τ wi,k,z(q) hi,l−τ ). (12)i,τi,l−τ͜ͷੜ੒Ϟσϧʹ‫࠷͍ͯͮج‬దͳύϥϝʔλΛ‫ٻ‬ΊΔ͜ͱ͸ɼԻ‫ݯ‬ͷ౸དྷํ޲ਪఆɾ࢒‫ڹ‬আ‫ڈ‬ɾԻ‫ڹ‬Πϕϯτ‫ݕ‬ग़ɾԻ‫ݯ‬෼཭ͷ໰୊Λ౷߹తʹղ͘͜ͱʹ૬౰
͍ͯ͠Δɽ

3ิॿؔ਺๏ʹ‫ͮ͘ج‬ύϥϝʔλਪ࿦໨తؔ਺Ͱ͋Δର਺ࣄ‫཰֬ޙ‬͸֤ύϥϝʔλ͕͓‫ޓ‬͍ʹؔ܎͠߹͓ͬͯΓɼҰൠʹ࠷దԽ͕ࠔ೉Ͱ͋Δ͕ɼ໨తؔ਺Λ‫࠷ॴہ‬େԽ͢ΔύϥϝʔλΛ‫ٻ‬ΊΔ൓෮Ξ

日本音響学会講演論文集(j)+ log |U k,l |

λj,i,l (αj − 1) log hi,l − hi,l /βj− αj log βj − log Γ(αj )
1−1+di,o − tr(C i,k,0 (J k,o + I) )2i,k,o−1γ−Mtr(Ũ i,k C i,k,0 )+2 (q)+ log |Ũ i,k | +λq,i,l log p(Z (q) )ͨ ͩ ͠ ρi= (ρi,1 , . . . , ρi,O ) Ͱ ͋ Δ ɻzi∈{1, . . . , O} ͸ i ൪໨ͷԻ‫Ͳʹݯ‬ͷ DOA ީิ஋ׂ͕Γ౰ͯΒΕΔ͔Λද͢Πϯδέʔλม਺Ͱ͋Γɼ্ࣜ(o)(o)
͸͜Ε͕཭ࢄ෼෍ (֤֬཰஋͕ ρi,1 , . . . , ρi,O ) ͔Βੜ੒͞ΕΔ͜ͱΛҙຯ͍ͯ͠Δɻͦͯ͠ɼ௚઀೾ʹରԠ(o)͢Δۭؒ૬ؔߦྻ C i,k,0 ͕ɼzi ͕‫ط‬஌ͷ৚݅ԼͰɼҎԼͷΑ͏ͳ΢Οογϟʔτ෼෍ʹै͏ͱԾఆ͢Δɽ

C i,k,0 |zi
j,i,l(9)(10)i(o)ϧΰϦζϜΛิॿؔ਺๏ͷ‫ݪ‬ཧʹ‫͖ͮج‬ಋग़ͨ͠ [3]ɽϞσϧʹ͓͚Δਪఆ͍ͨ͠ม਺͸ W = w1:I,1:K,1:Q ,H = h1:I,1:L , C = C 1:I,1:K,0:T Ͱ͋Δɽ্‫ه‬ͷม਺(q)(j)ͷू߹Λ Θ Ͱද͢ɽZ (q) = z1:I,1:L ɼZ (j) = z1:I,1:L ɼ+
j,i,lq,i,l(j)λj,i,l log p(Z (j) ) + CL+ ,(13)͜͜Ͱ Ri,k,l,τ,q ɼU k,l ɼŨ i,k ͸i,τ Ri,k,l,τ,q = I(q)(j)Λຬͨ͢Τϧϛʔτਖ਼ఆ஋ߦྻͰ͋Γɼλq,i,l ɼλj,i,l ɼ(q)(j)
di,o ͸ q λq,i,l = 1ɼ j λj,i,l = 1ɼ o di,o = 1 ΛͦΕͧΕຬͨ͢ඇෛ஋ͷεΧϥʔ஋ɼCL+ ͸ఆ਺߲Λ·ͱΊͨ΋ͷͰ͋Δɽࢴ໘ͷ౎߹্ৄࡉ͸লུ͢Δ͕ɼ্‫ه‬ͷิॿؔ਺ L+ (Θ, Λ) Λ‫࠷ॴہ‬େԽ͢ΔΑ͏ʹ Λ ͱ Θ ͷߋ৽Λަ‫܁ʹޓ‬Γฦ͢͜ͱͰɼ໨తؔ਺ L(Θ) Λؒ઀తʹ‫࠷ॴہ‬େԽ͢Δ͜ͱ͕Ͱ͖Δ [3]ɽ4ධՁ࣮‫ݧ‬

