Proportional population adaptive filter against impulse noise interference

Abstract

The present invention discloses a proportional overall adaptive filter resistant to impulse noise interference, belonging to the field of digital filter design. The proportional overall adaptive filter resistant to impulse noise interference is established by maximizing the overall correlation entropy cost function constrained by the weighted norm of the weight vector. The filter fully utilizes the sparsity of the system by introducing a proportional matrix, accelerates the convergence speed, and can still obtain a lower steady-state error when both the input and output signals are subject to noise interference, and has strong robustness in a pulse environment. The proportional overall adaptive filter resistant to impulse noise interference disclosed by the present invention can be applied to modern communication equipment such as video conferencing and hands-free phones.

Description

Technical Field

[0001] The invention discloses a proportional total adaptive filter resistant to impulse noise interference, in particular discloses a proportional maximum total correlation entropy adaptive filter, belonging to the field of digital filter design. Background Art

[0002] System identification is an important branch of adaptive signal processing. Many traditional problems such as adaptive channel equalization, adaptive noise elimination, adaptive echo cancellation, active noise control, etc. can be attributed to system identification problems.

[0003] In some applications, the unknown system is sparse, that is, most of the elements in the weight vector of the unknown system are zero or close to zero. The problem of sparse system identification is often involved in theory and engineering practice, and is one of the current research hotspots. For example, the application of zero-point attraction theory and proportional adaptive strategy in satellite transmission channels and echo cancellation channels. At present, research shows that the use of proportional updates and low-order norm regularization of weight vectors can effectively improve the convergence speed of adaptive filters.

[0004] Traditional LMS and NLMS adaptive filters are easy to implement, but their performance will drop sharply in some special environments. In some special environments, the output of the unknown system and the input of the adaptive filter may be interfered by noise. In response to this situation, a series of robust adaptive filters have been proposed, such as the deviation-compensated minimum mean square filter, the gradient descent-total least squares filter, etc. In addition, there may be pulse interference in the output noise of the unknown system. For this scenario, the deviation-compensated sign error filter and the maximum total correlation entropy filter have been proposed. These filters have a good convergence effect for general unknown systems, but when the system has sparse characteristics, they fail to fully utilize its sparsity and the convergence speed is relatively slow. Summary of the invention

[0005] In order to solve the above problems, the present application proposes a proportional total adaptive filter (hereinafter referred to as PMTC) that is resistant to impulse noise interference. The adaptive filter is suitable for the case where the system is a sparse system, and adopts a method of proportional update and conditionally constrained maximization of the total correlation entropy cost function to make full use of the sparse characteristics of the unknown system and improve the robustness when the input signal has white noise and the output signal has impulse interference.

[0006] The weight vector updating of the proportional population adaptive filter against impulse noise interference includes the following steps:

[0007] 1) The noisy input signal sampling values ​​at time n and the previous M-1 consecutive time points The noisy input signal vector that constitutes the adaptive filter Wherein: the superscript T represents the transpose operation.

[0008] 2) The M weights of the adaptive filter at time n form a weight vector w n =[w n,0 ,w n,1 ,...,w n,M-1 ] T .

[0009] 3) The noisy input signal vector and the weight vector w of the adaptive filter n Perform inner product to generate the output signal of the adaptive filter

[0010] 4) According to Calculate the error signal e n ,in: represents the noisy expected response of the adaptive filter. Calculate the intermediate variable p(w n,i )=min(γ|w n,i |,1), where: i is a positive integer greater than or equal to 0 and less than M, and γ is a positive constant used to control the strength of the estimated sparse system.

[0011] Construct the vector p(w n )=[p(w n,0 ),p(w n,1 ),...,p(w n,M-1 )] T .

[0012] according to Calculate the proportionality factor g n,i , where: α is the proportional coefficient control parameter, and its value range is -1≤α<1; ε is a small positive constant to avoid the denominator being zero; || ||1 represents the l1 norm of the vector.

