Constrained total least log-cosh adaptive filter

Abstract

The application discloses a constrained total least log hyperbolic cosine adaptive filter and belongs to the field of digital filter design. The adaptive filter is established by linear constraint conditions and a log hyperbolic cosine function, and a total least square method is introduced. The linear constraint makes the adaptive filter better meet the actual environment, the log hyperbolic cosine function is minimized to improve the robustness and convergence speed of the algorithm, and the total least square method is used to effectively solve the performance decline problem of the algorithm when the input signal is polluted by noise. The constrained total least log hyperbolic cosine adaptive filter can be applied to electronic and communication systems in which the input and output signals are interfered by noise.

Description

Technical Field

[0001] This invention discloses an adaptive filter, specifically a constrained total minimum logarithmic hyperbolic cosine adaptive filter, belonging to the field of digital filter design. Background Technology

[0002] Constrained adaptive algorithms are widely used in system identification, beamforming, and blind interference suppression. Linear constraints typically arise from prior knowledge of certain parameters or properties of the problem under consideration, such as the direction of arrival (DOA) information of user signals in beamforming applications. The Constrained Least Mean Square (CLMS) algorithm was the first linearly constrained adaptive algorithm, originating from an adaptive solution to the linearly constrained minimum variance (LCMV) problem in beamforming. This algorithm boasts excellent performance and ease of implementation, but its convergence speed is slow, especially under highly correlated input conditions. To address this issue, the Constrained Recursive Least Squares (CRLS) algorithm and the Constrained Affine Projection (CAP) algorithm were subsequently proposed. However, these algorithms perform poorly or even fail to function properly when the environment contains impulse noise. To address the problem caused by impulse noise, Siyuan Peng et al. proposed a constrained maximum correlation entropy adaptive filtering algorithm [Peng S, Chen B, Sun L, et al. Constrained maximum correntropy adaptive filtering[J]. Signal Processing, 2017, 140: 116-126]. However, this algorithm performs poorly when the input signal is noisy.

[0003] In some cases, the input signal of a system may be affected by noise such as sampling errors or environmental interference, resulting in a large steady-state MSE. This problem can be described by the error-in-variable (EIV) model, and two important methods under the EIV model are bias compensation and total least squares (TLS). However, TLS is not robust to impulse noise. Therefore, based on the maximum correlation entropy criterion, researchers have proposed the maximum total correlation entropy (MTC) algorithm. Later, Qian et al. proposed a constrained maximum total correlation entropy algorithm [Qian G, He F, Wang S, et al. Robust constrained maximum total correntropy algorithm[J]. Signal Processing, 2021, 181: 107903] to solve the robust constrained adaptive filtering problem. However, under heavy-tailed impulse noise, the performance of this algorithm is still unsatisfactory. Summary of the Invention

[0004] To address the aforementioned issues, this invention proposes a constrained total minimum logarithmic hyperbolic cosine adaptive filter (CLTL).

[0005] This filter employs a linear constraint strategy and a log-hyperbolic cosine cost function to update its coefficient vector, while also combining the overall least squares method to improve its ability to combat impulse noise. This effectively solves the problem of performance degradation caused by noise contamination of the input and output signals.

[0006] To achieve the above-mentioned solution, the present invention aims to propose a CLTL filter, which is used to better simulate the characteristics of a linearly constrained system in an environment where both the input and output signals are contaminated by noise, thereby achieving more effective system identification.

[0007] The CLTL filter update coefficient vector includes the following steps:

[0008] 1) Input signal at time n and expected signal Calculate the error signal e n ,Right now in For the noise u n Input signals of pollution, For the noise v n The expected signal of pollution, x n =[x n ,x n-1 ,...x n-M+1 ] T The first M samples {x} of the input signal n ,x n-1 ,...x n-M+1 The input vector formed by}, w n =[w 0,n ,w 2,n ,...w M-1,n ] T Let T be the coefficient vector consisting of the M tap coefficients of the adaptive filter, and let T denote the transpose operation.

[0009] 2) From the coefficient vector w n The modified augmented weight vector can be calculated. in For output noise v n and input noise u n The variance ratio between sequences.

[0010] 3) From the input vector Error signal e n The adjustment parameter λ and augmented weight vector of the lncosh function According to the calculation formula Update intermediate variable g LTL (w n );

[0011] 4) Calculate the intermediate variable P = I L -C(C T C) -1 C T , q=C(C T C) -1 f, where C is an M×K dimensional linear constraint matrix and f is a K×1 dimensional linear constraint vector.

[0012] 5) Use the calculation formula w n+1 =P(w n -μg LTL (w n The coefficient vector of the adaptive filter is updated by ))+q, where μ is the step size.

[0013] Beneficial effects

[0014] Compared to existing solutions, the CLTL filter and algorithm proposed in this application possess both strong robustness and the ability to effectively simulate the characteristics of linearly constrained systems. Furthermore, experimental results demonstrate that the adaptive filter proposed in this invention can address the performance degradation of constrained adaptive filters when input and output signals are corrupted by noise, while simultaneously improving its resistance to impulse interference. Attached Figure Description

[0015] The present invention will be further described below with reference to the accompanying drawings and embodiments:

[0016] Figure 1 This is a schematic diagram of the constrained total minimum logarithm hyperbolic cosine adaptive filter structure according to an embodiment of the present invention;

[0017] Figure 2 This section compares the normalized mean square error of the adaptive filter in this embodiment of the invention under the condition of white signal input.

