Deviation compensated affine projection adaptive filter based on a logical distance criterion

Abstract

The application relates to the technical field of adaptive filtering, and discloses a deviation compensation affine projection adaptive filter based on a logical distance criterion, wherein a desired signal vector, a noisy input signal vector and a matrix, and an adaptive weight vector are respectively constructed according to a desired signal sample value, a noisy input signal sample value and an adaptive weight value; an anti-impulse error square median is obtained according to an estimated error signal, an error signal variance estimation value is calculated, and an input noise variance estimation value is calculated in combination with a noisy input signal vector and an adaptive weight vector variance power estimation value; a derivative and a second derivative of a logical distance function are calculated according to an estimated error signal vector; a deviation compensation matrix is calculated by using the second derivative of the logical distance function, an intermediate matrix, a vector formed by a diagonal line of the intermediate matrix, a deviation compensation vector and the input noise variance estimation value, the adaptive weight value is updated, and adaptive filtering of a system output signal to be estimated is realized.

Description

Technical Field

[0001] This invention relates to the field of adaptive filtering technology, and in particular to a bias-compensated affine projection adaptive filter based on a logical distance criterion. Background Technology

[0002] In the field of adaptive filters, the goal of system identification is to estimate the transmission characteristics such as frequency response and time delay spread of an unknown system to be estimated using an adaptive filter. Then, by adjusting the coefficients of the adaptive filter itself, the distortion of the channel is compensated so that the output signal of the system to be estimated can better recover the characteristics of the original input signal.

[0003] System identification is an important branch of adaptive signal processing. Many problems, such as traditional adaptive channel equalization, adaptive noise cancellation, adaptive echo cancellation, and active noise control, can be reduced to system identification problems. Traditional Least Mean Square (LMS) and Normalized Least Mean Square (NLMS) adaptive filters are easy to implement, but their performance degrades sharply in certain environments. For example, when the input signal is a highly correlated colored signal, the convergence speed of LMS and NLMS adaptive filters drops significantly. To overcome this drawback, Affine Projection (APA) adaptive filters have been proposed. They achieve decorrelation of the input signal by repeatedly using multiple past input signals, thereby improving the convergence speed of the filter under colored signals. However, in some cases, the output signal of an unknown system may be contaminated by impulse noise, which severely affects the stability of the APA filter. To enhance the impulse noise immunity of APA adaptive filters, a series of impulse noise-resistant APA adaptive filters have been proposed, such as the Affine Projection Symbol (APSA) adaptive filter, the Maximum Correlation Entropy Affine Projection (APLMC) adaptive filter, and the Affine Projection-like M-Estimation (MAPL) adaptive filter.

[0004] In the aforementioned application scenarios, the adaptive filters typically used are designed based on standard regression models, assuming that the obtained input signal is identical to the unknown system. However, due to sampling errors and other factors in practical applications, noise is introduced into the input signal, significantly impacting the performance of traditional adaptive filters and resulting in large errors in the system's output signal. To address this issue, a common approach is to utilize bias compensation methods for error elimination, such as bias-compensated affine projection (BC-APA) adaptive filters, bias-compensated maximum correlation entropy class affine projection (BC-APLMC) adaptive filters, bias-compensated novel affine projection symbol (BC-NAPSA) adaptive filters, bias-compensated M-estimation class affine projection (BC-MAPL) adaptive filters, and bias-compensated Versoria affine projection (BC-APV) adaptive filters. Among these methods, the BC-APA adaptive filter exhibits a sharp performance degradation in impulse noise environments. While the other methods offer some resistance to impulse noise in scenarios with highly correlated and noisy input signals, they are all APA adaptive filters that avoid the matrix inversion framework, and their impulse noise resistance performance remains insufficient. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problem that the adaptive filter in the prior art cannot solve the problem of slow convergence speed when the input signal is highly correlated and simultaneously contaminated by noise, and poor robustness in the context of impulse noise.

