Adaptive transfer function estimating method and estimating device using the same

Claim 1

A method for adaptive estimation of an acoustic transfer function of an unknown system, comprising the steps of: (1) calculating an error signal e(k)=y(k)-y(k) between an estimated output signal y(k) of the unknown system and an output signal y(k) produced by the unknown system in response to an input signal x(k); (2) computing a forward linear prediction coefficient vector a(k) of said input signal x(k), the sum of forward posteriori prediction error squares F(k) of said input signal x(k), a backward linear prediction coefficient vector b(k) of said input signal x(k) and the sum of backward posterior prediction error squares B(k); (3) obtaining a pre-filter coefficient vector g(k) by a recursion formula expressed by the following first and second equations using a pre-filter deriving coefficient vector f(k): ##EQU28## where e(k) and μ represent a vector of said error signal e(k) and a predetermined correcting step size, respectively; and (4) repeatedly correcting an estimated transfer function h(k) of the unknown system by the following equation h(k+1)=h(k)+μδh(k) to cause said error signal e(k) to approach zero using an estimated transfer function correcting vector δh(k) expressed by the following equation δh(k)=[x(k),x(k-1), . . . , x(k-p+1)]g(k) where x(k) represents a vector of said input signal x(k).

Claim 2

A method for adaptive estimation of an acoustic transfer function of an unknown system, comprising the steps of: (1) calculating an error signal e(k)=y(k)-y(k) between an estimated output signal y(k) of the unknown system and an output signal y(k) produced by the unknown system in response to an input signal x(k); (2) computing a forward linear prediction coefficient vector a(k) of said input signal x(k), the sum of forward posteriori prediction error squares F(k) of said input signal x(k), a backward linear prediction coefficient vector b(k) of said input signal x(k) and the sum of backward posterior prediction error squares B(k); (3) obtaining a pre-filter coefficient vector g(k) by a recursion formula expressed by the following first and second equations using a pre-filter deriving coefficient vector f(k): ##EQU28## where e(k) and μ represent a vector of said error signal e(k) and a predetermined correcting step size, respectively; and (4) repeatedly correcting an estimated transfer function h(k) of the unknown system by the following equation h(k+1)=h(k)+μδh(k) to cause said error signal e(k) to approach zero using an estimated transfer function correcting vector δh(k) expressed by the following equation δh(k)=[x(k),x(k-1), . . . , x(k-p+1)]g(k) where x(k) represents a vector of said input signal x(k).

Claim 3

A method for adaptive estimation of an acoustic transfer function of an unknown system, comprising the steps of: (1) calculating an error signal e(k)=y(k)-y(k) between an estimated output signal y(k) of the unknown system and an output signal y(k) produced by the unknown system in response to an input signal x(k); (2) obtaining a pre-filter coefficient vector g(k) composed of pre-filter coefficients g i (k) by solving the following simultaneous linear equation with p unknowns R.sub.p (k)g(k)=e(k) where R p (k) represents a covariance matrix of said input signal x(k) and e(k) represents a vector of said error signal e(k); (3) smoothing said pre-filter coefficients g i (k) by the following equations ##EQU29## to obtain a smoothing coefficient s i (k); (4) obtaining an approximate estimated transfer function z(k+1) as an approximation of said estimated transfer function h(k) using said smoothing coefficient s p (k) based on the following equation z(k+1)=z(k)+s.sub.p (k)x(k-p+1); (5) calculating convolution x(k) T z(k) of said approximate estimated transfer function z(k) with said input signal x(k); (6) calculating an inner product s p-1 (k-1) T r p-1 (k), setting the vector of said smoothing coefficient s i (k) and the correlation vector r p-1 (k) of said input signal to s.sub.p-1 (k-1)=[s.sub.1 (k-1), s.sub.2 (k-1), . . . , s.sub.p-1 (k-1)].sup.T and r.sub.p-1 (k)=[x(k).sup.T x(k-1), x(k).sup.T x(k-2), . . . , x(k).sup.T x(k-p+1)].sup.T respectively; and (7) obtaining the sum of said convolution result x(k) T z(k) and said inner product as said estimated output signal y(k).