4.1 Ի‫ݯ‬෼཭ੑೳͷධՁ࣮‫ݧ‬ఏҊ๏ͷԻ‫ݯ‬෼཭ੑೳͷධՁͷͨΊʹɼT = 0ɼࠞ߹ DOA Ϟσϧͳ͠ͷ৔߹ͷఏҊ๏Λ༻͍ͯɼ‫ͳࢣڭ‬͠/‫͋ࢣڭ‬Γͷ 2 ͭͷ৚݅ԼͰ࣮‫ݧ‬ΛߦͬͨɽRWCPσʔλϕʔεඇԻ੠υϥΠιʔε [8] ͷதͷ 15 छྨͷԻʹରͯ͠ಉ͘͡ RWCP σʔλϕʔεͷΠϯύϧεԠ౴ (࢒‫ ؒ࣌ڹ‬0 msɼϚΠΫؒ‫ ཭ڑ‬11.48 cmɼϚΠΫͷ਺ M = 2) Λ৞ΈࠐΈɼਓ޻తʹଟνϟϯωϧͷࠞ߹৴߸Λ࡞੒ͨ͠ɽ15 छྨͷԻΛͦΕͧΕ 2 ճͣͭ࢖༻͠ɼϥϯμϜʹ 3 ͭͷԻΛࠞ߹͢Δ͜ͱͰɼ10छྨͷࠞ߹ԻΛ࡞੒ͨ͠ɽ3 ͭͷԻ‫ݯ‬͸ΠϯύϧεԠ౴Λ৞Έࠐ·ΕΔ͜ͱͰϚΠΫ͔Β 30◦ ɼ90◦ ɼ130◦ͷҐஔʹਓ޻తʹͦΕͧΕ഑ஔ͞ΕͨɽαϯϓϦϯά
प೾਺͸ 16 kHz ͱͨ͠ɽϑϨʔϜ௕ 16 msɼϑϨʔϜγϑτ௕ 8 ms Ͱ STFT Λߦ͍ɼ࣌ؒप೾਺ల։Λߦͬͨɽ‫ج‬ఈύϫʔεϖΫτϧͷঢ়ଶ਺ Q Λ 1, 3, 5,10 ͱม࣮͑ͯ‫ݧ‬ΛߦͬͨɽԻྔͷঢ়ଶ਺ J = 2 ͱ͠ɼ
α1 ͱ β1 Λ 1ɼ10−3 ͱͦΕͧΕઃఆ͠ɼα2 ͱ β2 Λ 1- 576 -

2015年3月

1110
98
765
4329(b)

25

ᥦ᱌ἲ
MNMF

28
27
26
25
24
23
22
2120

13510ྛ㡢※䛻ᑐᛂ䛩䜛ᇶᗏ䝟䝽䞊䝇䝨䜽䝖䝹䛾ᩘ

(c)

50

23

SIR Improvement [dB]30

SDR Improvement [dB]

(a)

12

SIR Improvement [dB]SDR Improvement [dB]

13

21
191715131197513510ᥦ᱌ἲMNMF

40353025201510501ྛ㡢※䛻ᑐᛂ䛩䜛ᇶᗏ䝟䝽䞊䝇䝨䜽䝖䝹䛾ᩘ

(d)

