Real-time loudspeaker distance estimation with stereo audio

摘要

A method for estimating a distance between a first and a second loudspeaker characterized by playing back a first stereo source signal vector s1 on the first loudspeaker, and playing back a second stereo source signal vector s2 on the second loudspeaker, acquiring a first recorded signal vector x1, using a first microphone arranged adjacent to the first loudspeaker, and acquiring a second recorded signal vector x2 from a second microphone arranged adjacent to the second loudspeaker, wherein x1 and x2 are N-dimensional vectors, setting the distance equal to ηv/f, where v is the speed of sound, f is the sampling frequency, and η is an estimated sample delay of a source signal played back on one of the loudspeakers and a recording acquired by a microphone at the other loudspeaker.

主权项

1. A method for estimating a distance between a first and a second loudspeaker characterized by:
(a) playing back a first stereo source signal vector s1 on the first loudspeaker, and playing back a second stereo source signal vector s2 on the second loudspeaker; (b) acquiring a first recorded signal vector x1, using a first microphone arranged adjacent to the first loudspeaker, and acquiring a second recorded signal vector x2 from a second microphone arranged adjacent to the second loudspeaker, wherein x1 and x2 are N-dimensional vectors; (c) setting the distance equal to ηv/f, where v is the speed of sound, f is the sampling frequency, and η is an estimated sample delay of a source signal played back on one of the loudspeakers and a recording acquired by a microphone at the other loudspeaker, (d) where the delay η is estimated byη^=argmaxη∈[M,K]⁢max⁡(J⁡(η),0) having a cost function J(η) given byJ⁡(η)=s2H⁡(η)⁢C1-1⁢R1⁢x1+s1H⁡(η)⁢C2-1⁢R2⁢x2s2H⁡(η)⁢C1-1⁢R1⁢s2⁡(η)+s1H⁡(η)⁢C2-1⁢R2⁢s1⁡(η). where:si(η)=ZAid(η)
is the source signal vector to loudspeaker i shifted by i samples, where
z(ω)=[1 exp(jω) . . . exp(jω(N−1))]T Z=[z(−2πL/N) . . . 1 . . . z(2πL/N)]d(η)=[exp(j2πηL/N) . . . 1 . . . exp(−j2πηL/N)]T Ai=N−1diag(ZHsi(0))N is the number of elements in the vector Si(η), and L=N/2 if N is even and L=(N−1)/2 if N is odd;
where:
Ci=γσ2[Z(A1A1H+A2A2H)ZH+γ−1IN].is a covariance matrix modeling both reverberation and measurement noise, where σ2 is an unknown variance of the measurement noise and γ is a scaling factor; and
where:
Ri=IN−Bi(BiHCi−1Bi)−1BiHCi−1 is a matrix filtering out the loudspeakers own signal in the microphone recordings, where
Bi=ZAiFF=[d(0)d(1) . . . d(M−1)]and M is a user-defined length of the filter.