[0013] Construct the scale matrix G from the scale coefficients n =diag(g n,0 ,g n,1 ,...,g n,M-1 ), where diag represents the element g n,0 ,g n,1 ,...,g n,M-1 As the diagonal elements form a diagonal matrix.

[0014] 5) According to Calculate the vector f n ,in: is the augmented weight vector of the adaptive filter, is the variance of the measurement noise in the desired signal without the impulse interference, is the variance of the noise contained in the input signal of the adaptive filter, and σ is the kernel width parameter of the correlation entropy with a positive value.

[0015] 6) Use expression Update the weight vector w n , where: μ is the step size; Represents the vector f n The matrix G n Weighted l2 norm, δ is a small positive constant to avoid zero denominator.

[0016] Beneficial Effects

[0017] Compared with the solutions in the prior art, the proportional overall adaptive filter resistant to pulse noise interference proposed in this application can fully utilize the sparse characteristics of the system to accelerate the convergence speed, and has strong robustness to the situations where the input signal has noise interference and the output signal has pulse interference. BRIEF DESCRIPTION OF THE DRAWINGS

[0018] The present invention will be further described below in conjunction with the accompanying drawings and embodiments:

[0019] Figure 1 The principle block diagram of the proportional population adaptive filter for resisting impulse noise interference;

[0020] Figure 2 is a speech input signal used in the embodiment of the present invention;

[0021] Figure 3 is a weight vector of the unknown system used in the embodiment of the present invention;

[0022] Figure 4 1 is a comparison of the normalized mean square deviation curves of MTC, RZA-MTC and PMTC in the embodiment of the present invention. DETAILED DESCRIPTION

[0023] Example

[0024] This embodiment uses a computer experiment method to verify the performance of the PMTC adaptive filter (its principle block diagram is shown in FIG. Figure 1In the experiment, the PMTC disclosed in the present application is used to identify an unknown sparse system in an environment where the input signal has white noise interference and the output signal has pulse interference, and its performance is compared with that of MTC [Maximum total correntropy adaptive filtering against heavy-tailed noises, Signal Processing, 2017, 141, 84-95] and RZA-MTC [Zero attracting maximum total correntropy algorithm for sparse system identification, IFAC Papers On Line, 2019, 52 (24), 103–106] adaptive filters.

[0025] The PMTC adaptive filter proposed in this application includes the following steps for identifying unknown sparse systems:

[0026] 1) The noisy input signal sampling values ​​at time n and the previous M-1 consecutive time points The noisy input signal vector that constitutes the adaptive filter Wherein: the superscript T represents the transpose operation.

[0027] 2) The M weights of the adaptive filter at time n form a weight vector w n =[w n,0 ,w n,1 ,...,w n,M-1 ] T .

[0028] 3) The noisy input signal vector and the weight vector w of the adaptive filter n Perform inner product to generate the output signal of the adaptive filter

[0029] 4) According to Calculate the error signal e n ,in: represents the noisy expected response of the adaptive filter. Calculate the intermediate variable p(w n,i )=min(γ|w n,i |, 1), wherein: i is a positive integer greater than or equal to 0 and less than M, and γ is a positive constant used to control the strength of the estimated sparse system. Preferably, 4) further includes:

[0030] Construct the vector p(w n )=[p(w n,0 ),p(wn,1 ),...,p(w n,M-1 )] T .

[0031] according to Calculate the proportionality factor g n,i , where: α is the proportional coefficient control parameter, and its value range is -1≤α<1; ε is a small positive constant to avoid the denominator being zero; || ||1 represents the l1 norm of the vector.

[0032] Construct the scale matrix G from the scale coefficients n =diag(g n,0 ,g n,1 ,...,g n,M-1 ), where diag represents the element g n,0 ,g n,1 ,...,g n,M-1 As the diagonal elements form a diagonal matrix.