[0018] Figure 3 This section compares the normalized mean square error of the adaptive filter in this embodiment of the invention under the condition of colored signal input. Detailed Implementation

[0019] This application proposes a constraint total minimum logarithmic hyperbolic cosine adaptive filter (CLTL) to better simulate the characteristics of linear constraint systems in environments where both input and output signals are contaminated by noise, thereby achieving more effective system identification.

[0020] Example

[0021] The working process of the CLTL filter proposed in this application is as follows:

[0022] First, by combining the minimum logarithmic hyperbolic cosine function based on the absolute error and mean square error criteria with the linear constraint conditions, the cost function J is obtained. CLTL Then, its gradient g is calculated using the method of finding partial derivatives. LTL ,

[0023] Then, the steepest descent method is used, and this gradient g is used... LTL The initial coefficient update formula is obtained.

[0024] Then the cost function J CLTL The Lagrange multiplier γ in g is calculated, and finally g is... LTL Substituting both γ and γ into the initial coefficient update formula, we finally obtain the coefficient update formula for the adaptive filter proposed in this application.

[0025] This embodiment uses a computer experiment to verify the performance of the CLTL filter. The experiment uses the CLTL filter disclosed in this invention to identify a linearly constrained unknown system under an environment where the input and output signals are corrupted by noise, and its performance is compared with that of CLMS, CLL, and CMTC adaptive filters. The CLTL adaptive filter disclosed in this application identifies the linearly constrained unknown system by comprising the following steps:

[0026] 1) Input signal at time n and expected signal Calculate the error signal e n ,Right now in For the noise u n Input signals of pollution, For the noise v n The expected signal of pollution, x n =[x n ,x n-1 ,...x n-M+1 ] T The first M samples {x} of the input signal n ,x n-1 ,...x n-M+1 The input vector formed by}, w n =[w 0,n ,w 2,n ,...w M-1,n ] T Let T be the coefficient vector consisting of the M tap coefficients of the adaptive filter, and let T denote the transpose operation.

[0027] 2) From the coefficient vector w n The modified augmented weight vector can be calculated. in For output noise v n and input noise u n The variance ratio between sequences.

[0028] 3) From the input vector Error signal e n The adjustment parameter λ and augmented weight vector of the lncosh function According to the calculation formula Calculate the intermediate variable g LTL (w n );

[0029] 4) Use the calculation formula w n+1 =P(w n -μg LTL (w n The adaptive filter coefficient vector is updated with q, where μ is the step size and P = I. L -C(C T C) -1 C T , q=C(C T C) -1 f, C, and f' are linear constraint matrices and vectors.

[0030] To make the experimental results more general, this paper selected two inputs, white signal and colored signal, for the experiments. The variances of both white signal and colored signal are 0. The colored input signal is generated by a first-order autoregressive (AR) model, and the model's transfer function is F(z) = 1 / (1-0.8z). -1 In the experiment, the normalized mean squared error (NMSD) was used as a measure of algorithm performance, i.e.: NMSD = 10log(w n -w 2 / ||w o || 2 ), in dB, where log represents taking the logarithm, w o The optimal weight vector is defined as follows. Furthermore, the NMSD curves obtained from the simulation in the figure are all obtained by averaging 1000 independent Monte Carlo experiments.

[0031] In the experiment, Gaussian-Bernoulli noise was used to simulate non-Gaussian heavy-tailed noise, which is composed of (1-φ n A n +φ n B n Composition, where A n and B n The variances are respectively and A Gaussian noise process. φ n It is a Bernoulli process, and P[φ] n=1]=0.02,P[φ n =0]=0.98.

[0032] Depend on Figure 2 and Figure 3 It can be seen that the CLTL filter of this application has good anti-pulse performance under both signal input conditions. It still performs well when the input signal has noise, and has the fastest convergence speed.

[0033] The experimental results show that the CLTL adaptive filter disclosed in this invention has a faster convergence speed and stronger anti-pulse interference performance. At the same time, the algorithm can still maintain good performance when both the input signal and the output signal are destroyed by noise.

[0034] The above embodiments are only for illustrating the technical concept and features of the present invention, and are intended to enable those skilled in the art to understand the content of the present invention and implement it accordingly. They should not be construed as limiting the scope of protection of the present invention. All equivalent changes or modifications made in accordance with the spirit and essence of the present invention should be covered within the scope of protection of the present invention.

Claims

1. A constrained total minimum logarithmic hyperbolic cosine adaptive filter, characterized in that, Its updated coefficient vector includes the following steps: 1) Through Input signal at time and expected signal Calculate error signal ,Right now ,in, For noise Input signals of pollution, For noise Expected signals of pollution For the input signal before Sample value The input vector formed For adaptive filters A coefficient vector consisting of tap coefficients. Indicates the transpose operation; 2) From the input vector Error signal Adjustment parameters of the lncosh function and augmented weight vector , Update intermediate variables ; 3) Use calculation formula Update the coefficient vector of the adaptive filter. in, Step size, , , It is a linear constraint matrix. It is a linear constraint vector; In step 2), according to the calculation formula Update intermediate variables ; In step 2), To augment the weight vector, , in, This represents the variance ratio.

2. The adaptive filter according to claim 1, characterized in that: , For output noise and input noise The variance ratio between sequences.

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