Logistic hyperbolic tangent function-based bias compensation adaptive filtering method and system

Abstract

The present application relates to the technical field of adaptive filtering, and discloses a deviation compensation adaptive filtering method and system based on a logistic hyperbolic tangent function, wherein based on an estimated error signal, a non-impulsive interference error square median is constructed, and then a non-impulsive interference error signal variance estimation value and an adaptive weight vector power estimation value are further constructed to obtain an input noise variance estimation value; based on the input noise variance estimation value, the non-impulsive interference error signal variance estimation value and the adaptive weight vector, a deviation compensation term is constructed; based on the foregoing parameters and a hyperbolic cotangent function, a plurality of parameter values are constructed to update an adaptive weight error power estimation value at a current moment, and obtain an adaptive weight error power estimation value at n+1 moment; based on the plurality of parameter values, an optimal step length is constructed and smoothed to obtain a target step length, and an adaptive weight vector at the current moment is updated to obtain an adaptive weight vector at n+1 moment.

Description

Technical Field

[0001] This invention relates to the field of adaptive filtering technology, and in particular to a deviation compensation adaptive filtering method and system based on the logarithmic hyperbolic tangent function. Background Technology

[0002] System identification is an important branch of adaptive signal processing, widely used in various practical engineering scenarios such as echo cancellation, noise suppression, channel equalization, and active noise control. Traditional adaptive filtering algorithms, such as the Least Mean Square (LMS) algorithm and its normalized form (NLMS) algorithm, are widely used in system identification problems due to their simple structure, low computational complexity, and ease of implementation. However, these algorithms are usually designed based on the least mean square error criterion. While they achieve good performance in Gaussian noise environments, their performance deteriorates significantly when the system output is affected by impulse noise, resulting in slower convergence speeds or even large steady-state misalignments.

[0003] To address the aforementioned issues, researchers have proposed various robust adaptive filtering algorithms, such as those based on symbol error, mixture norm, and maximum correlation entropy criterion. These algorithms improve the system's ability to suppress impulse noise to some extent. However, commonly used adaptive filtering systems are designed based on standard regression models, assuming that the obtained input signal is identical to the unknown system. In practical applications, the input signal is often inevitably contaminated by noise due to factors such as sampling errors, quantization errors, or signal transmission interference. In this case, traditional adaptive algorithms produce significant estimation biases, further degrading the performance of the adaptive filter. To solve this problem, a common approach is to use bias compensation for error elimination, which significantly improves the steady-state imbalance and robustness of adaptive filtering.

[0004] Furthermore, existing bias compensation algorithms mostly employ a fixed step size mechanism, making it difficult to balance convergence speed and steady-state misalignment, thus leading to a decline in adaptive filtering performance. Therefore, designing a robust adaptive filtering method that simultaneously possesses anti-impact interference capability, bias compensation capability, and adaptive step size adjustment capability in error variable models and impulse noise environments has become a key technical problem that urgently needs to be solved. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the technical difficulties in the prior art, such as the serious steady-state estimation deviation caused by noise contamination of the input signal and the poor robustness in the impulsive noise environment, as well as the irreconcilable contradiction between the system convergence speed and steady-state imbalance in the fixed step size strategy.

[0006] To address the aforementioned technical problems, this invention provides a bias-compensated adaptive filtering method based on the logarithmic hyperbolic tangent function. Moments, including: Obtain the dot product of the adaptive weight vector of the adaptive filter and the noisy input signal vector as the output signal; calculate the difference between the noisy expected signal and the output signal to obtain the estimation error signal; Based on the estimated error signal, the median square of the error without pulse interference is constructed. Based on a preset smoothing factor, the median of the squared error without pulse interference and The variance estimates of the error signal without pulse interference at time 1 are weighted and summed to obtain the variance estimate of the error signal without pulse interference. Based on the preset smoothing factor, filter length, and adaptive weight vector and its transpose, an adaptive weight vector power estimate is constructed. The input noise variance estimate is obtained based on the ratio of the variance estimate of the pulse-free interference error signal to the power estimate of the adaptive weight vector. Based on the input noise variance estimate, the variance estimate of the error signal without impulse interference, and the adaptive weight vector, a deviation compensation term is constructed. Multiple parameter values ​​are constructed based on the noisy input signal vector, the estimation error signal, the adaptive weight vector, the variance estimate of the error signal without impulse interference, the input signal power, the adaptive weight error power estimate, the input noise variance estimate, and the hyperbolic cosecant function. Based on multiple parameter values, construct the optimal step size and smooth it to obtain the target step size; Based on multiple parameter values ​​and the target step size, the adaptive weight error power estimate at the current time is updated to obtain... The adaptive weighted error power estimate at time step; The adaptive weight vector at the current time is updated using the target step size, the estimated error signal, the noisy input signal vector, the estimated input noise variance, and the estimated variance of the error signal without impulse interference. The adaptive weight vector at time step.