Claim 4

A method for adaptive estimation of an acoustic transfer function of an unknown system, comprising the steps of: (1) calculating an error signal e(k)=y(k)-y(k) between an estimated output signal y(k) of the unknown system and an output signal y(k) produced by the unknown system in response to an input signal x(k); (2) obtaining a pre-filter coefficient vector g(k) composed of pre-filter coefficients g i (k) by solving the following simultaneous linear equation with p unknowns R.sub.p (k)g(k)=e(k) where R p (k) represents a covariance matrix of said input signal x(k) and e(k) represents a vector of said error signal e(k); (3) smoothing said pre-filter coefficients g i (k) by the following equations ##EQU29## to obtain a smoothing coefficient s i (k); (4) obtaining an approximate estimated transfer function z(k+1) as an approximation of said estimated transfer function h(k) using said smoothing coefficient s p (k) based on the following equation z(k+1)=z(k)+s.sub.p (k)x(k-p+1); (5) calculating convolution x(k) T z(k) of said approximate estimated transfer function z(k) with said input signal x(k); (6) calculating an inner product s p-1 (k-1) T r p-1 (k), setting the vector of said smoothing coefficient s i (k) and the correlation vector r p-1 (k) of said input signal to s.sub.p-1 (k-1)=[s.sub.1 (k-1), s.sub.2 (k-1), . . . , s.sub.p-1 (k-1)].sup.T and r.sub.p-1 (k)=[x(k).sup.T x(k-1), x(k).sup.T x(k-2), . . . , x(k).sup.T x(k-p+1)].sup.T respectively; and (7) obtaining the sum of said convolution result x(k) T z(k) and said inner product as said estimated output signal y(k).

Claim 7

A method for adaptive estimation of an acoustic transfer function of an unknown system, comprising the steps of: (1) calculating an error signal e(k)=y(k)-y(k) between an estimated output signal y(k) of the unknown system and an output signal y(k) produced by said unknown system in response to an input signal x(k); (2) computing a forward linear prediction coefficient vector a(k) of said input signal x(k), the sum of forward posteriori prediction error squares F(k) of said input signal x(k), a backward linear prediction coefficient vector b(k) of said input signal x(k) and the sum of backward posterior prediction error squares B(k); (3) obtaining a pre-filter coefficient vector g(k) by a recursion formula expressed by the following first and second equations using a pre-filter deriving coefficient vector f(k): ##EQU32## where e(k) and μ represent a vector of said error signal e(k) and a predetermined correcting step size, respectively; (4) smoothing said pre-filter coefficients g i (k) of said pre-filter coefficient vector g(k) by the following equations s.sub.i (k)=s.sub.i-1 (k-1)+μg.sub.i (k) for 2≦i≦p=μg.sub.1 (k) for i=1 to obtain a smoothing coefficient s i (k); (5) obtaining an approximate estimated transfer function z(k+1) as an approximation of said estimated transfer function h(k) using said smoothing coefficient s p (k) based on the following equation z(k+1)=z(k)+s.sub.p (k)x(k-p+1); (6) calculating convolution x(k) T z(k) of said approximate estimated transfer function z(k) with said input signal x(k); (7) calculating an inner product s p-1 (k-1) T r p-1 (k), setting the vector of said smoothing coefficient s i (k) and the correlation vector r p-1 (k) of said input signal to s.sub.p-1 (k-1)=[s.sub.1 (k-1), s.sub.2 (k-1), . . . , s.sub.p-1 (k-1)].sup.T and r.sub.p-1 (k)=[x(k).sup.T x(k-1), x(k).sup.T x(k-2), . . . , x(k).sup.T x(k-P+1)].sup.T respectively; and (8) obtaining the sum of said convolution result x(k) T z(k) and said inner product as said estimated output signal y(k).