[0006] To address the aforementioned technical problems, this invention provides a bias-compensated affine projection adaptive filter based on a logical distance criterion, comprising:

[0007] Get Time and consecutive moments before The sampled values ​​of the noisy input signal to the system to be estimated at each time step constitute... The noisy input signal vector at time t, Indicates the number of adaptive weights;

[0008] based on Time and consecutive moments before The noisy input signal vector at each time step forms The noisy input signal matrix at time t, Indicates the projection order;

[0009] Get Time and consecutive moments before The sampled values ​​of the desired signal at each time point constitute... The expected signal vector at time t;

[0010] Obtaining the adaptive filter in Moment Each adaptive weight is composed of The adaptive weight vector at time step, and calculation The adaptive weight vector variance power estimate at time step;

[0011] make The desired signal vector at time step is obtained by subtracting the product of the adaptive weight vector and the noisy input signal matrix. The estimated error signal vector at time step is obtained, and the calculation is performed. The derivative and second derivative of the time-space logical distance function;

[0012] based on Time and consecutive moments before The estimation error signal at each time point is obtained. The median of the squared anti-pulse error at time t is then used to calculate... The variance estimate of the error signal at time t. Indicates the window length for taking the median value;

[0013] based on Calculate the noisy input signal vector, the error signal variance estimate, and the adaptive weight vector variance power estimate at time t. The estimated variance of the input noise at time t;

[0014] based on Calculate the second derivative of the noisy input signal matrix and the logical distance function at time t. The intermediate matrix at each time point, combined with... The variance estimate of the input noise at time step is used to construct... The deviation compensation matrix at time points;

[0015] based on The time-bias compensation matrix, the noisy input signal matrix, and the estimation error signal vector are used to... The derivative of the logistic distance function at time step is updated. The adaptive weight vector at time step is obtained. The adaptive weight vector at time step.

[0016] Preferably, the adaptive filter is obtained in Moment Each adaptive weight is composed of The adaptive weight vector at time step, and calculation The adaptive weight vector variance power estimate at time step includes:

[0017] Obtaining the adaptive filter in Moment Adaptive weights ,composition Adaptive weight vector at time step , is represented as: ;

[0018] based on Adaptive weight vector at time step ,calculate Adaptive weight vector variance power estimate at time step , is represented as:

[0019] ;

[0020] in, This represents the forgetting factor, which takes positive values. This indicates the transpose operation.

[0021] Preferably, let The desired signal vector at time step is obtained by subtracting the product of the adaptive weight vector and the noisy input signal matrix. The estimation error signal vector at time t includes:

[0022] based on The expected signal vector at time 1 Adaptive weight vector With noisy input signal matrix transpose Calculate the adaptive filter Estimation error signal vector at time step , is represented as: .

[0023] Preferably, calculation is obtained The derivative and second derivative of the time-space logistic distance function include:

[0024] calculate The derivative of the time-space logistic distance function , is represented as:

[0025] ;

[0026] calculate Second derivative of the time-space logistic distance function , is represented as:

[0027] ;

[0028] in, express The vector function, that is, the function of vectors Each component in the vector is processed separately and then combined into a single vector. Similarly, express The estimated error signal vector at time t. This represents the natural exponential function. This represents the kernel width, which is a positive number.

[0029] Preferably, based on Time and consecutive moments before The estimation error signal at each time point is obtained. The median of the squared anti-pulse error at time t is expressed as:

[0030] ;

[0031] in, express The median of the squared anti-pulse error at time t. This represents a threshold parameter that takes a positive value. This indicates taking the median. express The square of the estimation error signal at time 1. express The square of the estimation error signal at time 1. , This represents the median filter length, which takes positive integer values. express The variance estimate of the error signal at time t.

[0032] Preferably, obtain The median of the squared anti-pulse error at time t is then used to calculate... The variance estimate of the error signal at time t is expressed as:

[0033] ;

[0034] in, express The variance estimate of the error signal at time t. This represents the forgetting factor, which takes a positive value.

[0035] Preferably, based on Calculate the noisy input signal vector, the error signal variance estimate, and the adaptive weight vector variance power estimate at time t. The estimated variance of the input noise at time t is expressed as:

[0036] ;

[0037] in, express The estimated variance of the input noise at time t. The ratio of the variance of the output noise to the variance of the input noise is expressed as follows: , This represents the variance of measurement noise excluding impulse noise. Represents the variance of the input noise; express The variance estimate of the error signal at time t. express The adaptive weight vector variance power estimate at time step [time]. express The noisy input signal vector at time t; This represents taking the square of the L2 norm.

