Spatial Active Noise Control Based on Noise Field Interpolation From Reference Microphone Signals

Presentation slides for IEEE ICASSP 2023

Transcript

1. Spatial Active Noise Control Based on Noise Field Interpolation from Reference Microphone Signals Kazuyuki Arikawa1, Shoichi Koyama2, and Hiroshi Saruwatari1 1The University of Tokyo, Japan 2National Institute of Informatics, Japan 2023 IEEE International Conference on Acoustics, Speech and Signal Processing
2. Spatial active noise control Ø Environmental noise is still unsolved problem Ø Active noise control (ANC) is aimed at canceling noise by loudspeaker signals, but its effect is limited to local region Ø Spatial ANC is aimed at canceling noise over spatial region by multiple loudspeakers May 1, 2023 2 Quiet zone
3. Kernel-interpolation-based spatial ANC Ø Cost function of regional noise power is estimated by kernel interpolation of sound field to obtain optimal filter Ø Higher level of regional noise reduction than conventional multichannel ANC May 1, 2023 3 ANC in spatial region based on kernel interpolation of sound field Ø Cost function in conventional ANC Ø Cost function in spatial ANC : Power of error mics : Regional noise power [Ito+ ICASSP 2019, Koyama+ IEEE TASLP 2021] <latexit sha1_base64="Tj5AB6t2i82FuP7237lMFBz8JOI=">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</latexit> JPE = E Z ⌦ |ue(r, n)|2dr <latexit sha1_base64="SoL7IIJJlO97H5Hd6NUl0H9zno8=">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</latexit> Je = E ⇥ ken k2 2 ⇤ <latexit sha1_base64="5fsSw5dzXnOd3TaEe1+cGnieDdQ=">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</latexit> Wn <latexit sha1_base64="+c5NKpy42km5pNh2R1FxkIXAGCs=">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</latexit> (yn = Wnxn)
4. Spatial ANC based on interpolation from reference mics May 1, 2023 4 How can we reduce error mics to keep a space in target region ? Kernel interpolation of sound field from reference mics instead of error mics Reduce the number of error mics and increase the number of reference mics
5. Proposed #1: Fixed filter based on kernel interpolation Ø Sound field is estimated as – and are vector and matrix consisting of kernel functions that constrain the interpolated function with the solution of Helmholtz eq. Ø Fixed filter minimizing the cost function May 1, 2023 5 <latexit sha1_base64="SlPDMtGflZlFZ019QEzbqPkL0K0=">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</latexit> ue(r, n) = up(r, n) + us(r, n) = (r)T ⇥ (K + I) 1 ⇤ xn + [G(r, r1), . . . , G(r, rL)]yn <latexit sha1_base64="GazK4Vw0J1CD6i8pXENLSV6/ieY=">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</latexit> zx(r)T <latexit sha1_base64="dDFqztWhRAg8BXGawgyZXj1wTGw=">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</latexit> ⇣y(r)T Primary field Secondary field : Kernel interpolation filter : Free-field Green s functions <latexit sha1_base64="8QTIkG839VfkGfY8Ulwm8DnoLhE=">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</latexit> (r) <latexit sha1_base64="ebVZeCcxUC50/CFCZNspK+zdrYY=">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</latexit> K <latexit sha1_base64="XTPhZCXJKG8JRW40KA8HOXv4IHY=">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</latexit> Ayy := Z ⌦ ⇣y(r)⇤⇣y(r)Tdr Ayx := Z ⌦ ⇣y(r)⇤zx(r)Tdr <latexit sha1_base64="p2Iwh5OizjCNo0yIqA+U4bPHuf4=">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</latexit> Wfixed = A 1 yy Ayx <latexit sha1_base64="PZHkqQe36P1mrvdWOWRNjdjlTfU=">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</latexit> @JPE @W ⇤ n ' (AyyWn + Ayx)xnxH n
6. Proposed #2: NLMS transitioning from fixed filter Ø Cost function of time-varying weighted sum of and to compensate the estimation error of sound field Ø NLMS algorithm transitioning from fixed filter is obtained as May 1, 2023 6 <latexit sha1_base64="3OxtJ51HVEzPrB5lznUmUQlsivE=">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</latexit> JPE <latexit sha1_base64="9JtDS10VsQe+kaY9n6MKvYuSx/A=">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</latexit> Je <latexit sha1_base64="NiNAADijtEMi1Vda2LnIZQMjYq4=">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</latexit> Jtrans,n = nJPE + ken k2 2 <latexit sha1_base64="LZMYIx8py8eSbDPvwxryudezQbM=">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</latexit> Wn+1 = Wn µn @Jtrans,n @W ⇤ n = Wn µn ⇥ n(Ayyyn + Ayxxn) + GHen ⇤ xH Secondary path Forgetting factor <latexit sha1_base64="3fi9+jS0va27ce95rGE7bCJ7Xs4=">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</latexit> 2 (0, 1) Transitioning from to control filter of multichanel NLMS <latexit sha1_base64="u7dop2CGcwSzzrX618Mo4djR5JE=">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</latexit> Wfixed
7. Experiments Ø Numerical simulation in 2D free field – Target region: Circular region of radius 0.5 m – Rigid circular object of radius 0.15 m – 12 secondary sources – 2 error mics and 6 reference mics Ø Comparison – Conventional NLMS (NLMS) – Proposed fixed filter (Fixed-KIR) – Proposed NLMS transitioning from Fixed-KIR (NLMS w/ Fixed-KIR) Ø Evaluation measure – Regional noise reduction over target region May 1, 2023 7
8. Experiments May 1, 2023 8 Good Bad Ø Regional noise reduction w.r.t. frequency Ø Power distribution at 400 Hz NLMS Fixed-KIR NLMS w/ Fixed-KIR NLMS w/ Fixed-KIR achieved the largest noise reduction at all frequencies
9. Conclusion Ø Spatial ANC based on kernel interpolation from reference mics – Sound field estimation from mics is essential for spatial ANC, but small number of error mics is preferable to keep a space for ANC users – Proposed to use reference mics instead of error mics for kernel interpolation of primary noise field – (1) Fixed filter minimizing the estimated sound field, and (2) NLMS algorithm for transitioning from the fixed filter to control filter of multichannel NLMS – Achieved large noise reduction over target region by NLMS with fixed filter, compared with conventional NLMS May 1, 2023 9 Thank you for your attention!