A robust adaptive filtering method combining newton recursion and random data multiplexing

Abstract

The application discloses a kind of robust adaptive filtering method combining Newton recursion and random data multiplexing, comprising the following steps: S1: determining adaptive filter parameter, input signal vector is collected, and the input matrix of input signal vector is determined according to adaptive filter parameter;S2: according to the input matrix of input signal vector, calculate priori error signal;S3: according to priori error signal, determine the cost function of adaptive filter, and calculate the heather matrix according to cost function;S4: according to heather matrix, the weight vector of adaptive filter is updated using Newton recursion method, and adaptive filtering is completed.The application uses random data multiplexing method to modify cost function, so that it shows more excellent performance than traditional GB-GMCC algorithm when input signal correlation is too strong.

Description

Technical Field

[0001] This invention belongs to the field of filter design technology, specifically relating to a robust adaptive filtering method that combines Newton recursion and random data multiplexing. Background Technology

[0002] Adaptive filters have been widely applied in various engineering fields, with typical applications including system identification, active noise control, acoustic echo cancellation, and channel equalization. Adaptive filtering algorithms based on the mean square error (MSE) criterion mainly include the least mean square (LMS) algorithm family, the affine projection algorithm family, and the least squares algorithm family. Among them, the LMS algorithm is widely used due to its simple structure, low computational complexity, and good convergence in smooth environments. However, the aforementioned algorithms based on the MSE criterion exhibit significant performance degradation in non-Gaussian environments, especially in environments with heavy-tailed noise distributions. Typical heavy-tailed noise distributions include Laplace noise, Cauchy noise, Gaussian mixture noise, and Alpha-stable noise.

[0003] To enhance the ability of adaptive filtering algorithms to suppress impulse noise and improve their robustness, researchers both domestically and internationally have proposed and studied a series of nonlinear optimization criteria or cost functions in terms of similarity metrics. Typical examples include: l for p∈[1,2). p - Norms, M-estimation theory, and information-theoretic learning criteria families, etc. Among the ITL criterion family, the minimization of error entropy and maximum correlation entropy criteria contain all even-order moment information of the error signal, thus they are widely used in robust signal processing and machine learning. Generally, the MCC criterion has higher computational efficiency compared to the MEE criterion. Although correlation entropy can provide a generalized similarity measure between two random variables, the Gaussian kernel function used in the MCC criterion may not always be the optimal choice. Therefore, as an extension of the MCC criterion, the correlation entropy criterion based on the generalized Gaussian density function, often called the generalized maximum correlation entropy criterion, has been proposed and widely applied in the field of robust adaptive filtering. Similar to the LMS algorithm family, as the correlation of the input signal gradually increases, the generalized maximum correlation entropy criterion algorithm based on the gradient method exhibits a significant convergence performance degradation problem. Furthermore, the gradient method can only provide the first-order derivative information of the correlation, leading to certain deficiencies in the filtering performance of correlation algorithms. Summary of the Invention

[0004] To address the above problems, this invention proposes a robust adaptive filtering method that combines Newtonian recursion and random data reuse.

[0005] The technical solution of this invention is: a robust adaptive filtering method combining Newtonian recursion and random data multiplexing, comprising the following steps:

[0006] S1: Determine the adaptive filter parameters, acquire the input signal vector, and determine the input matrix of the input signal vector based on the adaptive filter parameters;

[0007] S2: Calculate the prior error signal based on the input matrix of the input signal vector;

[0008] S3: Determine the cost function of the adaptive filter based on the prior error signal, and calculate the Hesser matrix based on the cost function;

[0009] S4: Based on the Heather matrix, update the weight vector of the adaptive filter using Newton's recursive method to complete the adaptive filtering.

[0010] Furthermore, in step S1, the adaptive filter parameters include the adaptive filter tap length L, the data multiplexing order M, the buffer window length C, the smoothing factor ε of Newton's recursion method, the step size η, the kernel parameter τ, and the shape parameter s.

