A frequency domain adaptive filtering method for blind identification of multi-channel low-rank acoustic systems

Abstract

The present invention discloses a frequency domain adaptive filtering method for blind identification of multi-channel low-rank acoustic systems. The nearest Kronecker product (NKP) decomposition method is extended to the blind identification of multi-channel low-rank acoustic systems in the frequency domain, and a normalized multi-channel frequency domain least mean square (NKP-NMCFLMS) adaptive algorithm based on NKP decomposition is proposed. Specifically, a longer multi-channel adaptive filter is decomposed into two groups of short sub-filters by using NKP, two groups of generalized multi-channel frequency domain block signal models are established, and then the collected data are transformed into the frequency domain, and the adaptive sub-filter coefficient vector calculation is completed according to the frequency domain data.

Description

Technical Field

[0001] The present invention belongs to the technical field of adaptive filters, and more specifically, relates to a frequency domain adaptive filtering method for blindly identifying a multi-channel low-rank acoustic system. Background Art

[0002] Adaptive filters are widely used in signal processing, communication, automatic control and other technical fields. Scholars have developed a large number of adaptive filtering methods to improve the convergence speed and stability of adaptive filters, reduce computational complexity, reduce steady-state errors and sensitivity to noise.

[0003] Blind system identification, first proposed by Sato, estimates the impulse response of the acoustic channel using only the output signal of the system, and plays an important role in speech processing systems such as speech dereverberation and sound source localization. In the past two decades, scholars have developed a variety of batch processing methods and adaptive methods for the problem of blind system identification. Among these methods, the normalized multichannel frequency domain least mean square algorithm (NMCFLMS) is particularly attractive in real-time systems due to its high computational efficiency generated by the use of fast Fourier transform (FFT). However, in practical applications, especially in dereverberation tasks, the acoustic impulse response has a length of tens of thousands of sampling points and time-varying characteristics. It is challenging for adaptive filters to accurately and quickly track such a long time-varying acoustic system.

[0004] In order to solve this challenging problem, in recent years, acoustic impulse response shortening schemes have been widely studied, among which the Kronecker product (NKP) decomposition method has recently received great attention. This method uses the Kronecker product and low-rank approximation to decompose the impulse response of the acoustic system, thereby converting a high-dimensional system identification problem into a low-dimensional system identification problem. The computational efficiency of this method and its good tracking performance in white Gaussian noise environment have been verified in identifying the impulse response of the echo channel with a long tail. Summary of the invention

[0005] The purpose of the present invention is to overcome the deficiencies of the prior art and provide a frequency domain adaptive filtering method for blind identification of multi-channel low-rank acoustic systems, which greatly improves the performance of the adaptive algorithm and improves the tracking capability of the adaptive filter.

[0006] To achieve the above-mentioned object of the invention, the frequency domain adaptive filtering method for blindly identifying a multi-channel low-rank acoustic system of the present invention is characterized by comprising the following steps:

[0007] (1) Adaptive filter parameter setting;

[0008] Set the length of the adaptive filter to L, set the lengths of the two sets of adaptive sub-filter coefficients to L1 and L2, where L = L1 × L2, the number of the two sets of adaptive sub-filters is P, set two step sizes to ρ1 and ρ2, where 0 < ρ1, ρ2 < 1, and set two forgetting factors λ1 and λ2;

[0009] (2) Initialize two sets of adaptive sub-filter coefficients and two parameterized power spectrum matrices for each channel;

[0010] set up and They are the sub-vectors of the two sets of adaptive sub-filter coefficient vectors with lengths of L1 and L2 at the m-th block time of the j-th channel, p = 1, 2, ... P, and the coefficient vector at the 0th block time The L1 coefficients and The first coefficient of the L2 coefficients in is set to η, and the remaining coefficients are set to 0, that is, [η0…0] T ; Wherein, the superscript T represents transposition, j = 1, 2, ..., M, M is the number of channels;