[0038] Preferably, based on Calculate the second derivative of the noisy input signal matrix and the logical distance function at time t. The intermediate matrix at time step is represented as:

[0039] ;

[0040] Intermediate matrix at time step The Chinese number is The vector formed by the diagonals , its first element , is represented as:

[0041] ;

[0042] in, and They represent The noisy input signal matrix at time t and its transpose; This represents a regularization factor that takes a positive value. Indicates size is The identity matrix, This indicates the inverse operation. Indicates diagonalization operation; express The second derivative of the logistic distance function at time t; This indicates the index of the vector formed by the diagonals in the middle matrix. ; hour, represent The first one above the main diagonal A vector formed by two diagonals; hour, represent The vector formed by the main diagonal; hour, represent The first one below the main diagonal A vector formed by two diagonals.

[0043] Preferably, calculation The intermediate matrix at each time point, combined with... The variance estimate of the input noise at time step is used to construct... The time-of-flight deviation compensation matrix includes:

[0044] based on Intermediate matrix at time step The Chinese number is The vector formed by the diagonals and combined Input noise variance estimate at time step ,calculate Time Deviation Compensation Vector , is represented as:

[0045] ;

[0046] The element , is represented as: ;

[0047] based on Time-of-flight deviation compensation vector ,calculate Time-of-flight deviation compensation matrix The Middle line, number Column elements , is represented as:

[0048] ;

[0049] in, express The estimated variance of the input noise at time t. The difference between rows and columns is expressed by the formula: ; Represents the deviation compensation vector The Middle Each element.

[0050] Preferably, based on The time-bias compensation matrix, the noisy input signal matrix, and the estimation error signal vector are used to... The derivative of the logistic distance function at time step is updated. The adaptive weight vector at time step is obtained. The adaptive weight vector at time step 1 is represented as:

[0051] ;

[0052] in, express The adaptive weight vector at time step, express The adaptive weight vector at time step, This represents the step size parameter that takes a positive value. and They represent The noisy input signal matrix at time t and its transpose. This represents a regularization factor that takes a positive value. Indicates size is The identity matrix; express The derivative of the logistic distance function at time t, express The deviation compensation matrix at time.

[0053] Compared with the prior art, the above-described technical solution of the present invention has the following advantages:

[0054] The bias-compensated affine projection adaptive filter based on the logical distance criterion described in this invention calculates the bias compensation matrix using the second derivative of the logical distance function, the intermediate matrix, the vector formed by the diagonal of the intermediate matrix, the bias compensation vector, and the estimated value of the input noise variance. This matrix is ​​then used to update the adaptive weights, thereby achieving adaptive filtering of the output signal of the system to be estimated. Meanwhile, this invention calculates the variance estimate by integrating error signals from multiple time points, which avoids over-adjustment of the weight vector due to abnormal errors at a single time point, thus improving compensation accuracy. Furthermore, by comprehensively considering adaptive weights and error signal variance estimates to estimate noise variance, it can more accurately grasp the noise situation in the system. In subsequent weight updates and signal processing, it can better compensate for or suppress noise, improving filtering accuracy. Additionally, in scenarios with noise at the input, this invention introduces a deviation compensation matrix based on the logical distance criterion to compensate for potential model biases in the system. In scenarios where the input signal is a highly correlated colored signal, it constructs an input signal matrix by adding multiple input signal vectors, thereby decorrelating the highly correlated colored input signal. This makes the adaptive filtering process more robust, resulting in faster convergence and better filtering performance. This invention enables the desired signal to achieve stronger robustness in scenarios containing impulse noise and effectively reduces the adverse effects of input noise. Attached Figure Description

[0055] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein:

[0056] Figure 1 This is a flowchart of the steps of the bias-compensated affine projection adaptive filter based on the logical distance criterion of the present invention;

[0057] Figure 2 This is a block diagram of an adaptive filter with input noise;

[0058] Figure 3 This is a comparison of the normalized mean square deviation curves of different adaptive filters in the system identification scenario. Detailed Implementation

[0059] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.

[0060] Reference Figure 1 The flowchart of the deviation-compensated affine projection adaptive filter based on the logical distance criterion of the present invention is shown below, with specific steps as shown in S101 to S109.