[0011] Further, in step S1, the specific method for determining the input matrix of the input signal vector is as follows: if the number of input signal vectors n is less than the data multiplexing order M, then the input signal vector and the zero vector are used as elements of the input matrix, and its expression is U. r1 (n)=[u(n),u(n-1),...,u(1),0,...,0] L×M Where L represents the tap length of the adaptive filter, and u(·) represents each input signal vector;

[0012] If the number of input signal vectors n is greater than the data multiplexing order M and less than the buffer window length C, then M vectors are randomly selected from the input signal vectors as elements of the input matrix to obtain the input matrix.

[0013] If the number of input signal vectors n is greater than the buffer window length C, then M vectors are randomly selected from the C vectors closest to the input signal vectors as elements of the input matrix, and the expression is as follows: in, This represents the i-th value randomly selected from the interval [n-C+1,n], where i∈[1,M].

[0014] Further, step S2 includes the following sub-steps:

[0015] S21: Calculate the expected output vector of the input matrix;

[0016] S22: Calculate the prior error signal based on the expected output vector of the input matrix.

[0017] Furthermore, in step S21, the expected output vector d of the input matrix... r The formula for calculating (n) is:

[0018]

[0019] in, d(·) represents the i-th value randomly selected in the interval [n-C+1,n], where i∈[1,M], d(·) represents the expected output signal containing additive noise, C represents the buffer window length, and n represents the number of input signal vectors;

[0020] In step S22, the prior error signal e r The formula for calculating (n) is:

[0021] e r (n)=[d r (n)-U r (n) T w(n)]

[0022] Among them, U r w(n) represents the input matrix of the input signal vector, and w(n) represents the weight vector of the previous time step.

[0023] Furthermore, step S3 includes the following sub-steps:

[0024] S31: Calculate the cost function of the adaptive filter based on the prior error signal;

[0025] S32: Calculate the first derivative of the cost function based on the cost function of the adaptive filter;

[0026] S33: Calculate the Hesser matrix based on the first derivative of the cost function.

[0027] Furthermore, in step S31, the cost function J(w) of the adaptive filter is calculated using the following formula:

[0028]

[0029] in, Indicate l s -norm to the power of s, e r (n) represents the prior error signal, τ represents the kernel parameter, and s represents the shape parameter;

[0030] In step S32, the formula for calculating the first derivative g(w) of the cost function is:

[0031]

[0032] Among them, U r (n) represents the input matrix of the input signal vector. Indicates the error factor;

[0033] In step S33, the formula for calculating the Heather matrix H(w) is:

[0034]

[0035] in, express The covariance matrix, This represents the covariance matrix of the input matrix.

[0036] Furthermore, in step S4, the formula for calculating the updated adaptive filter weight vector is:

[0037]

[0038] Where w(n+1) represents the weight vector at the current time step, w(n) represents the weight vector at the previous time step, τ represents the kernel parameter, η represents the step size, ε represents the smoothing factor of Newton's recursion method, and U r (n) represents the input matrix of the input signal vector, and I represents the identity matrix. Represents the covariance matrix of the input matrix. This represents the error factor.

[0039] The beneficial effects of this invention are:

[0040] (1) This invention uses a random data multiplexing method to adjust the cost function, making it perform better than the traditional GB-GMCC algorithm when the input signal is too correlated.

[0041] (2) This invention uses Newton’s recursive method to update the weight equation, so that it can not only use the first derivative information based on the gradient of the traditional GMCC algorithm, but also obtain the second derivative information, and overcome the drawback that the stationary points corresponding to the gradient ascent method are not all maxima. Attached Figure Description

[0042] Figure 1 The flowchart is for a robust adaptive filtering method;

[0043] Figure 2 This is a comparison chart of the filtering performance of this invention with other algorithms in the same environment during system identification;

[0044] Figure 3 This is a comparison chart of the echo cancellation performance of the present invention under no-pulse noise conditions;

[0045] Figure 4 This is a comparison chart of the echo cancellation performance of the present invention under impulse noise. Detailed Implementation

[0046] The embodiments of the present invention will be further described below with reference to the accompanying drawings.