[0011] set up They are the two parameterized power spectrum matrices of the j-th channel at the m-th block moment, and the power spectrum matrix of the 0th block moment is Initialize to zero matrices of size PL2×PL2 and PL1×PL1 respectively;

[0012] Initialization block time m=1;

[0013] (3) Signal acquisition;

[0014] The acoustic signal is collected, and the 2L most recent sampling values ​​of the ith channel of the acoustic system at the mth block time are taken as the input signal vector and recorded as x i (m), i = 1, 2, ..., M, M is the number of channels;

[0015] (4) transforming the collected data into the frequency domain;

[0016] Using the fast Fourier transform matrix, the data x of each channel is i (m) Transform to the frequency domain and arrange the transformed frequency domain data into a diagonal matrix:

[0017]

[0018] in, Represents x i (m) is transformed into a diagonal matrix after being arranged in the frequency domain. diag{·} represents a diagonal matrix that arranges the vectors in {·} on the diagonal line. F 2L×2L Represents a Fourier matrix of size 2L×2L;

[0019] (5) Calculate two equivalent prior error signals;

[0020] First calculate the matrix and

[0021]

[0022]

[0023] in, and are identity matrices of dimensions L1×L1 and L2×L2 respectively, is the Kronecker product;

[0024] Then calculate the matrix

[0025]

[0026]

[0027] Finally, the a priori error signal is calculated e i，j；1 (m), e i，j；2 (m)::

[0028]

[0029]

[0030] in, is an auxiliary matrix;

[0031] (6) Update the two parameterized power spectrum matrices

[0032] According to the matrix And two forgetting factors λ1 and λ2 update the power spectrum matrix of the mth block moment

[0033]

[0034]

[0035] Where Re{·} means taking the real part of a complex number, and the superscript H means taking the conjugate transpose of a matrix;

[0036] (7) Update two adaptive sub-filter coefficient vectors;

[0037] According to the power spectrum matrix of the mth block Two step sizes ρ1, ρ2, a priori error signal e i，j；1 (m), e i，j；2 (m), and the adaptive sub-filter coefficient vector at the m-1th block time Update the adaptive sub-filter coefficient vector

[0038]

[0039] Among them, the adaptive sub-filter coefficient vector Respectively composed of multiple sub-vectors:

[0040]

[0041]

[0042] (8) Calculate the adaptive filter coefficient vector;

[0043] Calculate the adaptive filter coefficient vector from the adaptive sub-filter coefficient vector

[0044]

[0045] m=m+1, return to step (3).

[0046] The object of the invention of the present invention is achieved in this way:

[0047] The present invention is a frequency domain adaptive filtering method for blind identification of multi-channel low-rank acoustic systems. The NKP decomposition method is extended to the blind identification of multi-channel low-rank acoustic systems in the frequency domain, and a normalized multi-channel frequency domain least mean square (NKP-NMCFLMS) adaptive algorithm based on NKP decomposition is proposed. Specifically, the NKP is used to decompose a longer multi-channel adaptive filter into two groups of short sub-filters, and two groups of generalized multi-channel frequency domain block signal models are established. Then the collected data is transformed into the frequency domain, and the adaptive sub-filter coefficient vector calculation is completed according to the frequency domain data.

[0048] At the same time, the frequency domain adaptive filtering method for blindly identifying a multi-channel low-rank acoustic system of the present invention also has the following beneficial effects:

[0049] (1) By using NKP decomposition to decompose a long multi-channel adaptive filter into two groups of short sub-filters, this method changes the structure of the traditional adaptive filter, making the filter length shorter, and also uses FFT to improve the computational efficiency of the filter algorithm of the present invention.

