JP2006148453A - Method, apparatus, and program for signal estimation, and recording medium for the program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To estimate an input signal with accuracy only from an observation signal without knowing the degree of a transfer function. <P>SOLUTION: The transfer function between each sensor and a signal source from output signals X<SB>1</SB>(n), X<SB>2</SB>(n) of sensors 13, 14 in a one-input and two-output transfer system 11 is estimated (40), and from the above estimation values h^<SB>1</SB>(z), h^<SB>2</SB>(z), a first and a second inverse filter coefficients are calculated (24). Then, the first and the second inverse filter coefficients are set into a pre-stage filters 31, 32, and the outputs signals x<SB>1</SB>(n), x<SB>2</SB>(n) are passed through the filters 31, 32, so as to add the output thereof. An item common to the both transfer functions is calculated using h^<SB>1</SB>(z), h^<SB>2</SB>(z) (36), and from the common item thereof, filter processing is performed on the output of an adder 33 by means of a post-stage filter 34 so as to eliminate the common item component, and thus the estimated value of the input signal is obtained. <P>COPYRIGHT: (C)2006,JPO&NCIPI

Description

  The present invention is used for, for example, indoor audio recording and the like, and is used for sound collection technology that eliminates and reduces reverberation distortion, which is the main cause of recorded audio quality deterioration, and prevents intelligibility degradation. This is applied to reception technology that reduces the multipath distortion caused by it and maintains good voice quality. In a 1-input 2-output transfer system, if the output signal is accompanied by distortion due to the transfer function of the system, the transfer function is unique. The present invention relates to a method, an apparatus and a program thereof, and a recording medium for blindly estimating an input signal with high accuracy without using the prior information.

Conventionally, there is a method of removing reverberation from reverberant speech without previously measuring an indoor acoustic transfer function as a method of estimating an input signal from a microphone sound reception signal in indoor sound recording or the like to achieve dereverberation. (For example, refer nonpatent literature 1). In this method, a transfer function is estimated from a microphone sound reception signal, an inverse filter is configured based on the estimated value of the transfer function, and the sound reception signal is processed by the inverse filter to remove dereverberation. This will be briefly described with reference to FIG.
Each transfer function between the input end 12 (for example, a sound source such as a speaker or a speaker) of the one-input two-output transfer system 11 and the two sensors 13 and 14 provided at the output end is represented by h Let ₁ (z) and h ₂ (z). Assume that these transfer functions do not have a common zero. A signal s (n) at time n is input to the transmission system 11 at the input terminal 12, and this signal is detected by sensors 13 and 14 provided at the two output terminals. The output signals x ₁ (n) and x ₂ (n) of the sensors 13 and 14 are first supplied to the filters 15 and 16 in the transfer function estimation unit 10. The output signals processed by these filters 15 and 16 are subtracted from each other by a subtractor 17. Each filter coefficient of the filters 15 and 16 is calculated by the filter calculation unit 19 so as to minimize the root mean square value of the output signal e (n) of the subtracter 17, and these calculated filter coefficients are supplied to the filters 15 and 16. Is set. The calculated transfer functions of the filters 15 and 16 are represented by h ^ ₂ (z, i) and h ^ ₁ (z, i). Here, i represents the filter order.

The output signal e (n) of the subtracter 17 is expressed by the following equation.
e (n) = x ₁ (n) h ₂ (z, i) −x ₂ (n) h ₁ (z, i)
= S (n) h ₁ (z) h ₂ (z, i) −s (n) h ₂ (z) h ₁ (z, i)
= S (n) {h ₁ (z) h ₂ (z, i) −h ₂ (z) h ₁ (z, i)} (1)
Here, if the transfer functions h ₁ (z) and h ₂ (z) can be modeled in the jth order, if i = j and e (n) is zero for all n,
h ^ ₁ (z, i) = αh ₁ (z), h ^ ₂ (z, i) = αh ₂ (z) (2)
Is obtained. Here, α is an arbitrary constant. That is, the transfer functions h ₁ (z) and h ₂ (z) are accurately estimated except for the difference of a constant multiple.