[0047] like Figure 1 As shown, this invention provides a robust adaptive filtering method combining Newtonian recursion and random data multiplexing, comprising the following steps:

[0048] S1: Determine the adaptive filter parameters, acquire the input signal vector, and determine the input matrix of the input signal vector based on the adaptive filter parameters;

[0049] S2: Calculate the prior error signal based on the input matrix of the input signal vector;

[0050] S3: Determine the cost function of the adaptive filter based on the prior error signal, and calculate the Hesser matrix based on the cost function;

[0051] S4: Based on the Heather matrix, update the weight vector of the adaptive filter using Newton's recursive method to complete the adaptive filtering.

[0052] In this embodiment of the invention, in step S1, the adaptive filter parameters include the adaptive filter tap length L, the data multiplexing order M, the buffer window length C, the smoothing factor ε of Newton's recursion method, the step size η, the kernel parameter τ, and the shape parameter s; wherein ε, η, τ, and s are all greater than 0, and the weight vector w(0) = 0 is initialized.

[0053] In this embodiment of the invention, the specific method for determining the input matrix of the input signal vector in step S1 is as follows: if the number of input signal vectors n is less than the data multiplexing order M, then the input signal vector and the zero vector are used as elements of the input matrix, and its expression is U. r1 (n)=[u(n),u(n-1),...,u(1),0,...,0] L×M Where L represents the tap length of the adaptive filter, and u(·) represents each input signal vector; all input signal vectors are used as elements of the input matrix, and any insufficient elements are padded with zero vectors.

[0054] If the number of input signal vectors n is greater than the data multiplexing order M and less than the buffer window length C, then M vectors are randomly selected from the input signal vectors as elements of the input matrix to obtain the input matrix.

[0055] If the number of input signal vectors n is greater than the buffer window length C, then M vectors are randomly selected from the C vectors closest to the input signal vectors as elements of the input matrix, and the expression is as follows: in, Let represent the i-th value randomly selected from the interval [n-C+1,n], where i∈[1,M], and satisfying .

[0056] In this embodiment of the invention, step S2 includes the following sub-steps:

[0057] S21: Calculate the expected output vector of the input matrix;

[0058] S22: Calculate the prior error signal based on the expected output vector of the input matrix.

[0059] In this embodiment of the invention, in step S21, the input vector u(n) at each time step has a corresponding desired output signal d(n) containing additive noise that can be acquired. Therefore, through the randomly multiplexed input matrix U r (n) also has its corresponding expected output vector, the expected output vector d of the input matrix. r The formula for calculating (n) is:

[0060]

[0061] in, d(·) represents the i-th value randomly selected in the interval [n-C+1,n], where i∈[1,M], d(·) represents the expected output signal containing additive noise, C represents the buffer window length, and n represents the number of input signal vectors;

[0062] In step S22, the prior error signal e r The formula for calculating (n) is:

[0063] e r (n)=[d r (n)-U r (n) T w(n)]

[0064] Among them, U r w(n) represents the input matrix of the input signal vector, and w(n) represents the weight vector at the previous time step. If it is the first update step, then w(n) = w(0).

[0065] In this embodiment of the invention, step S3 includes the following sub-steps:

[0066] S31: Calculate the cost function of the adaptive filter based on the prior error signal;

[0067] S32: Calculate the first derivative of the cost function based on the cost function of the adaptive filter;

[0068] S33: Calculate the Hesser matrix based on the first derivative of the cost function.