[0007] Preferably, based on the estimated error signal, constructing the median square of the error without impulse interference includes: like The square of the estimation error signal at time [time] Less than the preset positive threshold parameter and Variance estimate of the error signal without pulse interference at time 1 The product of these is then used as the square of the estimated error signal as the median of the square of the error without impulse interference. Conversely, the current time and the preceding consecutive moments are considered. The median of the square of the estimation error signal at each time step , as the median of the squared error without pulse interference; Median of squared error without pulse interference , is represented as: ; in, This indicates the median filter length.

[0008] Preferably, based on a preset smoothing factor Median of squared error for no-pulse interference and Variance estimate of the error signal without pulse interference at time 1 Perform weighted summation to obtain the variance estimate of the error signal without pulse interference. , is represented as: ; Based on preset smoothing factor Filter length With adaptive weight vector and its transpose Construct adaptive weight vector power estimates , is represented as: ; Based on the variance estimate of the error signal without pulse interference With adaptive weight vector power estimate The ratio is used to obtain the input noise variance estimate. , is represented as: ; in, The ratio of the output noise to the input noise variance is expressed as: ; This represents the variance of the measurement noise excluding impulse noise. This represents the variance of the input noise.

[0009] Preferably, based on the input noise variance estimate, the impulse-free error signal variance estimate, and the adaptive weight vector, a bias compensation term is constructed, expressed as: ; in, This indicates a preset fixed step size. express The estimated variance of the input noise at time t. express The variance estimate of the error signal without pulse interference at time 1. This represents the shape adjustment parameter of the hyperbolic cosecant function. express The adaptive weight vector at time step.

[0010] Preferably, multiple parameter values ​​are constructed based on the noisy input signal vector, the estimated error signal, the adaptive weight vector, the variance estimate of the error signal without impulse interference, the input signal power, the adaptive weight error power estimate, the input noise variance estimate, and the hyperbolic cosecant function, including: The first parameter value is constructed based on the product of the square of the L2 norm of the noisy input signal vector, the square of the hyperbolic cosecant function of the square of the estimation error signal, and the square of the estimation error signal. Calculate the square of the L2 norm of the adaptive weight vector to obtain the value of the second parameter; The third parameter value is constructed based on the transpose of the adaptive weight vector, the noisy input signal vector, the square of the hyperbolic cosecant function of the square of the estimation error signal, and the product of the estimation error signal. The fourth parameter value is constructed based on the square of the hyperbolic cosecant function of the variance estimate of the pulse-free interference error signal, the product of the input signal power and the adaptive weight error power estimate; The fifth parameter value is constructed based on the input noise variance estimate and the variance estimate of the error signal without impulse interference.

[0011] Preferably, the first parameter value , is represented as: ; Second parameter value , is represented as: ; Third parameter value , is represented as: ; Fourth parameter value , is represented as: ; Fifth parameter value , is represented as: ; in, express The noisy input signal vector at time t, This represents taking the square of the L2 norm. Let represent the hyperbolic cosecant function. This represents the shape adjustment parameter of the hyperbolic cosecant function. express Time estimation error signal The square of, and express The adaptive weight vector at time step and its transpose. express The variance estimate of the error signal without pulse interference at time 1. Indicates the input signal power. express The adaptive weighted error power estimate at time t. express The estimated variance of the input noise at time t.

[0012] Preferably, based on multiple parameter values, an optimal step size is constructed and smoothed to obtain the target step size, including: Based on multiple parameter values, construct Optimal step size at time step , is represented as: ; Smooth the optimal step size based on the step size smoothing factor to obtain Target step size at any given time , is represented as: ; in, and These represent taking the minimum value and taking the maximum value, respectively. Indicates the step size smoothing factor. express The target step size at any given moment and These represent the minimum and maximum preset step sizes, respectively.

[0013] Preferably, based on multiple parameter values ​​and the target step size, the adaptive weight error power estimate at the current time is updated to obtain... The adaptive weight error power estimate at time t is expressed as: .

[0014] Preferably, Adaptive weight vector at time step , is represented as: ; in, express The adaptive weight vector at time step, express The target step size at any given moment Let represent the hyperbolic cosecant function. This represents the shape adjustment parameter of the hyperbolic cosecant function. express Time estimation error signal The square of, express The noisy input signal vector at time t; express The estimated variance of the input noise at time t. express The variance estimate of the error signal without pulse interference at time 1. express The adaptive weight vector at time step.