45

3510ྛ㡢※䛻ᑐᛂ䛩䜛ᇶᗏ䝟䝽䞊䝇䝨䜽䝖䝹䛾ᩘ13510ྛ㡢※䛻ᑐᛂ䛩䜛ᇶᗏ䝟䝽䞊䝇䝨䜽䝖䝹䛾ᩘ

Fig. 1 ֤Ի‫ʹݯ‬ରԠ͢Δ‫ج‬ఈύϫʔεϖΫτϧΛม͑ͨͱ͖ͷ (a) ‫͠ͳࢣڭ‬෼཭࣮‫͚͓ʹݧ‬Δ SDR ͷվળྔͱ (b)SIR ͷվળྔɼ(c) ‫͋ࢣڭ‬Γ෼཭࣮‫͚͓ʹݧ‬Δ SDR ͷվળྔͱ (d)SIR ͷվળྔɽMNMF ͸ [6] ͷख๏Λද͢ɽͱ 1010 ͱઃఆ͢Δ͜ͱͰɼj = 1 ΛແԻঢ়ଶͱΈͳ(j)ͨ͠ɽρ(j) ͸ i = 1, . . . , 3 ʹ͓͍ͯ ρi,1 = (0.9, 0.1)ɼ
(j)ρi,2 = (0.1, 0.9) ͱ͠ɼࣗ‫ݾ‬ભҠͷ֬཰ΛߴΊʹઃఆ√ͨ͠ɽC ͷॳ‫ظ‬஋͸ 1/ M × I ͱͨ͠ɽH ͷॳ‫ظ‬஋͸͢΂ͯͷཁૉΛ 1 ͱͯ͠༩͑ͨɽλ(q) ͷॳ‫ظ‬஋
͸ 1/Qɼλ(j) ͷॳ‫ظ‬஋͸ 1/J ͱͨ͠ɽW ͱ ρ(q) ΛΫϦʔϯͳԻ͔Βֶश͠ɼ‫ݻ‬ఆͯ͠༻͍Δ‫͋ࢣڭ‬Γ࣮‫ݧ‬ͱɼW Λཚ਺Λॳ‫ظ‬஋ͱͯ͠ਪఆ͠ɼρ(q) ΛҰ༷ͱͯ͠‫ݻ‬ఆ͢Δ‫ݧ࣮͠ͳࢣڭ‬ͷ 2 छྨͷ࣮‫ݧ‬Λߦͬͨɽύϥϝʔλਪ࿦ΞϧΰϦζϜ͸ 100 ճ൓෮ͨ͠ɽൺֱର৅ʹ͸ [6] ͷख๏Λ༻͍ɼҰͭͷԻ‫ʹݯ‬ରԠ͢Δ‫ج‬ఈύϫʔεϖΫτϧͷ਺Λɼ1, 3, 5, 10 ͱม࣮͑ͯ‫ݧ‬Λߦͬͨɽ෼཭Ի͸ଟνϟϯωϧ΢ΟʔφʔϑΟϧλʹΑͬͯಘͨɽ٬‫؍‬ධՁ‫ج‬४ͱͯ͠ɼSDR ͱ SIR[9] Λ༻͍ͨɽߴ͍ SDRɼSIR ͸ͦΕͧΕߴ͍Ի‫ݯ‬෼཭ੑೳΛද͢ɽ‫͠ͳࢣڭ‬Ի‫ݯ‬෼཭࣮‫͚͓ʹݧ‬Δ SDR ͱ SIR ͷվળྔΛɼͦΕͧΕ Fig. 1 ͷ (a) ͱ (b) ʹɼ‫͋ࢣڭ‬ΓԻ‫ݯ‬෼཭࣮‫͚͓ʹݧ‬Δ SDR ͱ SIR ͷվળྔΛɼͦΕͧΕ (c) ͱ (d) ʹࣔ͢ɽఏҊ๏͸ [6] ͷख๏Λ্ճ͍ͬͯΔ͜ͱ͕෼͔Δɽಛʹɼ֤Ի‫ʹݯ‬ରԠ͢Δ‫ج‬ఈύϫʔεϖΫτϧͷ਺Λ૿΍ͨ͠ͱ͖ʹɼఏҊ๏͸ैདྷ๏Λେ্͖͘ճͬͨɽ͜ΕʹΑΓɼԻ੠ͳͲͷଟ਺ͷεϖΫτϧΛ࣋ͭԻ‫ݯ‬৴߸ͷ෼཭ʹ͓͍ͯ͸ɼ[6]ͷख๏ΑΓ΋ఏҊ๏͕༗ޮͰ͋Δ͜ͱ͕ࣔࠦ͞Εͨɽ
4.2࢒‫ڹ‬আ‫ڈ‬ɼԻ‫ڹ‬Πϕϯτ‫ݕ‬ग़ɼԻ‫ݯ‬෼཭ੑೳධՁ࣮‫ݧ‬࣍ʹɼఏҊ๏ͷԻ‫ݯ‬෼཭ੑೳɼ࢒‫ڹ‬আ‫ڈ‬ੑೳɼԻ‫ڹ‬Πϕϯτ‫ݕ‬ग़ੑೳͷධՁͷͨΊʹɼࠞ߹ DOA Ϟσϧͳ͠ͷ৔߹ͷఏҊ๏ʹ͓͍ͯɼT ͷ஋Λ 0, 3, 10 ͱม͑ͯɼ࢒‫ڹ‬ԼͰͷ‫͋ࢣڭ‬ΓԻ‫ݯ‬෼཭࣮‫ݧ‬Λߦͬͨɽલͷ࣮‫ͱݧ‬ಉ͡ 15 छྨͷԻʹରͯ͠ΠϯύϧεԠ౴(࢒‫ ؒ࣌ڹ‬600 msɼϚΠΫؒ‫ ཭ڑ‬11.48 cmɼϚΠΫͷ਺ M = 2) Λ৞ΈࠐΈɼਓ޻తʹଟνϟϯωϧͷࠞ߹৴߸Λ 10 ‫࡞ݸ‬੒ͨ͠ɽ3 ͭͷԻ‫ݯ‬͸ΠϯύϧεԠ౴Λ৞Έࠐ·ΕΔ͜ͱͰϚΠΫ͔Β 50◦ ɼ90◦ ɼ130◦ͷҐஔʹਓ޻తʹͦΕͧΕ഑ஔ͞ΕͨɽαϯϓϦϯά
प೾਺͸ 16 kHz ͱͨ͠ɽϑϨʔϜ௕ 64 msɼϑϨʔϜγϑτ௕ 16 ms Ͱ STFT Λߦ͍ɼ࣌ؒप೾਺ల։Λߦͬͨɽ‫ج‬ఈύϫʔεϖΫτϧͷঢ়ଶ਺Q͸1ͱ√ͨ͠ɽC 1:T ͷॳ‫ظ‬஋͸ɼ10−2 / M × I ͱͨ͠ɽWͱ ρ(q) ΛΫϦʔϯͳԻ͔Βֶश͠ɼ‫ݻ‬ఆͯ͠༻͍ͨɽͦͷଞͷύϥϝʔλ͸લͷ࣮‫ͱݧ‬ಉ༷ʹઃఆͨ͠ɽύϥϝʔλਪ࿦ΞϧΰϦζϜ͸ 100 ճ൓෮ͨ͠ɽT > 0ͷͱ͖ʹ๬·͘͠ͳ͍‫ॴہ‬ղΛආ͚ΔͨΊɼ࠷ॳͷ50 ճͷ൓෮͸ T = 0 ͱ͠ɼͦͷ‫ ޙ‬T Λ 3 ·ͨ͸ 10ͱͳΔ·Ͱঃʑʹ૿΍͠ͳ͕Β൓෮ͨ͠ɽԻ‫ݯ‬෼཭ɼ࢒‫ڹ‬আ‫ڈ‬ͷ٬‫؍‬ධՁ‫ج‬४ͱͯ͠ɼ࢒‫ڹ‬আ‫ࡁڈ‬Έ෼཭Իͷৼ෯εϖΫτϩάϥϜʹରͯ͠ɼࣨ಺ΠϯύϧεԠ౴Λ৞ΈࠐΉલͷԻ‫ݯ‬৴߸ͷৼ෯εϖΫτϩά