[0061] S101: Obtain Time and consecutive moments before The sampled value of the noisy input signal to the system to be estimated at each time step. ,composition Noisy input signal vector at time 1 , is represented as: ,in, This indicates the number of adaptive weights.

[0062] S102: Based on Time and consecutive moments before The noisy input signal vector at each time step ,composition Noisy input signal matrix at time 1 , is represented as: ;in, Indicates the projection order.

[0063] S103: Acquisition Time and consecutive moments before The sampled value of the desired signal at each time step ,composition The expected signal vector at time 1 , is represented as: .

[0064] S104: Obtain the adaptive filter in Moment Each adaptive weight is composed of The adaptive weight vector at time step, and calculation The adaptive weight vector variance power estimate at time step includes:

[0065] S104-1: Obtaining the adaptive filter in Moment Adaptive weights ,composition Adaptive weight vector at time step , is represented as: ;

[0066] S104-2: Based on Adaptive weight vector at time step ,calculate Adaptive weight vector variance power estimate at time step , is represented as:

[0067] ;

[0068] in, This represents the forgetting factor, which takes positive values. This indicates the transpose operation.

[0069] S105: Order The desired signal vector at time step is obtained by subtracting the product of the adaptive weight vector and the noisy input signal matrix. The estimated error signal vector at time step is obtained, and the calculation is performed. The derivative and second derivative of the time-space logistic distance function include:

[0070] S105-1: Based on Expected signal at time Adaptive weight vector With noisy input signal vector Calculate the adaptive filter Time estimation error signal , represented as: ;

[0071] S105-2: Based on The expected signal vector at time 1 Adaptive weight vector With noisy input signal matrix Calculate the adaptive filter Estimation error signal vector at time step , is represented as: ;

[0072] S105-3: Calculation The derivative of the time-space logistic distance function , is represented as:

[0073] ;

[0074] S105-4: Calculation Second derivative of the time-space logistic distance function , is represented as:

[0075] ;

[0076] in, express The vector function, that is, the function of vectors Each component in the vector is processed separately and then combined into a single vector. Similarly, express The estimated error signal vector at time t. This represents the natural exponential function. This represents the kernel width, which is a positive number.

[0077] S106: Based on Time and consecutive moments before The estimation error signal at each time point is obtained. The median of the squared anti-pulse error at time t is then used to calculate... The variance estimate of the error signal at time t includes:

[0078] S106-1: Based on Time and consecutive moments before The estimation error signal at each time point is obtained. Median of squared anti-pulse error at time 1 , is represented as:

[0079] ;

[0080] in, This represents a threshold parameter that takes a positive value. This indicates taking the median. express The square of the estimation error signal at time 1. express The square of the estimation error signal at time 1. , This represents the window length for taking the median, i.e., the median filter length with positive integer values; express The variance estimate of the error signal at time t;

[0081] S106-2: Calculation Error signal variance estimate at time 1 , is represented as:

[0082] ;

[0083] in, This represents the forgetting factor, which takes a positive value.

[0084] This invention calculates the variance estimate by integrating error signals from multiple time points, which can avoid over-adjustment of the weight vector due to abnormal errors at a single time point and improve compensation accuracy.

[0085] S107: Based on Noisy input signal vector at time 1 Error signal variance estimate With adaptive weight vector variance power estimate ,calculate Input noise variance estimate at time step , is represented as:

[0086] ;

[0087] in, The ratio of the variance of the output noise to the variance of the input noise is expressed as follows: , This represents the variance of measurement noise excluding impulse noise. Represents the variance of the input noise; This represents taking the square of the L2 norm.

[0088] This invention comprehensively considers adaptive weights and error signal variance estimates to estimate noise variance, which can more accurately grasp the noise situation in the system. In subsequent weight updates and signal processing, noise can be better compensated or suppressed, thus improving filtering accuracy.

[0089] S108: Based on Calculate the second derivative of the noisy input signal matrix and the logical distance function at time t. The intermediate matrix at each time point, combined with... The variance estimate of the input noise at time step is used to construct... The time-time deviation compensation matrix includes steps S108-1 to S108-3.