[0015] This embodiment also provides a system based on the deviation compensation adaptive filtering method based on the logarithmic hyperbolic tangent function as described above, including: The error signal construction module is used to obtain the inner product of the adaptive weight vector of the adaptive filter and the noisy input signal vector as the output signal; and to calculate the difference between the noisy expected signal and the output signal to obtain the estimated error signal. The correlation estimation construction module is used to construct the median square of the error without impulse interference based on the estimation error signal; and to compare the median square of the error without impulse interference with the signal based on a preset smoothing factor. The variance estimates of the pulse-free interference error signal at each time step are weighted and summed to obtain the variance estimate of the pulse-free interference error signal; based on the preset smoothing factor, filter length, and adaptive weight vector and its transpose, the power estimate of the adaptive weight vector is constructed; based on the ratio of the variance estimate of the pulse-free interference error signal to the power estimate of the adaptive weight vector, the variance estimate of the input noise is obtained. The deviation compensation construction module is used to construct a deviation compensation term based on the input noise variance estimate, the variance estimate of the error signal without impulse interference, and the adaptive weight vector. The relevant parameter value construction module is used to construct multiple parameter values ​​based on the noisy input signal vector, the estimated error signal, the adaptive weight vector, the variance estimate of the error signal without pulse interference, the input signal power, the adaptive weight error power estimate, the input noise variance estimate, and the hyperbolic cosecant function. The adaptive filtering module is used to construct the optimal step size based on multiple parameter values, smooth the result, and obtain the target step size; based on the multiple parameter values ​​and the target step size, it updates the adaptive weight error power estimate at the current time, and obtains... The adaptive weight error power estimate at time step is obtained; using the target step size, estimated error signal, noisy input signal vector, input noise variance estimate, and impulse-free error signal variance estimate, the adaptive weight vector at the current time step is updated to obtain... The adaptive weight vector at time step.

[0016] Compared with the prior art, the above-described technical solution of the present invention has the following advantages: The bias-compensated adaptive filtering method based on the logarithmic hyperbolic tangent function described in this invention addresses the problems of severe steady-state estimation bias and poor robustness in impulse noise environments by calculating a bias compensation term. Simultaneously, a variable step-size mechanism is introduced to update the adaptive weight vector, resolving the technical challenge of the irreconcilable contradiction between system convergence speed and steady-state instability when the step size is fixed. This invention exhibits stronger robustness in scenarios containing impulse noise and effectively reduces the adverse effects of input noise, achieving both rapid convergence and low steady-state instability.

[0017] This invention first constructs a median square of the error without impulse interference and combines it with a median filtering mechanism to suppress the error signal affected by impulse noise, thereby reducing the destructive effect of impulse noise on the algorithm's convergence process at its source. Based on this, a smoothing factor is introduced to recursively estimate the error variance, improving the stability and continuity of the estimation and avoiding the estimation instability caused by instantaneous error fluctuations in traditional methods. Furthermore, this invention derives an input noise variance estimate by constructing an adaptive weight vector power estimate and combining it with the variance estimate of the error signal without impulse interference. This allows for the construction of a corresponding deviation compensation term to address the deviation caused by noise contamination of the input signal. According to the unbiasedness criterion, this deviation compensation term mathematically approximates the error term caused by input noise, effectively offsetting the deviation caused by input noise during weight updates, reducing steady-state error, and improving the system's identification accuracy.

[0018] In adaptive filtering algorithms, the step size parameter determines the magnitude of weight updates. A larger step size can accelerate the convergence speed in the initial stage but exacerbates jitter in the steady-state stage, thus increasing steady-state imbalance. Conversely, a smaller step size can reduce steady-state error but significantly slows down the convergence speed. Therefore, a fixed step size cannot simultaneously achieve fast convergence and low steady-state error. Compared to traditional fixed step size methods, the variable step size mechanism of this invention allows for a larger step size in the early stages of convergence based on relevant parameter values ​​to improve convergence speed, while the step size decreases in the steady-state stage to reduce steady-state imbalance, thereby achieving a dynamic balance between convergence speed and steady-state performance. Attached Figure Description

[0019] 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: Figure 1 This is a flowchart of the steps of the deviation compensation adaptive filtering method based on the log-hyperbolic tangent function of the present invention; Figure 2 This is a block diagram of an adaptive filter with input noise; Figure 3 This is a comparison of the normalized mean square deviation curves of different adaptive filters in the system identification scenario under Gaussian white noise input. Figure 4 This is a comparison of the normalized mean square deviation curves of different adaptive filters in the system identification scenario under colored signal input. Figure 5 This is a block diagram of a bias-compensated adaptive filtering system based on the logarithmic hyperbolic tangent function. Detailed Implementation

[0020] 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.

[0021] Reference Figure 1 The flowchart shown illustrates the steps of the deviation compensation adaptive filtering method based on the logarithmic hyperbolic tangent function of this invention. At time 100, the specific filtering steps of the adaptive filter are shown in S101 to S110.