When the transfer function is estimated by the transfer function estimation unit 10, the dereverberation processing unit 20 uses the estimated transfer functions h ₁ (z, i) and h ₂ (z, i) to perform an inverse filter calculation unit. At 24, the first and second inverse filter transfer functions g ₁ (z) and g ₂ (z) are calculated (see, for example, Non-Patent Document 2). The inverse filter transfer functions g ₁ (z) and g ₂ (z) satisfy Expression (3).
h ₁ (z, i) g ₁ (z) + h ₂ (z, i) g ₂ (z) = 1 (3)
From equation (2)
αh ₁ (z) g ₁ (z) + αh ₂ (z) g ₂ (z) = 1
h ₁ (z) g ₁ (z) + h ₂ (z) g ₂ (z) = 1 / α
The inverse filter transfer functions g ₁ (z) and g ₂ (z) obtained in this way are set in the filters 21 and 22. The output signals x ₁ (n) and x ₂ (n) of the sensors 13 and 14 are respectively filtered by the filters 21 and 22, and the outputs of these filters 21 and 22 are added by the adder 23. As a result, the input signal s (n) is accurately estimated except for a constant multiple difference.

For example, as shown in Non-Patent Document 3, the transfer function is estimated by obtaining an autocorrelation matrix from each output signal x ₁ (n), x ₂ (n) of the sensor, and an eigenvector corresponding to the minimum eigenvalue of the autocorrelation matrix. May be obtained by obtaining.
In the prior art described above, it is very important to determine the filter order that simulates the transfer function. However, since the order of the transfer function is generally unknown, the filter order is determined by the following method. The above process is operated using various orders, and a cost function representing the estimation accuracy of the transfer function is calculated using the dereverberation speech signal. Then, the order that minimizes the cost function is adopted as the optimum order. That is, in this method, it is necessary to perform the above processing for all possible orders. That is, as shown in FIG. 2, first, a transfer function is estimated (step S1), and an inverse filter transfer function g ₁ is used by using these estimated transfer functions h ^ ₁ (z, i), h ^ ₂ (z, i). (z) and g ₂ (z) are respectively calculated (step S2), and the sensor output signal x ₁ (n is calculated using the inverse filter transfer functions g ₁ (z) and g ₂ (z) as described above. ), X ₂ (n) are processed to temporarily estimate the input signal s (n) (step S3), and a cost function representing the estimation accuracy of the transfer function is calculated using the temporarily estimated input signal (step S3). S4) If the cost function calculation has not been completed for all possible orders, the order is updated and the process returns to step S1 (step S5). When the cost function calculation has been completed for all orders, the minimum cost function is obtained. The order of the obtained transfer function is determined (step S6), and thereafter The input signal is estimated using the transfer function of the order (step S7).

When an insufficient value is given as the filter order simulating the transfer function, the transfer function is not accurately estimated, and good performance cannot be obtained. Further, when a value larger than the optimum value is given as the filter order, the estimated transfer function is as follows.
h ₁ (z, i) = c (z) h ₁ (z), h ₂ (z, i) = c (z) h ₂ (z) (4)
That is, an estimated transfer function multiplied by the common term c (z) is obtained. Using the value of this estimated transfer function, the inverse filter is obtained in the same manner as described above.
_{h ^ 1 (z, i)} g 1 (z) + h ^ 2 (z, i) g 2 (z) = 1 (5)
From equation (4)
c (z) h ₁ (z) g ₁ (z) + c (z) h ₂ (z) g ₂ (z) = 1 (6)
h ₁ (z) g ₁ (z) + h ₂ (z) g ₂ (z) = 1 / c (z)
From this result, when the input signal is estimated using a value that is too large as the filter order, the estimated input signal is affected by the common term c (z), and a correct input signal cannot be obtained.

