Variable step size robust adaptive filter and filter network

Abstract

The invention relates to the technical field of adaptive filtering, discloses a variable-step robust adaptive filter and a filter network, and aims to solve the technical problem that a traditional adaptive filter cannot effectively consider convergence speed, steady-state precision and impulse noise interference resistance. A non-linear error factor is introduced, large errors caused by impulse noise are effectively suppressed through a generalized function form of the non-linear error factor, and the robustness of the filtering process is remarkably improved; meanwhile, a variable step length mechanism is provided, the theoretically optimal candidate step length is calculated on line by minimizing the mean square deviation of the next moment, and a self-adaptive target variable step length is generated through truncation and time smoothing processing, so that dynamic balance is realized between rapid convergence and low-steady-state maladjustment. According to the invention, the filter is expanded to the distributed network, each node follows a diffusion strategy of first updating and then combining, and global information sharing and performance collaborative optimization are realized by using a combined coefficient.

Description

TECHNICAL FIELD

[0001] The present application relates to the field of adaptive filtering, in particular to a variable step-size robust adaptive filter and filter network. BACKGROUND

[0002] In the field of adaptive filter, the goal of system identification is to estimate the frequency response, time delay spread and other transmission characteristics of the unknown system to be estimated through adaptive filter, and then to compensate for the distortion of the channel by adjusting the coefficients of the adaptive filter itself, so that the output signal of the system to be estimated can better restore the characteristics of the original input signal.

[0003] System identification is an important branch of adaptive filter application, and many problems such as traditional adaptive channel equalization, adaptive noise cancellation, adaptive echo cancellation and active noise control can be attributed to the application of adaptive filter in system identification. The traditional least mean square (LMS) and normalized least mean square (NLMS) adaptive filter is easy to implement, but this kind of adaptive filter based on minimizing the instantaneous mean square error has a difficult contradiction between convergence speed, steady-state accuracy and filter robustness, which is specifically manifested as follows: fixed step size parameter leads to the adaptive filter being unable to balance between fast initial convergence and low steady-state misadjustment; large step size can accelerate convergence but will increase steady-state error, and small step size can improve accuracy but significantly prolongs the convergence time. The linear update rule based on quadratic cost function is extremely sensitive to outliers; when there is significant impulse noise in the system observation noise, a single impulse interference can cause a huge instantaneous error, leading to a dramatic disturbance of the adaptive filter weights and even divergence, and the performance is deteriorated sharply.

[0004] In order to cope with the challenge of impulse noise, a series of adaptive filters resistant to impulse noise are designed, for example, the sign error (SA) filter enhances stability by simplifying error information; the mixed norm adaptive filter attempts to combine the norms of different errors to achieve a balance between convergence speed and robustness; the maximum correlation criterion (MCC) adaptive filter uses information theory learning method to suppress impulse noise interference, thereby improving robustness. Although these filters improve the robustness to some extent, they often sacrifice the convergence speed or steady-state accuracy.

[0005] In recent years, research has delved deeper into embedding nonlinear error functions into update rules. These nonlinear factors can suppress drastic perturbations of weights by single pulses at large errors, while maintaining sufficient fine-tuning capability at small errors, thus enhancing robustness without significantly sacrificing convergence. The recently proposed Robust Generalized Adaptive (RGA) filter exhibits good robustness, but its fixed step size limits the optimal trade-off between convergence and steady-state accuracy. That is, while maintaining a relatively fast convergence speed, the steady-state time is relatively large, resulting in lower filtering accuracy for the adaptive filter. Summary of the Invention

[0006] 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 simultaneously have a fast convergence speed and a low steady-state offset, resulting in poor versatility and low filtering efficiency of the adaptive filter.

[0007] To address the aforementioned technical problems, this invention provides a variable step-size robust adaptive filter, comprising: Get Time and The sampled values ​​of the input signal input to the system to be estimated at multiple consecutive time points prior to time t are used to form an adaptive filter. The input signal vector at time t; Obtaining the adaptive filter in Multiple adaptive weights at time points constitute The adaptive weight vector at time step; Get The dot product of the adaptive weight vector and the input signal vector at time t is used as the adaptive filter's... Output signal at time; based on The preset expected signal and output signal at time are obtained. The estimation error signal at time; right After performing a nonlinear transformation on the time-estimation error signal, it is adjusted using preset shape parameters to construct... The nonlinear error factor at time; based on The input signal vector at time step 1, the estimation error signal, and the nonlinear error factor are obtained by minimizing the mean square deviation. Candidate variable step sizes for each time step are determined, and truncation and time smoothing are performed to obtain... The target step size can be changed at any given time. based on The input signal vector at time step, the nonlinear error factor, and the target variable step size, for The adaptive weight vector at time step is updated to obtain... The adaptive weight vector at time step.