[0022] S101: Obtain the inner product of the adaptive weight vector of the adaptive filter and the noisy input signal vector as the output signal; calculate the difference between the noisy expected signal and the output signal to obtain the estimation error signal, including: S101-1: Obtain Time-adaptive filter Adaptive weights and build Adaptive weight vector at time step , is represented as: ; superscript Indicates the transpose operation; S101-2: Obtain Time and preceding consecutive The sampled value of the noisy input signal at each moment , build Noisy input signal vector at time 1 , is represented as: ; S101-3: Perform an inner product between the adaptive weight vector and the noisy input signal vector to generate... Output signal at time , is represented as: ; In practical applications, this means using noisy input vectors... with weight vector Perform the inner product calculation to obtain The output signal of the echo canceller at that moment ; S101-4: Calculate the difference between the noisy desired signal and the output signal, and obtain... Time estimation error signal , is represented as: ; in, express The noisy echo signal at any given moment is the noisy expected signal.

[0023] S102: Based on the estimated error signal, construct the median square of the error without impulse interference, including: like The square of the estimation error signal at time [time] Less than the preset positive threshold parameter and Variance estimate of the error signal without pulse interference at time 1 The product of , then with The square of the error signal at time step is used as... The median square of the error without pulse interference at any given time; Conversely, the current time and the preceding consecutive moments are considered. The median of the square of the estimation error signal at each time step As The median square of the error without pulse interference at time 1; Median of squared error at time of pulse-free interference , is represented as: ; in, is an integer representing the median filter length.

[0024] S103: Median of squared error without pulse interference based on preset smoothing factor and Variance estimate of the error signal without pulse interference at time 1 Perform a weighted summation to obtain Variance estimate of the error signal without pulse interference at time 1 , is represented as: ; in, This is a preset smoothing factor, with a value ranging from 0.99 to 0.999, used for smoothing estimation.

[0025] In practical application scenarios, acquiring After estimating the error signal at time, based on Whether median filtering is performed depends on whether the time-estimation error signal is affected by impulse noise. If the median is taken, the median of the squared error without pulse interference is obtained; otherwise, the median of the squared error without pulse interference is... ,in, yes Estimated variance of the time error signal. This is a threshold parameter used to determine whether the device is affected by impulse noise, and it is typically set between 9 and 25. This embodiment calculates... Variance estimate of the error signal without pulse interference at time 1 ,in, It is a smoothing factor, which can usually be between 0.99 and 0.999, used to smooth the estimation and ensure the accuracy and smoothness of the estimation.

[0026] S104: Based on the preset smoothing factor, filter length, and adaptive weight vector and its transpose, construct... Adaptive weight vector power estimate at time step , is represented as: ; in, For filter length, express The adaptive weight vector at time step, with superscript This indicates the transpose operation.

[0027] S105: Obtain the ratio of the variance estimate of the pulse-free error signal to the power estimate of the adaptive weight vector. Input noise variance estimate at time step , is represented as: ; in, The ratio of the output noise to the input noise variance is expressed as: ; This represents the variance of the measurement noise excluding impulse noise. This represents the variance of the input noise.

[0028] S106: Based on the input noise variance estimate, the variance estimate of the error signal without impulse interference, and the adaptive weight vector, a deviation compensation term is constructed, expressed as: ; in, This indicates a preset fixed step size. express The estimated variance of the input noise at time t. express The variance estimate of the error signal without pulse interference at time 1. This represents the shape adjustment parameter of the hyperbolic cosecant function. express The adaptive weight vector at time step.

[0029] The deviation compensation and variable step-size adaptive filtering method based on the logarithmic hyperbolic tangent function described in this invention improves upon traditional methods by introducing a deviation compensation term, based on the error statistics characteristics of the adaptive filtering model. Specifically, because the input signal contains noise and the system output is affected by impulse noise, the weight updates in traditional methods shift, leading to estimation deviations. These deviations accumulate during iteration, eventually resulting in increased steady-state misalignment. This invention first constructs a median square of the error without impulse interference and combines it with a median filtering mechanism to suppress the error signal affected by impulse noise, reducing the destructive effect of impulse noise on the algorithm's convergence process at its source. Furthermore, by introducing a smoothing factor to recursively estimate the error variance, the stability and continuity of the estimation are improved, avoiding the estimation instability caused by instantaneous error fluctuations in traditional methods. Further, this invention derives an input noise variance estimate by constructing an adaptive weight vector power estimate and combining it with the variance estimate of the error signal without impulse interference. This allows for the construction of a corresponding deviation compensation term to address the deviation problem caused by noise contamination of the input signal. According to the unbiasedness criterion, the deviation compensation term approximates the error term caused by input noise in a mathematical expectation sense. It can offset the deviation caused by input noise during the weight update process, effectively reduce steady-state error, and improve the system identification accuracy.