In general, the upper limit of the order of the room transfer function can be obtained by using the reverberation time. When a degree corresponding to this upper limit, that is, an order longer than the order of the true transfer function is used, the estimated values h ^ ₂ (z, i) and h ^ ₁ (z, i) of the two transfer functions are The common term c (z) is convoluted. As a result, in the conventional method, the input signal is distorted.
M. Gurelli and C. Nikias, “EVAM: An eigenvector-based algorithm for multichannel blind deconvolution of input colored signals,” IEEE Trans.Signal Processing, vol.43, no.1,134-149 (1995). M. Miyoshi and Y. Kaneda, “Inverse filtering of room acoustics,” IEEE Trans. Acoustics, Speech, and Signal Proc., Vol. 36, 145-152 (1988). K. Furuya and Y. Kaneda, “Two-channel blind deconvolution of nonminimum phase FIR systems,” IEICE Trans. Fundamentals, vol. E80-A, no. 5, 804-808 (1997)

  As described above, in the prior art, it is important that the transfer function is accurately estimated including the order, and processing for that is necessary, so that the configuration becomes complicated. Furthermore, if the order of the transfer function cannot be accurately determined, the estimated transfer system is distorted. As a result, the performance of the dereverberation processing signal and the multipath distortion reduction processing signal is degraded. In the present invention, such a problem is solved by using a method that does not require accurate estimation of the transfer function.

In the present invention, a common term is estimated from the estimated values h ^ ₂ (z, i) and h ₁ (z, i) of the indoor transfer function, and a filter that eliminates the influence of the common term is installed in the subsequent stage. By doing so, input signal estimation is performed without accurately estimating the transfer function order, and the above-described problems are solved.
As in the prior art, the transfer function is estimated from the output signals of the first and second sensors provided at the output end of the one-input two-output transmission system, and the common term is obtained from the first and second autocorrelation matrices. The process of obtaining the estimated values of the two convolved transfer functions and the two inverse filter transfer functions are calculated, and the first and second sensor output signals are calculated by the first and second inverse filter transfer functions. In the present invention, a common term is obtained from the estimated values of the two transfer functions, and the added signal is filtered by the common term.

  In the present invention, the transfer function order is not estimated, the transfer function need not be determined so accurately at that point, the processing is simple, the influence based on the order estimation error is removed, and the input signal is correctly estimated. be able to.

FIG. 3 shows an example of a functional configuration of the input signal estimation apparatus according to the embodiment of the present invention. The same reference numerals are assigned to the portions corresponding to those in FIG.
The transfer function estimation unit 40 estimates each transfer function between the input terminal 12 and the sensors 13 and 14 from the output signals x ₁ (n) and x ₂ (n) of the sensors 13 and 14. This transfer function may be estimated by the method of the transfer function estimation unit 10 shown in FIG. 1, or an autocorrelation matrix is obtained from the sensor output signals x ₁ (n) and x ₂ (n) as described above. Each transfer function may be estimated from this autocorrelation matrix, or may be estimated by other methods.

Based on the transfer function values h ₁ (z) and h ₂ (z) estimated by the transfer function estimation unit 40, the inverse filter calculation unit 24 calculates the inverse filter transfer functions g ₁ (z) and g ₂ (z). Is done. These inverse filter transfer functions g ₁ (z) and g ₂ (z) are set in the pre-filters 31 and 32, respectively. The sensor output signals x ₁ (n) and x ₂ (n) are filtered by the pre-stage filters 31 and 32, and both output signals of these filters 31 and 32 are added by the adder 33.
On the other hand, a common term is calculated by the common term calculation unit 36 from the transfer function values h ₁ (z) and h ₂ (z) estimated by the transfer function estimation unit 40, and this common term is set in the post-filter 34. . The output signal of the adder 33 is processed by the post-stage filter 34 to output a signal from which the influence of the common term has been removed, that is, an estimated input signal s ^ (n).