日本音響学会講演論文集Fig. 3 ࢒‫ڹ‬ԼԻ‫ݯ‬෼཭࣮‫͚͓ʹݧ‬Δ (a) ࠞ߹ԻͷεϖΫτϩάϥϜྫɼ(b)T = 10 ͷͱ͖ͷ࢒‫ڹ‬আ‫ࡁڈ‬Έ෼཭ԻͷεϖΫτϩάϥϜɼ(c) ‫ݩ‬ͷԻ‫ݯ‬৴߸ͷεϖΫτϩάϥϜɼ(d) Ի‫ڹ‬ΠϕϯτΛද͢ λ(j) ͷਪఆ݁ՌɽϥϜΛࢀর͢Δ͜ͱͰಘΒΕͨ SDRɼSIR Λ༻͍ͨɽ෼཭ॲཧલͷ SDRɼSIR ͸ͦΕͧΕ-7.42, -3.86[dB]Ͱ͋ͬͨɽFig. 2 ͷ (a)ɼ(b) ʹ T ͷ஋Λม͑ͨͱ͖ͷ SDRɼSIR ͷվળྔΛͦΕͧΕࣔ͢ɽ৞ΈࠐΈࠞ߹ʹΑΔ࢒‫ڹ‬আ‫ڈ‬Λߦ͏͜ͱͰɼԻ‫ݯ‬෼཭ੑೳ͕޲্͍ͯ͠Δ
͜ͱ͕෼͔ΔɽFig. 3 ʹ (a) ࠞ߹ԻͷεϖΫτϩάϥ
Ϝྫɼ(b)T = 10 ͷͱ͖ͷ࢒‫ڹ‬আ‫ࡁڈ‬Έ෼཭ԻͷεϖΫτϩάϥϜɼ(c) ‫ݩ‬ͷԻ‫ݯ‬৴߸ͷεϖΫτϩάϥϜɼ(d) Ի‫ڹ‬ΠϕϯτΛද͢ λ(j) ͷਪఆ݁ՌΛࣔ͢ɽ
λ(j) ͸ࠇ͍΄Ͳͦͷ࣌ࠁʹͦͷঢ়ଶʹ͋ΔΒ͍͜͠ͱΛද͠ɼj = 2 ͕༗Իঢ়ଶʹରԠ͍ͯ͠ΔͷͰɼԻ‫ڹ‬Πϕϯτ͕͓͓ΉͶਖ਼͘͠‫ݕ‬ग़͞Ε͍ͯΔ͜ͱ͕‫ͯݟ‬औΕΔɽ- 577 -