[0030] S107: Based on the noisy input signal vector, the estimation error signal, the adaptive weight vector, the variance estimate of the error signal without impulse interference, the input signal power, the adaptive weight error power estimate, the input noise variance estimate, and the hyperbolic cosecant function, construct multiple parameter values, including: S107-1: Construct the first parameter value based on the product of the square of the L2 norm of the noisy input signal vector, the square of the hyperbolic cosecant function of the square of the estimation error signal, and the square of the estimation error signal. , is represented as: ; S107-2: Calculate the square of the L2 norm of the adaptive weight vector to obtain the value of the second parameter. , is represented as: ; S107-3: Construct the third parameter value based on the transpose of the adaptive weight vector, the noisy input signal vector, the square of the hyperbolic cosecant function of the square of the estimation error signal, and the product of the estimation error signal. , is represented as: ; S107-4: Construct the fourth parameter value based on the square of the hyperbolic cosecant function of the variance estimate of the pulse-free interference error signal, the product of the input signal power and the adaptive weight error power estimate. , is represented as: ; S107-5: Construct the fifth parameter value based on the input noise variance estimate and the variance estimate of the error signal without impulse interference. , is represented as: ; in, express The noisy input signal vector at time t, This represents taking the square of the L2 norm. Let represent the hyperbolic cosecant function. This represents the shape adjustment parameter of the hyperbolic cosecant function. express Time estimation error signal The square of, and express The adaptive weight vector at time step and its transpose. express The variance estimate of the error signal without pulse interference at time 1. Indicates the input signal power. express The adaptive weighted error power estimate at time t. express The estimated variance of the input noise at time t.

[0031] S108: Based on multiple parameter values, construct the optimal step size and smooth it to obtain the target step size, including: S108-1: Construct based on multiple parameter values Optimal step size at time step , is represented as: ; S108-2: Smoothing the optimal step size based on the step size smoothing factor to obtain... Target step size at any given time , is represented as: ; in, and These represent taking the minimum value and taking the maximum value, respectively. This represents the step size smoothing factor, with a value ranging from 0.99 to 0.999; express The target step size at any given moment and These represent the minimum and maximum preset step sizes, respectively.

[0032] This invention introduces a variable step-size mechanism during the weight update process to achieve adaptive adjustment of the step-size parameter. In adaptive filtering algorithms, the step-size parameter determines the magnitude of weight updates. A larger step-size can accelerate the convergence speed in the initial stage, but it can lead to increased jitter in the steady-state stage, thus increasing steady-state imbalance. Conversely, a smaller step-size can reduce steady-state error, but it significantly slows down the convergence speed. Therefore, a fixed step-size cannot simultaneously achieve fast convergence and low steady-state error. Compared to traditional fixed-step-size methods, the variable step-size mechanism of this invention can set a larger step-size in the early stages of convergence based on relevant parameter values ​​to improve the convergence speed, while decreasing the step-size in the steady-state stage to reduce steady-state imbalance, thereby achieving a dynamic balance between convergence speed and steady-state performance.

[0033] S109: Based on multiple parameter values ​​and the target step size, update the adaptive weight error power estimate for the current time step, and obtain... Adaptive weight error power estimate at time 1 , is represented as: .

[0034] S110: Using the target step size, estimated error signal, noisy input signal vector, estimated input noise variance, and estimated variance of the error signal without impulse interference, update the adaptive weight vector at the current time step to obtain... Adaptive weight vector at time step , is represented as: .

[0035] This invention presents a bias-compensated adaptive filtering method based on the logarithmic hyperbolic tangent function. By calculating a bias compensation term, it addresses the problems of severe steady-state estimation bias when the input signal is contaminated with noise and poor robustness in impulse noise environments. A variable step-size mechanism is introduced to update the adaptive weight vector, resolving the technical challenge of the irreconcilable contradiction between system convergence speed and steady-state instability when the step size is fixed. This invention exhibits stronger robustness in scenarios containing impulse noise and effectively reduces the adverse effects of input noise, achieving both rapid convergence and low steady-state instability.

[0036] Based on the above embodiments, to demonstrate the effectiveness of the present invention, this embodiment uses computer experiments to verify the performance of the variable step size-bias compensation-log hyperbolic tangent adaptive filter (VSS-BC-LHTAF) provided by the present invention. The experiment estimates an unknown system under an environment with impulse noise interference and a noisy input signal, and the results are compared with those of the bias compensation-log hyperbolic tangent adaptive filter (BC-LHTAF) and the log hyperbolic tangent adaptive filter (LHTAF).

[0037] 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; and two signals are used as inputs: one is Gaussian white noise, and the other is a colored signal. The system's scene recognition experiment uses Normalized Mean Square Deviation (NMSD) as a performance metric. The unit is dB, where, Indicates taking the logarithm. The weights represent the actual system weights. The NMSD curves obtained from the simulation in the figure are all obtained by averaging 100 independent iterations.