The common term calculation unit 36 obtains the common term from the estimated values h ^ ₁ (z) and h ^ ₂ (z) of the two transfer functions by, for example, the method shown in FIGS.
In this way, the transfer function matrix H, the shift matrix S, and the product matrix Q are used to obtain the common term. The relationship between them will be described.
In the present invention, since it is not necessary to obtain an accurate order for the estimated value of the transfer function, the argument i is omitted from the expression (4). First, consider the following relational expression.
h ₁ (z) w ₁ (z) + h ₂ (z) w ₂ (z) = z ⁺¹ h ₁ (z)
c (z) h ₁ (z) w ₁ (z) + c (z) h ₂ (z) w ₂ (z) = z ⁺¹ c (z) h ₁ (z) (7)
Here, z ⁺¹ h ₁ (z) represents a value obtained by advancing h ₁ (z) by one discrete time. H _i (z) = h _{i, 0} + h _{i, 1} z ⁻¹ +... + H _{i, j} z ^−j , i = 1,2
c (z) = c ₀ + c ₁ z ⁻¹ +... + c _m z ^−m
Consider filter coefficients w ₁ (z) and w ₂ (z) that satisfy this relationship. These w ₁ (z) and w ₂ (z) are filters for predicting one sensor output x ₁ (n + 1) one time ahead from _two sensor output signals x ₁ (n) and x ₂ (n). It corresponds to the filter coefficient. When the equation (7) is expressed as a matrix, it is as follows.
CHw = SCh ₁ (8)

ｈ_１＝［ｈ_i,0 ，ｈ_i,1 ，…，ｈ_i,j ，０，…，０］^Ｔ
ｗ＝［ｗ_1,0 ，ｗ_1,1 ，…，ｗ_1,k ，ｗ_2,0 ，ｗ_2,1 ，…，ｗ_2,k ］^Ｔ
［・］^Ｔは転置を表わす。
ここで、上記に示す通り、ベクトルｈ_１が行列Ｈの第１列目に一致することを利用して、ベクトルｈ_１を行列Ｈで置き換え、ベクトルｗを行列Ｑで置き換え、つまり第１列目がベクトルｗに一致する行列Ｑを生成する。

h ₁ = [h _{i, 0} , h _{i, 1} , ..., h _{i, j} , 0, ..., 0] ^T
w = [w _1,0 , w _1,1 , ..., w _{1, k} , w _2,0 , w _2,1 , ..., w _{2, k} ] ^T
[•] ^T represents transposition.
Here, using the fact that the vector h ₁ matches the first column of the matrix H as described above, the vector h ₁ is replaced by the matrix H, and the vector w is replaced by the matrix Q, that is, the first column Produces a matrix Q that matches the vector w.

In this way, equation (8) can be expressed by the following equation.
CHQ = SCH (9)
When this equation (9) is solved for Q, it is arranged as follows (see, for example, “Kodama, Suda, Matrix Theory for System Control, Corona, 1978, p. 332, p339”).
Q = (H ^{TC T} CH) ⁻¹ H ^T C ^T SCH
= (CH) ⁺ SCH
= H ^T (HH ^T ) ⁻¹ (C ^TC ) ⁻¹ C ^T SCH (10)
Here, (A) ⁺ represents a Moore-Penrose general inverse matrix of the matrix A.

The characteristic polynomial f _c (Q) of the matrix Q is expressed by the following equation.
f _c (Q) = f _c (H ^T (HH ^T ) ⁻¹ (C ^TC ) ⁻¹ C ^T SCH)
^{_{= F c (HH T (HH}} T) -1 (C T C) -1 C T SC)
= F _c ((C ^T C) ⁻¹ C ^T SC)) (11)
Here, Q ′ = (C ^T C) ⁻¹ C ^T SC is set. Focusing on the form of the matrix, as shown below, C ^TC is a Toeplitz-type correlation matrix, and C ^T SC is a form in which C ^T C is shifted up by one line.

従って、Ｑ′は、次の形の行列となる。

Therefore, Q ′ is a matrix of the following form.