[0069] In this embodiment of the invention, in step S31, the calculation formula for the cost function J(w) of the adaptive filter is as follows:

[0070]

[0071] in, Indicate l s -norm to the power of s, e r (n) represents the prior error signal, τ represents the kernel parameter, and s represents the shape parameter;

[0072] In step S32, the first derivative g(w) of the cost function can be obtained by taking the gradient of the cost function J(w) with respect to w. The formula for calculating the first derivative g(w) of the cost function is as follows:

[0073]

[0074]

[0075]

[0076]

[0077] Among them, U r (n) represents the input matrix of the input signal vector. represents the error factor, sgn(·) represents the sign function, and ⊙ represents the Hadmann product;

[0078] In step S33, the Heather matrix can be obtained by taking the gradient of g(w) with respect to w. The formula for calculating the Heather matrix H(w) is as follows:

[0079]

[0080] in, express The covariance matrix, This represents the covariance matrix of the input matrix.

[0081] In this embodiment of the invention, the formula for calculating the weight vector of the updated adaptive filter in step S4 is as follows:

[0082]

[0083] Where w(n+1) represents the weight vector at the current time step, w(n) represents the weight vector at the previous time step, τ represents the kernel parameter, η represents the step size, ε represents the smoothing factor of Newton's recursion method, and U r (n) represents the input matrix of the input signal vector, and I represents the identity matrix. Represents the covariance matrix of the input matrix. This represents the error factor.

[0084] like Figure 2As shown, 1) Compared to the GB-GMCC algorithm, the NR-RDR-GMCC (s=1.5) algorithm has a significant advantage in both convergence accuracy and convergence speed. Furthermore, compared to other algorithms, before system mutation, the NR-RDR-GMCC (s=1.5) algorithm achieved the fastest convergence speed and the best filtering accuracy; after system mutation, it maintained the best filtering accuracy while achieving a similar convergence speed to the NR-DR-GMCC algorithm. 2) Throughout the experiment, the NR-RDR-GMCC (s=2.0) algorithm was inferior to other algorithms in both convergence speed and convergence accuracy, thus providing some evidence that the GMCC criterion is superior to the MCC criterion.

[0085] like Figure 3 As shown: 1) Due to interference from near-end speech, the NR-RDR-GMCC algorithm, along with other related algorithms, exhibited slight jitter after convergence. 2) In a noise-free environment, the NR-RDR-GMCC algorithm outperformed other related algorithms in both convergence speed and accuracy. Moreover, even after system mutations, this algorithm still demonstrated its advantages of fastest convergence speed and highest convergence accuracy.

[0086] like Figure 4 As shown: 1) Under impulse noise interference, although the NR-RDR-GMCC algorithm exhibits greater jitter during convergence compared to the APSA and GMCC algorithms, it achieves a significantly faster convergence speed and higher filtering accuracy than other algorithms. Related results also confirm that the NR-RDR-GMCC algorithm designed in this paper possesses good stability and adaptability.

[0087] This invention proposes a novel robust adaptive filtering method using Newton's recursion method, data reuse, and the GMCC criterion for system identification tasks under colored input and impulse noise environments. This method is called the Generalized Maximum Entropy Robust Adaptive Filtering Method Combining Newton's Recursion and Random Data Reuse. This method has four main characteristics: 1) Utilizing Newton's recursion method, the second derivative information, i.e., the Hesser matrix, can be extracted for updating and changing the weight vector, thus overcoming the limitation of the gradient method which only utilizes the first derivative information, and achieving rapid convergence; 2) Based on the data reuse method, information contained in the most recent M sets of input vectors can be obtained to counteract the influence of colored input; 3) The GMCC criterion's ability to suppress impulse noise improves the algorithm's robustness; 4) Using a random strategy, a buffer window of length C is set in the robust adaptive filtering method to store the current input vector and the previous C-1 sets of input vectors, and then M sets of input vectors are randomly selected from this window to update the iterative weight vector. By employing this random strategy, the robust adaptive filtering method can obtain more historical information through the cache window and use it to update weights, thereby improving the filtering performance of the method.