[0038] The noise signal used in the experiment at the input terminal It is zero-mean Gaussian white noise, used to describe the interference encountered by the input signal during acquisition or transmission. The output noise signal. Contains a zero-mean Gaussian white noise and a pulse noise ,Right now It is used to simulate measurement noise in real-world environments. It is zero-mean Gaussian white noise. It is impulse noise, generated by a Bernoulli-Gaussian process, i.e. ,in It is a Bernoulli process, and the probability of it taking the value 0 is 0.99 and the probability of it taking the value 1 is 0.01. It is zero-mean Gaussian white noise. The algorithm module (Algo.) follows the bias-compensated adaptive filtering method based on the log-hyperbolic tangent function proposed in this invention, iteratively updating the weight vector of the adaptive filter and feeding it back to the adaptive filter. (Refer to...) Figure 3 As shown, the input signal is zero-mean Gaussian white noise. (Refer to...) Figure 4 As shown, the input signal is a colored signal, which is zero-mean Gaussian white noise passed through a transfer function of... The experiment involved a first-order autoregressive system generating a colored signal with unit variance. The signal-to-noise ratio (SNR) between the system input signal and the filter input noise was 10 dB, the SNR between the system output signal and Gaussian noise was 30 dB, and the signal-to-interference ratio (SIR) was -10 dB. The actual system weights in the experiment were... length Set it to 9.

[0039] Reference Figure 3 The figure shows a comparison of the normalized mean square deviation curves of different adaptive filters in the system's scene identification under Gaussian white noise input; LHTAF parameters: , ; BC-LHTAF parameters: , , , , Parameters of VSS-BC-LHTAF: , , , , .Depend on Figure 3 As can be seen, all algorithms can achieve convergence under Gaussian white noise input. However, compared with LHTAF, the BC-LHTAF algorithm and VSS-BC-LHTAF algorithm proposed in this invention have faster convergence speed and lower steady-state imbalance, showing better overall performance.

[0040] Reference Figure 4 The figure shows a comparison of the normalized mean square deviation curves of different adaptive filters in the system identification scenario under colored signal input; LHTAF parameters: , ; BC-LHTAF parameters: , , , , Parameters of VSS-BC-LHTAF: , , , , .Depend on Figure 4 It is evident that in complex environments where the input signal is correlated colored noise and simultaneously contains Gaussian noise and impulse noise, the performance differences among the algorithms become more pronounced. However, the BC-LHTAF and VSS-BC-LHTAF algorithms still maintain relatively fast convergence speeds and low steady-state imbalances, demonstrating stronger resistance to impulse interference and robustness.

[0041] Based on the above embodiments, this invention provides a bias-compensated adaptive filtering system based on the logarithmic hyperbolic tangent function, referring to... Figure 5 The diagram shown is a block diagram of a bias-compensated adaptive filtering system based on the log-hyperbolic tangent function; a specific system may include: The error signal construction module 100 is used to obtain the inner product of the adaptive weight vector of the adaptive filter and the noisy input signal vector as the output signal; and to calculate the difference between the noisy expected signal and the output signal to obtain the estimated error signal. The correlation estimation construction module 200 is used to construct the median square of the error without impulse interference based on the estimation error signal; and to compare the median square of the error without impulse interference with the signal based on a preset smoothing factor. The variance estimates of the pulse-free interference error signal at each time step are weighted and summed to obtain the variance estimate of the pulse-free interference error signal; based on the preset smoothing factor, filter length, and adaptive weight vector and its transpose, the power estimate of the adaptive weight vector is constructed; based on the ratio of the variance estimate of the pulse-free interference error signal to the power estimate of the adaptive weight vector, the variance estimate of the input noise is obtained. The deviation compensation construction module 300 is used to construct a deviation compensation term based on the input noise variance estimate, the variance estimate of the error signal without impulse interference, and the adaptive weight vector. The relevant parameter value construction module 400 is used to construct multiple parameter values ​​based on the noisy input signal vector, the estimated error signal, the adaptive weight vector, the variance estimate of the error signal without impulse interference, the input signal power, the adaptive weight error power estimate, the input noise variance estimate, and the hyperbolic cosecant function. The adaptive filtering module 500 is used to construct an optimal step size based on multiple parameter values, smooth the result, and obtain a target step size; based on the multiple parameter values ​​and the target step size, it updates the adaptive weight error power estimate at the current time, and obtains... The adaptive weight error power estimate at time step is obtained; using the target step size, estimated error signal, noisy input signal vector, input noise variance estimate, and impulse-free error signal variance estimate, the adaptive weight vector at the current time step is updated to obtain... The adaptive weight vector at time step.

[0042] The deviation compensation adaptive filtering system based on the log-hyperbolic tangent function in this embodiment is used to implement the aforementioned deviation compensation adaptive filtering method based on the log-hyperbolic tangent function. Therefore, the specific implementation of the deviation compensation adaptive filtering system based on the log-hyperbolic tangent function can be found in the embodiment section of the deviation compensation adaptive filtering method based on the log-hyperbolic tangent function above. For example, the error signal construction module 100 is used to implement step S101 in the above-mentioned deviation compensation adaptive filtering method based on the log-hyperbolic tangent function; the correlation estimate construction module 200 is used to implement the above-mentioned deviation compensation adaptive filtering method based on the log-hyperbolic tangent function. In the deviation compensation adaptive filtering method based on the logarithmic hyperbolic tangent function, steps S102, S103, S104, and S105; the deviation compensation construction module 300 and the related parameter value construction module 400 are used to implement steps S106 and S107 in the deviation compensation adaptive filtering method based on the logarithmic hyperbolic tangent function, respectively; the adaptive filtering module 500 is used to implement steps S108, S109, and S110 in the deviation compensation adaptive filtering method based on the logarithmic hyperbolic tangent function. Therefore, the specific implementation method can be referred to the description of the corresponding embodiments, and will not be repeated here.