ここで、１／ｃ（ｚ）＝１−（ｄ_１ｚ^-1＋…＋ｄ_m’ｚ^-m’ ）。すなわち、行列Ｑ′の一列目には共通項ｃ（ｚ）の逆特性を表す係数が並ぶ。行列Ｑの特性多項式は、次式となる。
ｆ_ｃ（Ｑ）＝ｆ_ｃ（Ｑ′）
＝１−（ｄ_１ｚ^-1＋…＋ｄ_m’ｚ^-m’） （12）
すなわち、行列Ｑの特性多項式は、共通項ｃ（ｚ）の逆特性を表わす多項式に一致する。

Here, 1 / c (z) = 1− (d ₁ z ⁻¹ +... + _{Dm ′} z ^{−m ′} ). That is, the coefficient representing the inverse characteristic of the common term c (z) is arranged in the first column of the matrix Q ′. The characteristic polynomial of the matrix Q is as follows.
f _c (Q) = f _c (Q ′)
= 1− (d ₁ z ⁻¹ +... + _{Dm ′} z ^{−m ′} ) (12)
That is, the characteristic polynomial of the matrix Q matches the polynomial that represents the inverse characteristic of the common term c (z).

このようにこの伝達関数行列Ｈ＾は列の要素数（ｊ′＋１）の２倍とし、行の数をｊ′の２倍＋１とし、１列目を１行目から始まるｈ＾₁(ｚ)の縦ベクトルとし、残りを０とし、第ｐ列目（ｐ＝２，…，ｊ′）をｐ−１個の０とｈ＾₁(ｚ)の縦ベクトルと、ｊ′−（ｐ−１）個の０とし、これらの次に、つまりｊ′＋１列目以後に、ｈ＾₂(ｚ)の縦ベクトルを順次１行ずらし、かつ２ｊ′要素中の残りの要素を０としたものである。 By the way, in equation (9), if H ^ = CH, this is a matrix composed of estimated transfer functions h ^ ₁ (z) and h ^ ₂ (z) as shown below.

Thus, this transfer function matrix H ^ is twice the number of column elements (j '+ 1), the number of rows is twice j' + 1, and h ^ ₁ (z starting from the first row in the first column) ), The rest is 0, the p-th column (p = 2,..., J ′) is p−1 0 and h ^ ₁ (z) vertical vectors, j ′ − (p− 1) The number of 0s, the next, that is, after the j '+ 1th column, the vertical vector of h ^ ₂ (z) is sequentially shifted by one row, and the remaining elements in the 2j' elements are set to 0 It is.

As described above, by substituting H ^ = CH into the equation (9) and solving this for the matrix Q, the following equation is obtained.
Q = (H ^ ^T H ^) ^-1 H ^ ^T SH ^ (14)
That is, the product matrix Q can be calculated using the matrix H ^ and the shift matrix S that are configured using the estimated transfer function. The characteristic polynomial of the product matrix Q obtained in this way matches the polynomial representing the inverse characteristic of the common term c (z).
A specific functional configuration of the common term calculation unit 36 is shown in FIG. 4, and an example of the processing procedure is shown in FIG. The transfer function estimation values h ^ ₁ (z) and h ^ ₂ (z) from the transfer function estimation unit 40 constitute a transfer function matrix H ^ in the transfer function matrix generation unit 41 (step S11). The transposed matrix H ^ ^T of ^ is constituted by the transposed unit 42 (step S12). The transfer function matrix H ^, its transposed matrix H ^ ^T, and the shift matrix S are input to the product matrix calculation unit 43, and the matrix calculation of equation (14) is performed to generate the product matrix Q (step S13). That, H ^ correlation matrix ^{H ^} T H ^ of the inverse matrix of the ^{(H ^ T H ^) -1} , is the product of the correlation matrix ^{H ^} T H ^ a row matrix shifted on ^H ^ T SH ^ Calculated by the product matrix calculator 43. A characteristic polynomial is calculated for the product matrix Q by the characteristic polynomial calculator 44 (step S14). The inverse characteristic of the characteristic polynomial is calculated by the inverse characteristic calculator 45, and as a result, the common term c (z) is obtained (step S15).