Claim 8

A method for adaptive estimation of an acoustic transfer function of an unknown system, comprising the steps of: (1) calculating an error signal e(k)=y(k)-y(k) between an estimated output signal y(k) of the unknown system and an output signal y(k) produced by said unknown system in response to an input signal x(k); (2) computing a forward linear prediction coefficient vector a(k) of said input signal x(k), the sum of forward posteriori prediction error squares F(k) of said input signal x(k), a backward linear prediction coefficient vector b(k) of said input signal x(k) and the sum of backward posterior prediction error squares B(k); (3) obtaining a pre-filter coefficient vector g(k) by a recursion formula expressed by the following first and second equations using a pre-filter deriving coefficient vector f(k): ##EQU32## where e(k) and μ represent a vector of said error signal e(k) and a predetermined correcting step size, respectively; (4) smoothing said pre-filter coefficients g i (k) of said pre-filter coefficient vector g(k) by the following equations s.sub.i (k)=s.sub.i-1 (k-1)+μg.sub.i (k) for 2≦i≦p=μg.sub.1 (k) for i=1 to obtain a smoothing coefficient s i (k); (5) obtaining an approximate estimated transfer function z(k+1) as an approximation of said estimated transfer function h(k) using said smoothing coefficient s p (k) based on the following equation z(k+1)=z(k)+s.sub.p (k)x(k-p+1); (6) calculating convolution x(k) T z(k) of said approximate estimated transfer function z(k) with said input signal x(k); (7) calculating an inner product s p-1 (k-1) T r p-1 (k), setting the vector of said smoothing coefficient s i (k) and the correlation vector r p-1 (k) of said input signal to s.sub.p-1 (k-1)=[s.sub.1 (k-1), s.sub.2 (k-1), . . . , s.sub.p-1 (k-1)].sup.T and r.sub.p-1 (k)=[x(k).sup.T x(k-1), x(k).sup.T x(k-2), . . . , x(k).sup.T x(k-P+1)].sup.T respectively; and (8) obtaining the sum of said convolution result x(k) T z(k) and said inner product as said estimated output signal y(k).

Claim 10

A device for adaptive estimation of an acoustic transfer function of an unknown system, comprising: convolution means for convolving an input signal x(k) with an estimated transfer function vector h(k) representing the unknown system and outputting an estimated output signal y(k) of said unknown system; error calculating means for calculating an error signal e(k)=y(k)-y(k) between said estimated output signal y(k) of the unknown system and said output signal y(k) from said unknown system; linear prediction means for computing a forward linear prediction coefficient vector a(k) of said input signal x(k), the sum of forward posteriori prediction error squares F(k) of said input signal x(k), a backward linear prediction coefficient vector b(k) of said input signal x(k) and the sum of backward posterior prediction error squares B(k); pre-filter coefficient vector correcting means for obtaining a pre-filter coefficient vector g(k) by a recursion formula expressed by the following first and second equations using a pre-filter deriving coefficient vector f(k): ##EQU33## where e(k) and μ represent a vector of said error signal e(k) and a predetermined correcting step size, respectively; and pre-filter deriving coefficient vector correcting means for repeatedly correcting said estimated transfer function h(k) by the following equation h(k+1)=h(k)+μδh(k) to cause said error signal e(k) to approach zero using an estimated transfer function correcting vector δh(k) expressed by the following equation δh(k)=[x(k), x(k-1), . . . , x(k-p+1)]g(k) where, x(k) represents a vector of said input signal x(k).

Claim 11

A device for adaptive estimation of an acoustic transfer function of an unknown system, comprising: convolution means for convolving an input signal x(k) with an estimated transfer function vector h(k) representing the unknown system and outputting an estimated output signal y(k) of said unknown system; error calculating means for calculating an error signal e(k)=y(k)-y(k) between said estimated output signal y(k) of the unknown system and said output signal y(k) from said unknown system; linear prediction means for computing a forward linear prediction coefficient vector a(k) of said input signal x(k), the sum of forward posteriori prediction error squares F(k) of said input signal x(k), a backward linear prediction coefficient vector b(k) of said input signal x(k) and the sum of backward posterior prediction error squares B(k); pre-filter coefficient vector correcting means for obtaining a pre-filter coefficient vector g(k) by a recursion formula expressed by the following first and second equations using a pre-filter deriving coefficient vector f(k): ##EQU33## where e(k) and μ represent a vector of said error signal e(k) and a predetermined correcting step size, respectively; and pre-filter deriving coefficient vector correcting means for repeatedly correcting said estimated transfer function h(k) by the following equation h(k+1)=h(k)+μδh(k) to cause said error signal e(k) to approach zero using an estimated transfer function correcting vector δh(k) expressed by the following equation δh(k)=[x(k), x(k-1), . . . , x(k-p+1)]g(k) where, x(k) represents a vector of said input signal x(k).