[0090] S108-1: Based on Noisy input signal matrix at time 1 The second derivative of the logical distance function ,calculate Intermediate matrix at time step , is represented as:

[0091] ;

[0092] in, and They represent The noisy input signal matrix at time t and its transpose; This represents a regularization factor that takes a positive value. Indicates size is The identity matrix, This indicates the inverse operation. This indicates the diagonalization operation.

[0093] Specifically, based on Intermediate matrix at time step ,calculate Intermediate matrix at time step The Chinese number is The vector formed by the diagonals , its first element , is represented as:

[0094] ;

[0095] in, This indicates the index of the vector formed by the diagonals in the middle matrix. ; hour, represent The first one above the main diagonal A vector formed by two diagonals; hour, represent The vector formed by the main diagonal; hour, represent The first one below the main diagonal A vector formed by two diagonals.

[0096] S108-2: Based on Intermediate matrix at time step The Chinese number is The vector formed by the diagonals and combined Input noise variance estimate at time step ,calculate Time Deviation Compensation Vector , is represented as:

[0097] ;

[0098] The element , is represented as: .

[0099] S108-3: Based on Time-of-flight deviation compensation vector ,calculate Time-of-flight deviation compensation matrix The Middle line, number Column elements , is represented as:

[0100] ;

[0101] in, The difference between rows and columns is expressed by the formula: ; Represents the deviation compensation vector The Middle Each element.

[0102] This invention addresses potential model biases in scenarios with noise at the input by introducing a bias compensation matrix based on a logical distance criterion. Furthermore, in scenarios where the input signal is a highly correlated colored signal, it constructs an input signal matrix by adding multiple input signal vectors, thereby decorrelating the highly correlated colored input signal. This makes the adaptive filtering process more robust, resulting in faster convergence and better filtering performance. This invention also enables the desired signal to achieve stronger robustness in scenarios containing impulse noise and effectively reduces the adverse effects of input noise.

[0103] S109: Based on Time-of-flight deviation compensation matrix Noisy input signal matrix With estimation error signal vector ,use The derivative of the time-space logistic distance function ,renew Adaptive weight vector at time step , obtain Adaptive weight vector at time step , is represented as:

[0104] ;

[0105] in, This represents the step size parameter, which takes a positive value.

[0106] The bias-compensated affine projection adaptive filter based on the logical distance criterion described in this invention calculates the bias compensation matrix using the second derivative of the logical distance function, the intermediate matrix, the vector formed by the diagonal of the intermediate matrix, the bias compensation vector, and the estimated value of the input noise variance. This matrix is ​​then used to update the adaptive weights, thereby achieving adaptive filtering of the output signal of the system to be estimated.

[0107] To demonstrate the effectiveness of this invention, this embodiment employs computer experiments to verify the performance of the bias-compensated affine projection (BC-LDM-APA) adaptive filter based on the logical distance criterion provided by this invention. The experiment was conducted in an environment with impulse noise interference and noisy input signals to estimate unknown systems in the application scenario. The results were compared with those of the logical distance affine projection (LDM-APA) adaptive filter and the bias-compensated M-estimation class affine projection (BC-MAPL) adaptive filter.

[0108] Reference Figure 2 The diagram shown is a block diagram of an adaptive filter with input noise. In this embodiment, the noise signal is Gaussian noise plus impulse noise; the input signal is colored noise; the system's scene identification experiment uses Normalized Mean Square Deviation (NMSD) as a performance metric. The unit is dB, where, Indicates taking the logarithm. These are the weights of the actual system.

[0109] Weights of the actual system in the experiment length Set to 16. Noise signal used. Contains a zero-mean Gaussian white noise and a pulse noise ,Right now Impulse noise Produced by Bernoulli Gaussian processes, i.e. ,in It is a Bernoulli process, and the probability of it taking the value 0 is 0.9 and the probability of it taking the value 1 is 0.1. Zero-mean Gaussian white noise. Input signal For zero-mean Gaussian white noise, pass through a transfer function of The experiment involved a first-order autoregressive system generating colored noise with unit variance. The signal-to-noise ratio (SNR) between the actual system input signal and the input noise of the interference filter was 10 dB, the SNR between the actual system output signal and impulse noise was 30 dB, and the signal-to-interference ratio (SIR) was -20 dB.