The transfer characteristic of the post-stage filter 34 in FIG. 3 is the common term c (z) obtained by the inverse characteristic calculator 45. Filter coefficients are set for the post-stage filter 34 so as to obtain this transfer characteristic. Accordingly, the estimated input signal s ^ (n) from which the influence of the common term c (z) is removed is obtained from the post-stage filter 34.
In addition to the method described above, the common term calculation method may be obtained by using Qiu's method for obtaining the greatest common divisor polynomial of two polynomials (for example, documents W. Qiu, Y. Hua, and K). Abed-Meraim, “A subspace method for the computation of the GCD of polynomials,” Automatica, vol. 33, no. 4, 741-743 (1997)). In this case, the common term calculation method can be summarized as follows.

中央の対角行列中のΣ_ｒはゼロでないｒ個の特異値を対角要素に持つ対角行列を表し、「０」は全ての要素が０のゼロ行列を表す。
［Ｕ_ｒＵ_０］は固有ベクトルから作られた行列であり、その零空間固有ベクトルＵ_０は次式で表せる。
Ｕ_０＝［ｕ_ｒ＋１，...，ｕ_{２ｊ′＋１}］
更に式（１６）を用いて行列Ｒを計算する。 The transfer function matrix H is represented by three matrix products by singular value decomposition, and the matrices on both sides thereof are represented by using two sub-matrices as shown in equation (15).

Σ _r in the central diagonal matrix represents a diagonal matrix having r non-zero r singular values as diagonal elements, and “0” represents a zero matrix in which all elements are zero.
[U _r U ₀ ] is a matrix made from eigenvectors, and the null space eigenvector U ₀ can be expressed by the following equation.
U ₀ = [ur _{+ 1} ,..., _{U2j ′ + 1} ]
Further, the matrix R is calculated using Equation (16).

この行列Ｒの最小固有値に対応する固有ベクトルを求めれば共通項ｃ（ｚ）となる。このｃ（ｚ）が後段フィルタ３４の伝達特性となるようにフィルタ係数を設定する。
従来技術では、図２を参照して説明したように様々な次数を用いて残響除去処理を行い、伝達関数の推定精度を表わすコスト関数を計算する。そして、このコスト関数を最小化する次数を最適な次数として採用する。これに対して、この実施形態では、一度残響除去処理を行えばよく、アルゴリズム構成が非常に簡単になる。

If the eigenvector corresponding to the minimum eigenvalue of this matrix R is obtained, the common term c (z) is obtained. The filter coefficient is set so that this c (z) becomes the transfer characteristic of the post-stage filter 34.
In the prior art, as described with reference to FIG. 2, dereverberation processing is performed using various orders, and a cost function representing the estimation accuracy of the transfer function is calculated. Then, the order that minimizes the cost function is adopted as the optimum order. On the other hand, in this embodiment, the dereverberation process only needs to be performed once, and the algorithm configuration becomes very simple.

In addition, the present invention is not limited to indoor audio recording, but can also be applied to the removal of effects due to multipath in mobile radio.In that case, an antenna is used as a sensor, and the antenna output signal is converted into a baseband signal. Processing is performed in the same manner as described above. The present invention can be applied to other similar problems.
An embodiment of the method of the present invention will be described with reference to FIG. First and second transfer function values are estimated from the first and second output signals x ₁ (n) and x ₂ (n) from the sensors 13 and 14 (step S31), and the first and second transfer function estimations are performed. First and second inverse filter coefficients are calculated from the values h ₁ (z) and h ₂ (z), respectively (step S32). The output signals x ₁ (n) and x ₂ (n) are respectively filtered using these first and second inverse filter coefficients (step S33), and the reverberation signal, diffracted wave signal, etc. are added by adding these processing results. Is obtained (step S34), while a common term common to these functions is calculated using the transfer function estimated values ＾ ₁ (z) and ＾ ₂ (z) (step S35). Is used to perform a filtering process to remove the common term component from the added signal obtained in step S34, and to obtain an estimated value of the input signal (step S36).