Claim 15

A device for adaptive estimation of an acoustic transfer function of an unknown system, comprising: error calculating means for calculating an error signal e(k)=y(k)-h(k) between an estimated output signal h(k) of the unknown system and an output signal y(k) produced by said unknown system in response to an input signal x(k); pre-filter coefficient vector calculating means for calculating a pre-filter coefficient vector g(k) composed of pre-filter coefficients g i (k) by solving the following simultaneous linear equation with p unknowns R.sub.p (k)g(k)=e(k) where R p (k) represents a covariance matrix of said input signal x(k) and e(k) represents a vector of said error signal e(k); pre-filter coefficient smoothing means for smoothing said pre-filter coefficients g i (k) by the following equations ##EQU36## to obtain a smoothing coefficient s i (k); approximate estimated transfer function calculating means for obtaining an approximate estimated transfer function z(k+1) as an approximation of said estimated transfer function h(k) using said smoothing coefficient s p (k) based on the following equation z(k+1)=z(k)+s.sub.p (k)x(k-p+1); convolution calculating means for calculating convolution x(k) T z(k) of said approximate estimated transfer function z(k) and said input signal x(k); inner product calculating means for calculating an inner product s p-1 (k-1) T r p-1 (k), setting the vector of said smoothing coefficient s i (k) and the correlation vector of said input signal to s.sub.p-1 (k-1)=[s.sub.1 (k-1), s.sub.2 (k-1), . . . , s.sub.p-1 (k-1)].sup.T and r.sub.p-1 (k)=[x(k).sup.T x(k-1),x(k).sup.T x(k-2), . . . , x(k).sup.T x(k-p+1)].sup.T respectively; and adding means for obtaining the sum of said convolution result x(k) T z(k) and said inner product as said estimated output signal y(k).

Claim 16

A device for adaptive estimation of an acoustic transfer function of an unknown system, comprising: error calculating means for calculating an error signal e(k)=y(k)-h(k) between an estimated output signal h(k) of the unknown system and an output signal y(k) produced by said unknown system in response to an input signal x(k); pre-filter coefficient vector calculating means for calculating a pre-filter coefficient vector g(k) composed of pre-filter coefficients g i (k) by solving the following simultaneous linear equation with p unknowns R.sub.p (k)g(k)=e(k) where R p (k) represents a covariance matrix of said input signal x(k) and e(k) represents a vector of said error signal e(k); pre-filter coefficient smoothing means for smoothing said pre-filter coefficients g i (k) by the following equations ##EQU36## to obtain a smoothing coefficient s i (k); approximate estimated transfer function calculating means for obtaining an approximate estimated transfer function z(k+1) as an approximation of said estimated transfer function h(k) using said smoothing coefficient s p (k) based on the following equation z(k+1)=z(k)+s.sub.p (k)x(k-p+1); convolution calculating means for calculating convolution x(k) T z(k) of said approximate estimated transfer function z(k) and said input signal x(k); inner product calculating means for calculating an inner product s p-1 (k-1) T r p-1 (k), setting the vector of said smoothing coefficient s i (k) and the correlation vector of said input signal to s.sub.p-1 (k-1)=[s.sub.1 (k-1), s.sub.2 (k-1), . . . , s.sub.p-1 (k-1)].sup.T and r.sub.p-1 (k)=[x(k).sup.T x(k-1),x(k).sup.T x(k-2), . . . , x(k).sup.T x(k-p+1)].sup.T respectively; and adding means for obtaining the sum of said convolution result x(k) T z(k) and said inner product as said estimated output signal y(k).