2015年3月

109876(b)

50.5

37.5
3736.53635.535

T=3T=010T=10T=3(d)90-0.5-1-1.587654321-234.5

T=10(c)SIR Improvement [dB]38

SDR Improvement [dB](a)
SIR Improvement [dB]SDR Improvement [dB]110᭷

T=0↓᭷ΰྜDOA䝰䝕䝹䛾᭷↓↓

Fig. 2 T ͷ஋Λม͑ͨͱ͖ͷ (a)SDR ͷվળྔɼ(b)SIR ͷվળྔɽ·ͨɼࠞ߹ DOA Ϟσϧͷ༗Γ/ແ͠Λม͑ͨͱ͖ͷ (c)SDR ͷվળྔɼ(d)SIR ͷվળྔɽ(a)ͨ SDRɼSIR Λ༻͍ͨɽ෼཭ॲཧલͷ SDRɼSIR ͸ͦΕͧΕ-4.77, -0.97[dB] Ͱ͋ͬͨɽFig. 2 ͷ (c)ɼ(d) ʹࠞ߹ DOA Ϟσϧ༗/ແͷͱ͖ͷ SDRɼSIR ͷվળྔΛࣔ͢ɽࠞ߹ DOA ϞσϧͷಋೖʹΑΓɼΑΓߴ͍෼཭ੑೳΛ͍ࣔͯ͠Δ͜ͱ͕෼͔ΔɽFig. 4(b) ʹɼ֤Ի‫֤͕ݯ‬౸དྷํ޲ʹͲͷ͘Β͍͍ΔΒ͍͔͠Λද͢ύϥϝʔλ d ͷਪఆ݁ՌΛԻ‫ʹͱ͝ݯ‬৭෼͚ͯࣔ͢͠ɽ໼ҹ͸ਖ਼ղͷ౸དྷํ޲Ͱ͋
Δɽ౸དྷํ޲͕͓͓ΉͶਖ਼͘͠ਪఆ͞Ε͍ͯΔ͜ͱ͕෼͔Δɽ

(b)