[0043] The bias-compensated adaptive filtering method based on the logarithmic hyperbolic tangent function described in this invention addresses the problems of severe steady-state estimation bias and poor robustness in impulse noise environments by calculating a bias compensation term. Simultaneously, a variable step-size mechanism is introduced to update the adaptive weight vector, resolving the technical challenge of the irreconcilable contradiction between system convergence speed and steady-state instability when the step size is fixed. This invention exhibits stronger robustness in scenarios containing impulse noise and effectively reduces the adverse effects of input noise, achieving both rapid convergence and low steady-state instability.

[0044] 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.

[0045] 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.

[0046] 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.

[0047] 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.

[0048] 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 adaptive filtering method based on the logarithmic hyperbolic tangent function, characterized in that, exist Moments, including: Obtain the dot product of the adaptive weight vector of the adaptive filter and the noisy input signal vector as the output signal; calculate the difference between the noisy expected signal and the output signal to obtain the estimation error signal; Based on the estimated error signal, the median square of the error without pulse interference is constructed. Based on a preset smoothing factor, the median of the squared error without pulse interference and The variance estimates of the error signal without pulse interference at time 1 are weighted and summed to obtain the variance estimate of the error signal without pulse interference. Based on the preset smoothing factor, filter length, and adaptive weight vector and its transpose, an adaptive weight vector power estimate is constructed. The input noise variance estimate is obtained based on the ratio of the variance estimate of the pulse-free interference error signal to the power estimate of the adaptive weight vector. Based on the input noise variance estimate, the variance estimate of the error signal without impulse interference, and the adaptive weight vector, a deviation compensation term is constructed. Multiple parameter values ​​are constructed based on the noisy input signal vector, the estimation error signal, the adaptive weight vector, the variance estimate of the error signal without impulse interference, the input signal power, the adaptive weight error power estimate, the input noise variance estimate, and the hyperbolic cosecant function. Based on multiple parameter values, construct the optimal step size and smooth it to obtain the target step size; Based on multiple parameter values ​​and the target step size, the adaptive weight error power estimate at the current time is updated to obtain... The adaptive weighted error power estimate at time step; The adaptive weight vector at the current time is updated using the target step size, the estimated error signal, the noisy input signal vector, the estimated input noise variance, and the estimated variance of the error signal without impulse interference. The adaptive weight vector at time step.

2. The bias compensation adaptive filtering method based on the logarithmic hyperbolic tangent function according to claim 1, characterized in that, Based on the estimated error signal, the median square of the error without impulse interference is constructed, including: like The square of the estimation error signal at time [time] Less than the preset positive threshold parameter and Variance estimate of the error signal without pulse interference at time 1 The product of these is then used as the square of the estimated error signal as the median of the square of the error without impulse interference. Conversely, the current time and the preceding consecutive moments are considered. The median of the square of the estimation error signal at each time step , as the median of the squared error without pulse interference; Median of squared error without pulse interference , represented as: ； in, Indicates the median filter length.

3. The bias compensation adaptive filtering method based on the logarithmic hyperbolic tangent function according to claim 1, characterized in that, Based on preset smoothing factor Median of squared error for no-pulse interference and Variance estimate of the error signal without pulse interference at time 1 Perform weighted summation to obtain the variance estimate of the error signal without pulse interference. , represented as: ； Based on preset smoothing factor Filter length With adaptive weight vector and its transpose Construct adaptive weight vector power estimates , represented as: ； Based on the variance estimate of the error signal without pulse interference With adaptive weight vector power estimate The ratio is used to obtain the input noise variance estimate. , represented as: ； in, The ratio of the output noise to the input noise variance is expressed as: ; This represents the variance of the measurement noise excluding impulse noise. This represents the variance of the input noise.

4. The bias compensation adaptive filtering method based on the logarithmic hyperbolic tangent function according to claim 1, characterized in that, Based on the input noise variance estimate, the variance estimate of the error signal without impulse interference, and the adaptive weight vector, a bias compensation term is constructed, expressed as: ； in, This indicates a preset fixed step size. express The estimated variance of the input noise at time t. express The variance estimate of the error signal without pulse interference at time 1. This represents the shape adjustment parameter of the hyperbolic cosecant function. express The adaptive weight vector at time step.