Claim 17

A device for adaptive estimation of an acoustic transfer function of an unknown system, comprising: error calculating means for calculating an error signal e(k)=y(k)-y(k) between an estimated output signal y(k) of the unknown system and an output signal y(k) produced by said unknown system in response to an input signal x(k); linear prediction means for computing a forward linear prediction coefficient vector a(k) of said input signal x(k), the sum of forward posteriori prediction error squares F(k) of said input signal x(k), a backward linear prediction coefficient vector b(k) of said input signal x(k) and the sum of backward posterior prediction error squares B(k); pre-filter coefficient vector correcting means for obtaining a pre-filter coefficient vector g(k) by a recursion formula expressed by the following first and second equations using a pre-filter deriving coefficient vector f(k): ##EQU37## where e(k) and μ represent a vector of said error signal e(k) and a predetermined correcting step size, respectively; pre-filter coefficient smoothing means for smoothing said pre-filter coefficients g i (k) by the following equations ##EQU38## to obtain a smoothing coefficient s i (k); approximate estimated transfer function calculating means for obtaining an approximate estimated transfer function z(k+1) as an approximation of said estimated transfer function h(k) using said smoothing coefficient s p (k) based on the following equation z(k+1)=z(k)+s.sub.p (k)x(k-p+1); convolution calculating means for calculating convolution x(k) T z(k) of said approximate estimated transfer function z(k) and said input signal x(k); inner product calculating means for calculating an inner product s p-1 (k-1) T r p-1 (k) setting the vector of said smoothing coefficient s i (k) and the correlation vector of said input signal to s.sub.p-1 (k-1)=[s.sub.1 (k-1), s.sub.2 (k-1), . . . , s.sub.p-1 (k-1)].sup.T and r.sub.p-1 (k)=[x(k).sup.T x(k-1),x(k).sup.T x(k-2), . . . x(k).sup.T x(k-p+1)].sup.T respectively; and adding means for obtaining the sum of said convolution result x(k) T z(k) and said inner product as said estimated output signal y(k).

Claim 18

A device for adaptive estimation of an acoustic transfer function of an unknown system, comprising: error calculating means for calculating an error signal e(k)=y(k)-y(k) between an estimated output signal y(k) of the unknown system and an output signal y(k) produced by said unknown system in response to an input signal x(k); linear prediction means for computing a forward linear prediction coefficient vector a(k) of said input signal x(k), the sum of forward posteriori prediction error squares F(k) of said input signal x(k), a backward linear prediction coefficient vector b(k) of said input signal x(k) and the sum of backward posterior prediction error squares B(k); pre-filter coefficient vector correcting means for obtaining a pre-filter coefficient vector g(k) by a recursion formula expressed by the following first and second equations using a pre-filter deriving coefficient vector f(k): ##EQU37## where e(k) and μ represent a vector of said error signal e(k) and a predetermined correcting step size, respectively; pre-filter coefficient smoothing means for smoothing said pre-filter coefficients g i (k) by the following equations ##EQU38## to obtain a smoothing coefficient s i (k); approximate estimated transfer function calculating means for obtaining an approximate estimated transfer function z(k+1) as an approximation of said estimated transfer function h(k) using said smoothing coefficient s p (k) based on the following equation z(k+1)=z(k)+s.sub.p (k)x(k-p+1); convolution calculating means for calculating convolution x(k) T z(k) of said approximate estimated transfer function z(k) and said input signal x(k); inner product calculating means for calculating an inner product s p-1 (k-1) T r p-1 (k) setting the vector of said smoothing coefficient s i (k) and the correlation vector of said input signal to s.sub.p-1 (k-1)=[s.sub.1 (k-1), s.sub.2 (k-1), . . . , s.sub.p-1 (k-1)].sup.T and r.sub.p-1 (k)=[x(k).sup.T x(k-1),x(k).sup.T x(k-2), . . . x(k).sup.T x(k-p+1)].sup.T respectively; and adding means for obtaining the sum of said convolution result x(k) T z(k) and said inner product as said estimated output signal y(k).