[0050] (2) By decomposing a long filter into two groups of short filters and optimizing each group of filters separately, each group of filters can be more flexibly iterated, and finally the filter of the present invention has a faster convergence speed and tracking speed. BRIEF DESCRIPTION OF THE DRAWINGS

[0051] Figure 1 It is a flow chart of a specific implementation method of the frequency domain adaptive filtering method for blindly identifying a multi-channel low-rank acoustic system of the present invention;

[0052] Figure 2 It is a convergence comparison curve of the present invention and the NMCFLMS algorithm in blindly identifying a six-channel acoustic system under white Gaussian sequence excitation;

[0053] Figure 3 is a comparison curve of the computational complexity of the present invention and the NMCFLMS algorithm in blindly identifying a six-channel acoustic system under white Gaussian sequence excitation;

[0054] Figure 4 It is a convergence comparison curve of the present invention and the NMCFLMS algorithm in blindly identifying a six-channel acoustic system under speech signal excitation;

[0055] Figure 5 It is a comparison curve of the computational complexity of the present invention and the NMCFLMS algorithm in blindly identifying a six-channel acoustic system under speech signal excitation; DETAILED DESCRIPTION

[0056] The specific implementation of the present invention is described below in conjunction with the accompanying drawings so that those skilled in the art can better understand the present invention. It should be noted that in the following description, when the detailed description of known functions and designs may dilute the main content of the present invention, these descriptions will be omitted here.

[0057] 1. Multi-channel frequency domain adaptive blind system identification algorithm based on NKP decomposition

[0058] 1.1 Multi-channel time domain signal model

[0059] Assuming a single-input multi-output acoustic system consists of a sound source and M microphones, the signal picked up by the (i=1, 2, ..., M)th microphone can be written as:

[0060] x i (n) = s(n) * h i +v i (n) (1)

[0061] Where s(n) is the sound source signal, * represents linear convolution, and h i is the impulse response between the sound source and the i-th microphone, u i(n) is the additive noise collected by the i-th microphone. If the noise term in (1) is ignored, the relationship between the signals of two different microphones is as follows:

[0062] x i (n)*h j =s(n)*h i *h j =x i (n)*hi,i,j=1,2,…,M,i≠j, (2)

[0063] This formula can be rewritten in vector-matrix form:

[0064]

[0065] Where h i =[h i，0 h i，1 …h i，L-1 ] T , i = 1, 2, ..., M, is an impulse response of length L, and x i (n) = [x i (n)x i (n-1)…x i (n-L+1)]T is the output signal vector of the i-th sensor.

[0066] When there is noise or the estimated impulse response deviates from the true impulse response, equation (3) will no longer be equal to zero, that is, the following a priori error signal is generated between the i-th and j-th channels:

[0067]

[0068] In the formula Yes i The estimated value at time n-1.

[0069] In indoor acoustic environments, most linear acoustic systems have low-rank characteristics due to reflections from the floor, walls, and ceiling of the room. Therefore, a low-rank model can be used to approximate the acoustic channel impulse response, which consists of a set of NKPs between short impulse responses. According to the principle of acoustic system identification, the Kronecker product can also be used to decompose the adaptive filter into the following form:

[0070]

[0071] In the formula and are sub-filters of length L1 and L2 respectively, Denote the Kronecker product, and assume that L = L1L2 and P ≤ 2min{L1, L2}. Use the following relationship:

[0072]

[0073] In the formula and are unit matrices of size L1×L1 and L2×L2 respectively. The error signal in (4) can be written in the following two equivalent forms:

[0074]

[0075]

[0076] In the formula

[0077]

[0078]

[0079]

[0080]

[0081]

[0082]

[0083] 1.2 Multi-channel frequency domain signal model

[0084] In order to derive the multi-channel frequency domain adaptive filtering algorithm, it is necessary to first write the block signal model. To this end, the error signal in (7) and (8) can be rewritten as the following vector form:

[0085]

[0086]

[0087] Where m is the block time index,

[0088] e i，j；1 (m) = [e i，j；1 (mL)e i，j；1 (mL+1)…e i，j；1 (mL+L-1)] T , (17)

[0089] e i，j；2 (m) = [e i，j；2 (mL)e i，j；2 (mL+1)…e i，j；2 (mL+L-1)] T , (18)