[0033] 5) According to Calculate the vector f n ,in: is the augmented weight vector of the adaptive filter, is the variance of the measurement noise in the desired signal without the impulse interference, is the variance of the noise contained in the input signal of the adaptive filter, and σ is the kernel width parameter of the correlation entropy with a positive value.

[0034] 6) Use expression Update the weight vector w n , where: μ is the step size; Represents the vector f n The matrix G n Weighted l2 norm, δ is a small positive constant to avoid zero denominator.

[0035] In the experiment, the unknown system input signal is Figure 2 The speech signal shown, the weight vector w of the unknown system o For Figure 3 The impulse response of the echo path is shown, with its length truncated to 512. The normalized mean square deviation (NMSD) is used as the performance measure, that is, NMSD = 10log 10 [||w n -w o || 2 / ||w o || 2 ], in dB. Input noise u n is zero-mean Gaussian white noise, u n The variance of Output noise v n Contains a zero-mean Gaussian white noise η n and an impulse noise z n . η n The variance of Impulse noise is generated by a Bernoulli Gaussian process, i.e., z n =t n k n , where t n is a Bernoulli process, with a probability of 0.01 for a value of 1 and a probability of 0.99 for a value of 0. n It has a mean of zero and a variance of 10 -3 Gaussian white noise.

[0036] The experimental results are from Figure 4 As shown in the figure, it can be seen that the proportional population adaptive filter resistant to impulse noise interference in the implementation mode of the present application has good robustness, and has the fastest convergence speed and the lowest steady-state misalignment in sparse system identification.

[0037] The above embodiments are only for illustrating the technical concept and features of the present invention, and their purpose is to enable people familiar with the technology to understand the content of the present invention and implement it accordingly, and they cannot be used to limit the protection scope of the present invention. Any equivalent transformation or modification made according to the spirit of the present invention should be included in the protection scope of the present invention.

Claims

1. A proportional population adaptive filter for immunity to impulse noise interference, characterized in that: The adaptive filter updates its weight vector by using proportional update and maximizing the overall correlation entropy cost function. The adaptive filter updates the weight vector including the following steps: 1) Construct the input signal vector, that is, the noisy input signal sampling values ​​at time n and the previous M-1 consecutive moments The noisy input signal vector that constitutes the adaptive filter Where: superscript T represents transposition operation; 2) Construct weight vector w n , that is, the M weights of the adaptive filter at time n constitute the weight vector w n =[w n,0 ,w n,1 ,...,w n,M-1 ] T ; 3) The noisy input signal vector and the weight vector w of the adaptive filter n Perform inner product to generate the output signal of the adaptive filter 4) According to Calculate the error signal e n ,in: represents the noisy expected response of the adaptive filter; and then includes: calculating the intermediate variable p(w n,i )=min(γ|w n,i |,1), where: i is a positive integer greater than or equal to 0 and less than M, γ is a positive constant used to control the strength of the estimated sparse system; the vector p(w n )=[p(w n,0 ),p(w n,1 ),...,p(w n,M-1 )] T ;according to Calculate the proportional coefficient, where: α is the proportional coefficient control parameter, the value range is -1≤α<1, ε is a small positive number to avoid the denominator being zero, || ||1 represents the l1 norm of the vector; construct the proportional matrix G from the proportional coefficient n =diag(g n,0 ,g n,1 ,...,g n,M-1 ), where diag represents the element g n,0 ,g n,1 ,...,g n,M-1 As diagonal elements form a diagonal matrix, 5) According to in: is the augmented weight vector of the adaptive filter, σ is the kernel width parameter with positive correlation entropy, The adaptive filter adopts the expression Update the weight vector w n , Where: μ is the step size; Represents the vector f n The matrix G n Weighted l2 norm, δ is a small positive constant to avoid zero denominator.

2. The adaptive filter according to claim 1, characterized in that: In step 5): in: is the variance of the measurement noise in the desired signal without the impulse interference, is the variance of the noise contained in the adaptive filter input signal.

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