5. The bias compensation adaptive filtering method based on the logarithmic hyperbolic tangent function according to claim 1, characterized in that, Based on the noisy input signal vector, the estimation error signal, the adaptive weight vector, the variance estimate of the error signal without impulse interference, the input signal power, the adaptive weight error power estimate, the input noise variance estimate, and the hyperbolic cosecant function, multiple parameter values ​​are constructed, including: The first parameter value is constructed based on the product of the square of the L2 norm of the noisy input signal vector, the square of the hyperbolic cosecant function of the square of the estimation error signal, and the square of the estimation error signal. Calculate the square of the L2 norm of the adaptive weight vector to obtain the value of the second parameter; The third parameter value is constructed based on the transpose of the adaptive weight vector, the noisy input signal vector, the square of the hyperbolic cosecant function of the square of the estimation error signal, and the product of the estimation error signal. The fourth parameter value is constructed based on the square of the hyperbolic cosecant function of the variance estimate of the pulse-free interference error signal, the product of the input signal power and the adaptive weight error power estimate; The fifth parameter value is constructed based on the input noise variance estimate and the variance estimate of the error signal without impulse interference.

6. The bias compensation adaptive filtering method based on the logarithmic hyperbolic tangent function according to claim 5, characterized in that, First parameter value , represented as: ； Second parameter value , represented as: ; Third parameter value , represented as: ; Fourth parameter value , represented as: ; Fifth parameter value , represented as: ; in, express The noisy input signal vector at time t, This represents taking the square of the L2 norm. Let represent the hyperbolic cosecant function. This represents the shape adjustment parameter of the hyperbolic cosecant function. express Time estimation error signal The square of, and express The adaptive weight vector at time step and its transpose. express The variance estimate of the error signal without pulse interference at time 1. Indicates the input signal power. express The adaptive weighted error power estimate at time t. express The estimated variance of the input noise at time t.

7. The bias compensation adaptive filtering method based on the logarithmic hyperbolic tangent function according to claim 6, characterized in that, Based on multiple parameter values, an optimal step size is constructed and smoothed to obtain the target step size, including: Based on multiple parameter values, construct Optimal step size at time step , represented as: ; Smooth the optimal step size based on the step size smoothing factor to obtain Target step size at any given time , represented as: ; in, and These represent taking the minimum value and taking the maximum value, respectively. Indicates the step size smoothing factor. express The target step size at any given moment and These represent the minimum and maximum preset step sizes, respectively.

8. The bias compensation adaptive filtering method based on the logarithmic hyperbolic tangent function according to claim 7, characterized in that, Based on multiple parameter values ​​and the target step size, the adaptive weight error power estimate at the current time is updated to obtain... Adaptive weight error power estimate at time 1 , represented as: 。 9. The bias compensation adaptive filtering method based on the logarithmic hyperbolic tangent function according to claim 1, characterized in that, Adaptive weight vector at time step , represented as: ； in, express The adaptive weight vector at time step, express The target step size at any given moment Let represent the hyperbolic cosecant function. This represents the shape adjustment parameter of the hyperbolic cosecant function. express Time estimation error signal The square of, express The noisy input signal vector at time t; express The estimated variance of the input noise at time t. express The variance estimate of the error signal without pulse interference at time 1. express The adaptive weight vector at time step.

10. A system based on the bias compensation adaptive filtering method based on the log-hyperbolic tangent function as described in any one of claims 1 to 9, characterized in that, include: The error signal construction module is used to obtain the inner product of the adaptive weight vector of the adaptive filter and the noisy input signal vector, as the output signal; Calculate the difference between the noisy expected signal and the output signal to obtain the estimation error signal; The relevant estimation construction module is used to construct the median squared error without impulse interference based on the estimation error signal; Based on a preset smoothing factor, the median of the squared error without pulse interference and The variance estimates of the pulse-free interference error signal at each time point are weighted and summed to obtain the variance estimate of the pulse-free interference error signal; based on the preset smoothing factor, filter length, and adaptive weight vector and its transpose, the adaptive weight vector power estimate is constructed. The input noise variance estimate is obtained based on the ratio of the variance estimate of the pulse-free interference error signal to the power estimate of the adaptive weight vector. The deviation compensation construction module is used to construct a deviation compensation term based on the input noise variance estimate, the variance estimate of the error signal without impulse interference, and the adaptive weight vector. The relevant parameter value construction module is used to construct multiple parameter values ​​based on the noisy input signal vector, the estimated error signal, the adaptive weight vector, the variance estimate of the error signal without pulse interference, the input signal power, the adaptive weight error power estimate, the input noise variance estimate, and the hyperbolic cosecant function. The adaptive filtering module is used to construct the optimal step size based on multiple parameter values, smooth the result, and obtain the target step size; based on the multiple parameter values ​​and the target step size, it updates the adaptive weight error power estimate at the current time, and obtains... The adaptive weight error power estimate at time step is obtained; using the target step size, estimated error signal, noisy input signal vector, input noise variance estimate, and impulse-free error signal variance estimate, the adaptive weight vector at the current time step is updated to obtain... The adaptive weight vector at time step.

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