[0090]

[0091] X i (m) = [x i (mL)x i (mL+1)…xi(mL+L-1)], (20)

[0092] Q i，j；2 (m) = [Q i，j；2，1 (m)Q i，j；2，2 (m)…Q i，j；2，P (m)], (21)

[0093]

[0094] Q i，j；1 (m) = [Q i，j；1，1 (m)Q i，j；1，2 (m)…Q i，j；1，P (m)], (23) In order to reduce the computational complexity of the adaptive filtering algorithm, fast block operations are required. Since the two matrices Q i，j；1，p (m) and Q i，j；2，p The sizes of (m) are L×L2 and L×L1 respectively, so it is impossible to diagonalize them. However is a square topological matrix, so it can be diagonalized as:

[0095]

[0096] Where 0 L×L is a zero matrix of size L×L, F 2L×2L is a Fourier matrix of size 2L×2L, whose elements can be expressed as:

[0097]

[0098] In the formula is an imaginary unit,

[0099]

[0100] diag{·} means to represent the vector as a diagonal matrix,

[0101] x i (m) 2L×1 =[x i (mL-L)x i (xL-L+1)…x i (mL+L-1)] T . (27)

[0102] Therefore, the block error signal in (15) and (16) can be expressed in the frequency domain as follows:

[0103]

[0104]

[0105] In the formula

[0106] e i，j；1 (m) = F L×L e i，j；1 (m), (30)

[0107]

[0108]

[0109]

[0110]

[0111] e i，j；2 (m) = F L×L e i，j；2 (m), (35)

[0112]

[0113]

[0114]

[0115] Note that the matrix and The sizes are 2L×PL1 and 2L×PL2 respectively, and the matrix The size is 2L×2L. Usually PL1≤2L and PL2≤2L, so and The dimension is less than This helps to reduce the computational complexity of the multi-channel adaptive filtering algorithm.

[0116] 1.3 Optimization Criteria and Adaptive Algorithms

[0117] In order to derive the multi-channel frequency domain adaptive filtering algorithm, consider using the recursive least squares criterion to define a set of cost functions:

[0118]

[0119] This set of cost functions contains the zero error term generated by the cross-correlation difference between the same channels i=j, which is intended to facilitate the derivation of the adaptive algorithm without affecting the effectiveness of the invented algorithm. In order to accelerate the convergence of the adaptive filter and reduce the gradient noise amplification problem caused by the large channel output amplitude, the Newton method is used to derive the adaptive filtering algorithm. According to the Newton iteration criterion, the update equation of the first multi-channel frequency domain adaptive sub-filter group can be expressed as:

[0120]

[0121] Where μ1 represents the step size, right The gradient of can be derived as:

[0122]

[0123] Hessian Matrix It can be deduced as

[0124]

[0125] If L is large, then

[0126]

[0127] Therefore, the Hessian matrix in (42) can be simplified to:

[0128]

[0129] In practical applications, the power spectrum matrix of the multi-channel output in (44) can be obtained by the following recursive estimation:

[0130]

[0131] Where λ1 is the forgetting factor.

[0132] Similarly, based on Newton's method, the update equation of the second multi-channel frequency-domain adaptive sub-filter bank can be derived as:

[0133]

[0134] Where μ2 is the step size,

[0135]

[0136]

[0137] λ2 is the forgetting factor.

[0138] Since the algorithm uses NKP to derive in the frequency domain, it is called the NKP-NMCFLMS algorithm. Using (40), (41), (45) and (46 to (48), two sets of adaptive sub-filters can be estimated alternately. Thus, the global filter It can be obtained from (5).

[0139] Figure 1 It is a flow chart of a specific implementation of the frequency domain adaptive filtering method for blindly identifying a multi-channel low-rank acoustic system of the present invention.