This signal estimation process may be executed by a computer, that is, the apparatus shown in FIG. 3 may be caused to function by the computer. The computer is schematically shown in FIG. For example, a signal estimation program for causing a computer to execute each step of each processing procedure shown in FIG. 6 is installed in the memory 51 from a recording medium such as a CD-ROM, a magnetic disk, or a semiconductor storage device, or a transmission line is connected. The CPU 52 executes this program, fetches the output signal from the sensor into the storage unit 54 via the interface 53 with the outside, performs processing based on the execution of the program on the fetched output signal, The estimated input signal is output from the output unit 55. A transfer function estimation unit 56 and a common term calculation unit 57 that execute programs themselves such as a digital signal processing module (DSP) and independently process them may be provided, and these may be operated based on instructions from the CPU 52. . The transfer function estimated values h ₁ (z) and h ₂ (z) may be obtained by methods other than the two methods described above.

The block diagram which shows the function structure of the dereverberation apparatus by a prior art. The flowchart which shows the process sequence of the apparatus shown in FIG. The block diagram which shows the function structure of the input signal estimation apparatus in one Embodiment of this invention. FIG. 4 is a block diagram illustrating a specific functional configuration example of a common term calculation unit 36 in FIG. 3. 5 is a flowchart showing an example of a processing procedure of a common term calculation unit 36. The flowchart which shows the example of the process sequence of the input signal estimation method by this invention. The block diagram which shows the outline of the computer made to function as this invention apparatus.

Claims (6)

Estimating the first and second transfer functions from the output signals of the first and second sensors provided at the output end of the one-input two-output transmission system;
Calculating first and second inverse filter coefficients using estimated values of the first and second transfer functions;
Filtering the first and second sensor output signals with the first and second inverse filter coefficients, respectively;
Adding these filtered signals; and
Calculating a common term multiplied by these estimated values from the estimated values of the first and second transfer functions;
A signal estimation method comprising a step of filtering the added signal according to the common term to estimate an input signal. The method of claim 1, wherein
In the process of calculating the common term, the transfer function matrix H ^ is constructed using the first and second transfer function values,
Find the transpose matrix H ^ ^T of the transfer function matrix H ^,
And the transfer function matrix H ^ correlation matrix H ^ T ^{H ^} of the inverse matrix of the transfer function matrix H correlation matrix obtained by shifting up one row matrix of ^ H ^ T ^SH ^ the product of the calculated product matrix Q Produces
Calculate the characteristic polynomial of the product matrix Q,
A signal estimation method characterized by being a process of calculating a reverse characteristic of the characteristic polynomial to obtain a common term. The first and second sensor output signals provided at the output end of the one-input two-output transmission system are input, and these both output signals obtain the estimated values of the first and second transfer functions between the input end and both output ends. A transfer function estimator;
An inverse filter calculator that receives the first and second transfer function estimates and calculates the first and second inverse filter coefficients;
First and second pre-filters, which are respectively set with first and second inverse filter coefficients, and respectively input first and second sensor output signals;
An adder for adding the output signals of the first and second pre-filters;
A common term calculation unit that receives the first and second transfer function estimates and calculates a common term of these transfer functions;
And a post-stage filter configured to receive the adder output signal, remove the common term component from the added output signal, and output an estimated input signal. The apparatus of claim 3.
The common term calculation unit receives the first and second transfer function estimation values, and forms a transfer function matrix H ^.
A transfer function matrix H ^ is input, and a transpose section constituting the transpose matrix H ^ ^T ;
A transfer function matrix, and its transposed matrix, and the matrix S to shift the matrix on one line is input, and product matrix calculator for calculating the ^{(H ^ T H ^) -1} H ^ T SH ^ = Q,
A signal estimation apparatus comprising: a characteristic polynomial calculation unit that receives a product matrix Q, calculates a characteristic polynomial thereof, calculates an inverse characteristic of the characteristic polynomial, and obtains a common term.   A signal estimation program for causing a computer to execute each step of the input signal estimation method according to claim 1.   A computer-readable recording medium on which the signal estimation program according to claim 5 is recorded.

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