[0088] Those skilled in the art will recognize that the embodiments described herein are intended to help the reader understand the principles of the invention, and should be understood that the scope of protection of the invention is not limited to such specific statements and embodiments. Those skilled in the art can make various other specific modifications and combinations based on the technical teachings disclosed in this invention without departing from the spirit of the invention, and these modifications and combinations are still within the scope of protection of this invention.

Claims

1. A robust adaptive filtering method combining Newtonian recursion and random data reuse, characterized in that, Includes the following steps: S1: Determine the adaptive filter parameters, acquire the input signal vector, and determine the input matrix of the input signal vector based on the adaptive filter parameters; The specific method for determining the input matrix of the input signal vector is as follows: if the number of input signal vectors... n Less than the order of data reuse M Then, the input signal vector and the zero vector are used as elements of the input matrix, and its expression is: ,in, L Indicates the tap length of the adaptive filter. u (·) represents each input signal vector; If the number of input signal vectors n Greater than the order of data reuse M And less than the cache window length C Then, randomly select from the input signal vector M We take a vector as an element of the input matrix to obtain the input matrix; If the number of input signal vectors n Greater than the cache window length C Then the closest to the input signal vector C Randomly select from vectors M The vectors, as elements of the input matrix, are expressed as follows: ,in, Indicates the interval [ n-C+ 1, n The randomly selected number i A number, i ∈[1, M ]; S2: Calculate the prior error signal based on the input matrix of the input signal vector; S3: Determine the cost function of the adaptive filter based on the prior error signal, and calculate the Hesser matrix based on the cost function; including the following sub-steps: S31: Calculate the cost function of the adaptive filter based on the prior error signal; the cost function of the adaptive filter. J ( w The formula for calculating ) is: in, express l s -norm s Power of 1 e r ( n ) represents the prior error signal. τ Represents kernel parameters, s Indicates shape parameters; S32: Calculate the first derivative of the cost function based on the cost function of the adaptive filter; the first derivative of the cost function. g ( w The formula for calculating ) is: in, U r ( n ) represents the input matrix of the input signal vector. φ r ( n () indicates the error factor; S33: Calculate the Hesser matrix based on the first derivative of the cost function; Hesser matrix H ( w The formula for calculating ) is: in, express U r ( n ) φ r ( n The covariance matrix of ) Represents the covariance matrix of the input matrix; S4: Based on the Hesser matrix, update the weight vector of the adaptive filter using Newton's recursive method to complete the adaptive filtering; the formula for calculating the updated weight vector of the adaptive filter is: in, w ( n +1) represents the weight vector at the current moment. w ( n () represents the weight vector at the previous time step. τ Represents kernel parameters, η Indicates step size, ε This represents the smoothing factor of Newton's recursion method. U r ( n ) represents the input matrix of the input signal vector. I Represents the identity matrix. Represents the covariance matrix of the input matrix. φ r ( n ) represents the error factor.

2. The robust adaptive filtering method combining Newton recursion and random data multiplexing according to claim 1, characterized in that, In step S1, the adaptive filter parameters include the adaptive filter tap length. L Data reuse order M Cache window length C Smoothing factor of Newton's recursion method ε Step length η nuclear parameters τ and shape parameters s .

3. The robust adaptive filtering method combining Newton recursion and random data multiplexing according to claim 1, characterized in that, Step S2 includes the following sub-steps: S21: Calculate the expected output vector of the input matrix; S22: Calculate the prior error signal based on the expected output vector of the input matrix.

4. The robust adaptive filtering method combining Newtonian recursion and random data multiplexing according to claim 3, characterized in that, In step S21, the expected output vector of the input matrix. d r ( n The formula for calculating ) is: in, Indicates the interval [ n-C+ 1, n The randomly selected number i A number, i ∈[1, M ], d ( · () represents the desired output signal containing additive noise. C Indicates the length of the cache window. n Indicates the number of input signal vectors; In step S22, the prior error signal e r ( n The formula for calculating ) is: in, U r ( n ) represents the input matrix of the input signal vector. w ( n ) represents the weight vector at the previous time step.

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