[0140] In this embodiment, a frequency domain adaptive filtering method for blindly identifying a multi-channel low-rank acoustic system includes the following steps:

[0141] Step S1: Adaptive filter parameter setting

[0142] Set the length of the adaptive filter to L, set the lengths of the two sets of adaptive sub-filter coefficients to L1 and L2, where L = L1 × L2, the number of the two sets of adaptive sub-filters is P, set the two step sizes to ρ1 and ρ2, where 0 < ρ1, ρ2 < 1, and set two forgetting factors λ1 and λ2;

[0143] Step S2: Initialize two sets of adaptive sub-filter coefficients and two parameterized power spectrum matrices for each channel;

[0144] set up and They are the sub-vectors of the two sets of adaptive sub-filter coefficient vectors with lengths of L1 and L2 at the m-th block time of the j-th channel, p = 1, 2, ... P, and the coefficient vector at the 0th block time The L1 coefficients and The first coefficient of the L2 coefficients in is set to η, and the remaining coefficients are set to 0, that is, [η0…0] T ; Wherein, the superscript T represents transposition, j = 1, 2, ..., M, M is the number of channels;

[0145] set up They are the two parameterized power spectrum matrices of the j-th channel at the m-th block moment, and the power spectrum matrix of the 0th block moment is Initialize to zero matrices of size PL2×PL2 and PL1×PL1 respectively;

[0146] Initialization block time m=1;

[0147] Step S3: Signal acquisition

[0148] The acoustic signal is collected, and the 2L most recent sampling values ​​of the ith channel of the acoustic system at the mth block time are taken as the input signal vector and recorded as x i(m), i = 1, 2, ..., M, M is the number of channels;

[0149] Step S4: transforming the collected data into the frequency domain;

[0150] Using the fast Fourier transform matrix, the data x of each channel is i (m) Transform to the frequency domain and arrange the transformed frequency domain data into a diagonal matrix:

[0151]

[0152] in, Represents x i (m) is transformed into a diagonal matrix after being arranged in the frequency domain. diag{·} represents a diagonal matrix that arranges the vectors in {·} on the diagonal line. F 2L×2L Represents a Fourier matrix of size 2L×2L;

[0153] Step S5: Calculate two equivalent a priori error signals;

[0154] First calculate the matrix and

[0155]

[0156]

[0157] in, and are identity matrices of dimensions L1×L1 and L2×L2 respectively, is the Kronecker product;

[0158] Then calculate the matrix

[0159]

[0160]

[0161] Finally, the a priori error signal is calculated e i，j；1 (m), e i，j；2 (m):

[0162]

[0163]

[0164] in, is an auxiliary matrix;

[0165] Step S6: updating two parameterized power spectrum matrices;

[0166] According to the matrix And two forgetting factors λ1 and λ2 update the power spectrum matrix of the mth block moment

[0167]

[0168]

[0169] Where Re{·} means taking the real part of a complex number, and the superscript H means taking the conjugate transpose of a matrix;

[0170] Step S7: Update two adaptive sub-filter coefficient vectors;

[0171] According to the power spectrum matrix of the mth block Two step sizes ρ1, ρ2, a priori error signal e i，j；1 (m), e i，j；2 (m), and the adaptive sub-filter coefficient vector at the m-1th block time Update the adaptive sub-filter coefficient vector

[0172]

[0173] Among them, the adaptive sub-filter coefficient vector They are composed of multiple sub-vectors:

[0174]

[0175]

[0176] Step S8: Calculate the adaptive filter coefficient vector;

[0177] Calculate the adaptive filter coefficient vector from the adaptive sub-filter coefficient vector

[0178]

[0179] m=m+1, return to step S3.