[0110] Reference Figure 3 The figure shows a comparison of the normalized mean square deviation curves of different adaptive filters in the system identification scenario; the parameters of each method are LDM-APA ( , , , ), BC-MAPL( , , , , ), BC-LDM-APA( , , , , , , ).Depend on Figure 3 As can be seen, in the system identification scenario, the BC-LDM-APA adaptive filter of this application has good anti-impulse performance, and has the lowest steady-state imbalance in the scenario where the input signal is correlated colored noise and noise exists at the same time.

[0111] The bias-compensated affine projection adaptive filter based on the logical distance criterion described in this invention calculates the bias compensation matrix using the second derivative of the logical distance function, the intermediate matrix, the vector formed by the diagonal of the intermediate matrix, the bias compensation vector, and the estimated value of the input noise variance. This matrix is ​​then used to update the adaptive weights, thereby achieving adaptive filtering of the output signal of the system to be estimated. This invention calculates the variance estimate by integrating error signals from multiple time points, avoiding over-adjustment of the weight vector due to abnormal errors at a single time point and improving compensation accuracy. Furthermore, by comprehensively considering adaptive weights and error signal variance estimates to estimate noise variance, it can more accurately grasp the noise situation in the system. In subsequent weight updates and signal processing, it can better compensate for or suppress noise, improving filtering accuracy. Simultaneously, in scenarios with noise at the input, this invention introduces a deviation compensation matrix based on the logical distance criterion to compensate for potential model biases in the system. In scenarios where the input signal is a highly correlated colored signal, it constructs an input signal matrix by adding multiple input signal vectors, thereby decorrelating the highly correlated colored input signal. This makes the adaptive filtering process more robust, resulting in faster convergence and better filtering performance. This invention enables the desired signal to achieve stronger robustness in scenarios containing impulse noise and effectively reduces the adverse effects of input noise.

[0112] Those skilled in the art will understand that embodiments of this application can be provided as methods, systems, or computer program products. Therefore, this application can take the form of a completely hardware embodiment, a completely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, this application can take the form of a computer program product embodied on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program code.

[0113] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.

[0114] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.

[0115] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.

[0116] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.

Claims

1. A bias-compensated affine projection adaptive filter based on logical distance criterion, characterized in that, include: Get Time and consecutive moments before The sampled values ​​of the noisy input signal to the system to be estimated at each time step constitute... The noisy input signal vector at time t, Indicates the number of adaptive weights; based on Time and consecutive moments before The noisy input signal vector at each time step forms The noisy input signal matrix at time t, Indicates the projection order; Get Time and consecutive moments before The sampled values ​​of the desired signal at each time point constitute... The expected signal vector at time t; Obtaining the adaptive filter in Moment Each adaptive weight is composed of The adaptive weight vector at time step, and calculation The adaptive weight vector variance power estimate at time step; make The desired signal vector at time step is obtained by subtracting the product of the adaptive weight vector and the noisy input signal matrix. The estimated error signal vector at time step is obtained, and the calculation is performed. The derivative and second derivative of the time-space logistic distance function include: calculate The derivative of the time-space logistic distance function , is represented as: ； calculate Second derivative of the time-space logistic distance function , is represented as: ； in, express The vector function, that is, the function of vectors Each component in the vector is processed separately and then combined into a single vector. Similarly, express The estimated error signal vector at time step, This represents the natural exponential function. This indicates the kernel width, which takes a positive value. based on Time and consecutive moments before The estimation error signal at each time point is obtained. The median of the squared anti-pulse error at time t is then used to calculate... The variance estimate of the error signal at time t. Indicates the window length for taking the median value; based on Calculate the noisy input signal vector, the error signal variance estimate, and the adaptive weight vector variance power estimate at time t. The estimated variance of the input noise at time t; based on Calculate the second derivative of the noisy input signal matrix and the logical distance function at time t. The intermediate matrix at each time point, combined with... The variance estimate of the input noise at time step is used to construct... The time-of-flight deviation compensation matrix includes: The intermediate matrix at time step is represented as: ; Intermediate matrix at time step The Chinese number is The vector formed by the diagonals , its first element , is represented as: ;in, and They represent The noisy input signal matrix at time t and its transpose; This represents a regularization factor that takes a positive value. Indicates size is The identity matrix, This indicates the inverse operation. Indicates diagonalization operation; express The second derivative of the logistic distance function at time t; This indicates the index of the vector formed by the diagonals in the middle matrix. ; hour, represent The first one above the main diagonal A vector formed by two diagonals; hour, represent The vector formed by the main diagonal; hour, represent The first one below the main diagonal A vector formed by two diagonals; Build The time-bias compensation matrix includes: based on Intermediate matrix at time step The Chinese number is The vector formed by the diagonals and combined Input noise variance estimate at time step ,calculate Time Deviation Compensation Vector , is represented as: ; The element , is represented as: ;based on Time-of-flight deviation compensation vector ,calculate Time-of-flight deviation compensation matrix The Middle line, number Column elements , is represented as: ;in, express The estimated variance of the input noise at time t. The difference between rows and columns is expressed by the formula: ; Represents the deviation compensation vector The Middle One element; based on The time-bias compensation matrix, the noisy input signal matrix, and the estimation error signal vector are used to... The derivative of the logistic distance function at time step is updated. The adaptive weight vector at time step is obtained. The adaptive weight vector at time step.