5Fig. 4 Ի‫ʹͱ͝ݯ‬৭෼͚͞Εͨɼ֤Ի‫ݯ‬ͷ౸དྷํ޲Λද͢ύϥϝʔλ d ͷ (a) ॳ‫ظ‬஋ͱ (b) ਪఆ݁Ռɽ4.3Ի‫ݯ‬෼཭ɼ࢒‫ڹ‬আ‫ڈ‬ɼ౸དྷํ޲ਪఆੑೳධՁ࣮‫ݧ‬ఏҊ๏ͷԻ‫ݯ‬෼཭ɼ࢒‫ڹ‬আ‫ڈ‬ɼ౸དྷํ޲ਪఆੑೳͷධՁͷͨΊʹɼࠞ߹ DOA Ϟσϧͷ͋Γ/ͳ͠Λม͑ͯɼ࢒‫ڹ‬ԼͰͷ‫͠ͳࢣڭ‬Ի‫ݯ‬෼཭࣮‫ݧ‬ΛߦͬͨɽATR
Ի੠σʔλϕʔε [10] ͷதͷ 3 ਓͷൃ࿩ऀ (ঁੑ 2 ਓɼஉੑ 1 ਓ) ʹΑΔ 15 छྨͷൃ࿩ʹରͯ͠ɼΠϯύϧεԠ౴ (࢒‫ ؒ࣌ڹ‬380 msɼϚΠΫؒ‫ ཭ڑ‬11.48 cmɼ
ϚΠΫͷ਺ M = 2) Λ৞ΈࠐΈɼਓ޻తʹଟνϟϯωϧͷࠞ߹৴߸Λ 5 ͭ࡞੒ͨ͠ɽ3 ͭͷԻ‫ݯ‬͸ΠϯύϧεԠ౴Λ৞Έࠐ·ΕΔ͜ͱͰϚΠΫ͔Β 30◦ ɼ90◦ ɼ130◦ ͷҐஔʹਓ޻తʹͦΕͧΕ഑ஔ͞ΕͨɽαϯϓϦϯάप೾਺͸ 16 kHz ͱͨ͠ɽ΢Οογϟʔτ෼෍ͷϋΠύʔύϥϝʔλ γ ͸ 3 ͱͨ͠ɽ‫ج‬ఈύϫʔεϖΫτϧͷঢ়ଶ਺ Q = 15ɼ = 10−3 ɼ౸དྷํ޲ͷ෼ׂ਺ O = 30ɼT = 3 ͱͨ͠ɽW ͷॳ‫ظ‬஋͸ཚ਺ͱ͠ɼρ(q) ͸Ұ༷ͱͨ͠ɽd ͷॳ‫ظ‬஋͸ Fig. 4(a) ͷΑ͏ʹઃఆͨ͠ɽ·ͨ θi ͷऔΓ͏ΔൣғΛ ϑ1+10(i−1)͔Β ϑ10i ʹ‫ݶ‬ఆ͢ΔΑ͏ʹ ρ(o) ͷ஋Λઃఆ͠ɼ֤Ի‫ʹͱ͝ݯ‬ਪఆ͢Δ౸དྷํ޲͕ॏͳΒͳ͍Α͏ʹͨ͠ɽύϥϝʔλਪ࿦ΞϧΰϦζϜ͸ 50 ճ൓෮ͨ͠ɽ๬·͘͠ͳ͍‫ॴہ‬ղΛආ͚ΔͨΊɼ࠷ॳͷ 25 ճͷ൓෮͸T = 0 ͱ͠ɼͦͷ‫ޙ‬ঃʑʹ T Λ 3 ͱͳΔ·Ͱ૿΍͠ͳ͕Β൓෮ͨ͠ɽ·ͨ T > 0 ͷ৔߹ʹɼW ͱ C i,k,1:TΛ྆ํͱ΋ߋ৽͢Δͱ਺஋‫ʹࠩޡ‬ΑΓ͏·͘਺஋‫ܭ‬ࢉͰ͖ͳ͍͜ͱ͕͋ͬͨɽ͜Ε͸ɼW ͱ C i,k,1:T ͸֤प೾਺͝ͱʹ‫ٻ‬ΊΒΕΔͨΊɼͦͷੵΛ‫؍‬ଌ৴߸ʹରͯ͠ϑΟοςΟϯά͢Δ৔߹ɼͦΕͧΕͷεέʔϧʹؔͯ͠͸೚ҙੑ͕ੜͯ͡͠·͍ɼC i,k,1:T ͕ඇৗʹେ͖ͳ஋ͱͳͬͯ͠·͔ͬͨΒͰ͋Δͱߟ͑ΒΕΔɽ
ͦ͜Ͱɼ࠷ॳͷ 25 ճͷ൓෮͸ W Λߋ৽͠ɼͦͷ‫ޙ‬T Λ૿΍͠ T > 0 ͱͳ͔ͬͯΒ͸ W Λߋ৽ͤͣʹ‫ݻ‬ఆͨ͠ɽԻ‫ݯ‬෼཭ɼ࢒‫ڹ‬আ‫ڈ‬ͷ٬‫؍‬ධՁ‫ج‬४ͱͯ͠ɼ࢒‫ڹ‬আ‫ࡁڈ‬Έ෼཭Իͷৼ෯εϖΫτϩάϥϜʹରͯ͠ɼࣨ಺ΠϯύϧεԠ౴Λ৞ΈࠐΉલͷԻ‫ݯ‬৴߸ͷৼ෯εϖΫτϩάϥϜΛࢀর͢Δ͜ͱͰಘΒΕ

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