[0180] Experimental verification

[0181] In order to evaluate the performance of the proposed multi-channel frequency-domain adaptive filtering algorithm, numerical simulations were performed using impulse responses measured in a real room, which are considered to correspond to ideal single-input multi-output linear systems. The room size is 6.7m×6.1m×2.9m, and the reverberation time is about 280ms. A uniform linear array consists of six omnidirectional microphones. A set of impulse responses is used to simulate a time-invariant multi-channel acoustic system, and another set of different impulse responses is added to simulate a time-varying multi-channel acoustic system. The six microphones are located at (2.537, 0.5, 1.4), (2.737, 0.5, 1.4), (2.937, 0.5, 1.4), (3.137, 0.5, 1.4), (3.337, 0.5, 1.4) and (3.537, 0.5, 1.4), respectively. The first sound source position is (0.337, 3.938, 1.6), and the second sound source position is (4.337, 1.438, 1.6). The sampling rate of the impulse response and the excitation speech is 8kHz, and the length of the impulse response is truncated to 1024. The additive noise is white Gaussian noise, and the signal-to-noise ratio SNR = 30dB. Normalized projection misalignment (NPM) is used as the evaluation index of the algorithm performance, which is defined as follows

[0182]

[0183] The first set of simulation experiments examines the performance of the present invention when a white Gaussian sequence is used as an excitation. The relevant parameters are set to L1 = 64, L2 = 16, P = 8, μ1 = μ2 = 0.02, μ NMCFLMS =0.5,λ1=λ2=λ NMCFLMS =[1-1 / (3L)] L . Figure 2 The convergence curves of NMCFLMS and the NKP-NMCFLMS algorithm proposed in this invention for blind identification of (a) time-invariant six-channel acoustic system and (b) time-varying six-channel acoustic system are plotted. Among them, white Gaussian sequence is used as the excitation signal, signal-to-noise ratio SNR = 30dB, L = 1024, L1 = 64, L2 = 16, P = 8. It can be seen that the convergence performance and tracking ability of the proposed NKP-NMCFLMS algorithm are better than those of the NMCFLMS algorithm. The reason is that the NKP-NMCFLMS algorithm designs and optimizes the shorter sub-filters separately under appropriate parameter conditions, rather than directly identifying the global long filter. Compared with the NMCFLMS algorithm, under the same scale of observed signals, the proposed NKP-NMCFLMS algorithm is easier to obtain robust channel estimation.

[0184] from Figure 3It can also be seen that under the white Gaussian sequence excitation, the computational efficiency of the proposed NKP-NMCFLMS algorithm is higher than that of the NMCFLMS algorithm, where the parameter values ​​in (a) are L = 1024, L1 = 64, L2 = 16, and the parameter values ​​in (b) are L1 = 0.5L, P = 8;

[0185] The second set of experiments investigated the performance of the proposed algorithm under speech signal stimulation. The relevant parameters were set as L1 = 256, L2 = 4, P = 2, μ1 = μ2 = 0.02, μ NMCFLMS =0.5,λ1=λ2=λ NMCFLMS =[1-1 / (3L)] L . Figure 4 The convergence curves of NMCFLMS and the NKP-NMCFLMS algorithm proposed in this invention for blind recognition of (a) time-invariant six-channel acoustic system and (b) time-varying six-channel acoustic system are plotted. It can be seen that the non-stationarity of the speech signal reduces the convergence speed of the two adaptive algorithms, but the convergence of the proposed NKP-NMCFLMS algorithm is better than that of the NMCFLMS algorithm.

[0186] In addition, under a given parameter configuration, the computational complexity of NKP-NMCFLMS is significantly smaller than that of the NMCFLMS algorithm, e.g. Figure 5 As shown, in which, in (a), the parameter values ​​are L=1024, L1=256, L2=4, and in (b), the parameter values ​​are L1=0.25L, P=2;

[0187] In summary, the present invention uses NKP to decompose a longer multi-channel adaptive filter into two groups of short sub-filters, and establishes two groups of generalized multi-channel frequency domain block signal models. According to these models, a set of cost functions of adaptive filters are defined, and a multi-channel frequency domain adaptive filtering algorithm is derived according to the Newton iteration criterion. Numerical simulation is carried out using the acoustic channel impulse response measured in a real room. The results show that no matter whether the system excitation is a white sequence or a speech signal, the proposed NKP-NMCFLMS algorithm has a faster convergence speed and tracking speed than the traditional NMCFLMS algorithm. As long as the parameters are set reasonably, the computational complexity of the proposed NKP-NMCFLMS algorithm is much lower than that of the traditional NMCFLMS algorithm.