2. The bias-compensated affine projection adaptive filter based on the logical distance criterion according to claim 1, characterized in that, Obtaining the adaptive filter in Moment Each adaptive weight is composed of The adaptive weight vector at time step, and calculation The adaptive weight vector variance power estimate at time step [time]. include: Obtaining the adaptive filter in Moment Adaptive weights ,composition Adaptive weight vector at time step , is represented as: ; based on Adaptive weight vector at time step ,calculate Adaptive weight vector variance power estimate at time step , is represented as: ； in, This represents the forgetting factor, which takes a positive value. This indicates the transpose operation.

3. The bias-compensated affine projection adaptive filter based on the logical distance criterion according to claim 1, characterized in that, make The desired signal vector at time step is obtained by subtracting the product of the adaptive weight vector and the noisy input signal matrix. The estimation error signal vector at time t, including: based on Expected signal vector at time 1 Adaptive weight vector With noisy input signal matrix transpose Calculate the adaptive filter Estimation error signal vector at time step , is represented as: .

4. The bias-compensated affine projection adaptive filter based on the logical distance criterion according to claim 1, characterized in that, based on Time and consecutive moments before The estimation error signal at each time point is obtained. The median of the squared anti-pulse error at time t is expressed as: ； in, express The median of the squared anti-pulse error at time t. This represents a threshold parameter that takes a positive value. This indicates taking the median. express The square of the estimation error signal at time 1. express The square of the estimation error signal at time 1. , This represents the median filter length, which takes positive integer values. express The variance estimate of the error signal at time t.

5. The bias-compensated affine projection adaptive filter based on the logical distance criterion according to claim 4, characterized in that, Get The median of the squared anti-pulse error at time t is then used to calculate... The variance estimate of the error signal at time t is expressed as: ； in, express The variance estimate of the error signal at time t. This represents the forgetting factor, which takes a positive value.

6. The bias-compensated affine projection adaptive filter based on the logical distance criterion according to claim 1, characterized in that, based on Calculate the noisy input signal vector, the error signal variance estimate, and the adaptive weight vector variance power estimate at time t. The estimated variance of the input noise at time t is expressed as: ； in, express The estimated variance of the input noise at time t. The ratio of the variance of the output noise to the variance of the input noise is expressed as follows: , This represents the variance of measurement noise excluding impulse noise. Represents the variance of the input noise; express The variance estimate of the error signal at time t. express The adaptive weight vector variance power estimate at time step [time]. express The noisy input signal vector at time t; This represents taking the square of the L2 norm.

7. The bias-compensated affine projection adaptive filter based on the logical distance criterion according to claim 1, characterized in that, based on The time-bias compensation matrix, the noisy input signal matrix, and the estimation error signal vector are used to... The derivative of the logistic distance function at time step is updated. The adaptive weight vector at time step is obtained. The adaptive weight vector at time step 1 is represented as: ； in, express The adaptive weight vector at time step, express The adaptive weight vector at time step, This represents the step size parameter that takes a positive value. and They represent The noisy input signal matrix at time t and its transpose. This represents a regularization factor that takes a positive value. Indicates size is The identity matrix; express The derivative of the logistic distance function at time t, express The deviation compensation matrix at time.

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