[0188] Although the above describes the illustrative specific embodiments of the present invention to facilitate those skilled in the art to understand the present invention, it should be clear that the present invention is not limited to the scope of the specific embodiments. For those of ordinary skill in the art, as long as various changes are within the spirit and scope of the present invention as defined and determined by the attached claims, these changes are obvious, and all inventions and creations using the concept of the present invention are protected.

Claims

1. A frequency domain adaptive filtering method for blind identification of multi-channel low-rank acoustic systems, characterized in that: The following steps are involved: (1) Adaptive filter parameter setting; Set the length of the adaptive filter to L, set the lengths of the two groups of adaptive sub-filters to L1 and L2, where L = L1 × L2, the number of the two groups of adaptive sub-filters is P, set two step sizes to ρ1 and ρ2, where 0 < ρ1, ρ2 < 1, and set two forgetting factors λ1 and λ2; (2) Initialize two sets of adaptive sub-filter coefficients and two parameterized power spectrum matrices for each channel; set up and They are the sub-vectors of the two sets of adaptive sub-filter coefficient vectors with lengths of L1 and L2 at the m-th block time of the j-th channel, p = 1, 2, ... P, and the coefficient vector at the 0th block time The L1 coefficients and The first coefficient of the L2 coefficients in is set to η, and the remaining coefficients are set to 0, that is, [η 0 … 0] T ; Wherein, the superscript T represents transposition, j = 1, 2, ..., M, M is the number of channels; Let S j；1 (m), S j；2 (m) are the two parameterized power spectrum matrices of the j-th channel at the m-th block moment, and the power spectrum matrix S at the 0th block moment j；1 (0), S j；2 (0) Initialize to zero matrices of size PL2×PL2 and PL1×PL1 respectively; Initialization block time m=1; (3) Signal acquisition; The acoustic signal is collected, and the 2L most recent sampling values ​​of the ith channel of the acoustic system at the mth block time are taken as the input signal vector and recorded as x i (m), i = 1, 2, ..., M, M is the number of channels; (4) transforming the collected data into the frequency domain; Using the fast Fourier transform matrix, the data x of each channel is i (m) Transform to the frequency domain and arrange the transformed frequency domain data into a diagonal matrix: in, Represents x i (m) is transformed into a diagonal matrix after being arranged in the frequency domain. diag{·} represents a diagonal matrix that arranges the vectors in {·} on the diagonal line. F 2L×2L Represents a Fourier matrix of size 2L×2L; (5) Calculate two equivalent prior error signals; First calculate the matrix and in, and are identity matrices of dimensions L1×L1 and L2×L2 respectively, is the Kronecker product; Then calculate the matrix Finally, the a priori error signal is calculated e i，j；1 (m), e i，j；2 (m): in, is an auxiliary matrix; (6) Update the two parameterized power spectrum matrices According to the matrix And two forgetting factors λ1, λ2 update the power spectrum matrix S of the mth block moment j；1 (m), S j；2 (m): Where Re{·} means taking the real part of a complex number, and the superscript H means taking the conjugate transpose of a matrix; (7) Update two adaptive sub-filter coefficient vectors; According to the power spectrum matrix S of the mth block j；1 (m), S j；2 (m), two step sizes ρ1, ρ2, a priori error signal e i，j；1 (m), e i，j；2 (m), and the adaptive sub-filter coefficient vector at the m-1th block time Update the adaptive sub-filter coefficient vector Among them, the adaptive sub-filter coefficient vector They are composed of multiple sub-vectors: (8) Calculate the adaptive filter coefficient vector; Calculate the adaptive filter coefficient vector from the adaptive sub-filter coefficient vector m=m+1, return to step (3).

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