[0008] Preferably, the inner product of the adaptive weight vector at the time instant and the input signal vector is obtained as the output signal of the adaptive filter at the time instant ; wherein denotes the output signal of the adaptive filter at the time instant denotes the transpose of the adaptive weight vector at the time instant , denotes the adaptive weight value in the adaptive weight vector at the time instant , denotes the total number of adaptive weight values; denotes the input signal vector at the time instant , denotes the sample value of the input signal at the time instant denotes the sample value of the input signal at the time instant

[0009] Preferably, the nonlinear error factor at the time instant is constructed by performing a nonlinear transformation on the estimation error signal at the time instant and adjusting the nonlinear transformation by using a preset shape parameter, and is expressed as ; wherein denotes the nonlinear error factor at the time instant denotes a preset size parameter; denotes the estimation error signal at the time instant , denotes a preset expected signal at the time instant denotes the output signal of the adaptive filter at the time instant denotes a sign function, denotes a negative shape parameter and a positive shape parameter, respectively, denotes an absolute value operation. Preferably, the nonlinear error factor at the time instant is constructed by performing a nonlinear transformation on the estimation error signal at the time instant and adjusting the nonlinear transformation by using a preset shape parameter, and is expressed as

[0010] ​​​​​​​​​​​​​​​​​The input signal vector at time step 1, the estimation error signal, and the nonlinear error factor are obtained by minimizing the mean square deviation. Candidate variable step sizes for each time step are determined, and truncation and time smoothing are performed to obtain... The target step size at any given time is variable, including: based on The effective error estimation at time step is performed using the exponential moving average method. The estimated error signal at time step is exponentially smoothed with a nonlinear error factor to obtain... Effective error estimation at time step; based on The average error at time step is estimated using the exponential moving average method. The square of the estimation error signal at time step is exponentially smoothed to obtain... Mean error estimation at time step; use The average error estimate at time t is The effective error estimate at time step is standardized to obtain Correlation coefficient at time; based on The nonlinear error estimation at time step is performed using the exponential moving average method. The square of the nonlinear error factor at time step is exponentially smoothed to obtain... Nonlinear error estimation at time step; based on The correlation coefficient at each time step, the average error estimate, the nonlinear error estimate, the noise variance, and the trace of the correlation matrix of the input signal vector are used to obtain... Candidate variable step size at time step; Using a preset safety step size, for The candidate variable step size at time step is truncated to obtain Optimization of timing with variable step size; Will Optimization of time step size and the first step The target at each time step is weighted and fused to obtain the result. The target step size can be changed at any given time.

[0011] Preferably, Obtaining the correlation coefficient at each time point includes: based on Effective error estimation at time point Using the exponential moving average method, for Time estimation error signal With nonlinear error factor Perform exponential smoothing to obtain Effective error estimation at time point is expressed as: ; Based on the average error estimate at time , the squared error signal at time is exponentially smoothed to obtain the average error estimate at time , which is expressed as: ; ; The effective error estimate at time is normalized by the average error estimate at time to obtain the correlation coefficient at time , which is expressed as: ; ; wherein denotes a preset forgetting factor, is a regularization factor to prevent the denominator from being zero.

[0012] Preferably, based on the correlation coefficient, the average error estimate, the nonlinear error estimate, the noise variance value at time , and the trace of the correlation matrix of the input signal vector, a candidate variable step size at time is obtained, including: Based on the nonlinear error estimate at time , the squared nonlinear error factor at time is exponentially smoothed to obtain the nonlinear error estimate at time , which is expressed as: ; ; ; Based on the correlation coefficient at time , the average error estimate at time , the nonlinear error estimate at time , the noise variance value at time , and the trace of the correlation matrix of the input signal vector at time , a candidate variable step size at time is obtained, which is expressed as: ; ; ; wherein the correlation matrix of the input signal vector at time is expressed as , denotes an expectation operation, and denote ​​​The input signal vector at time t and its corresponding transpose.

[0013] Preferably, based on Acquisition of candidate variable step size at time step The target step size at any given time is variable, including: Using preset safety step size ,right Candidate variable step size at time Truncate and obtain Time-based optimization with variable step size , represented as: ; Using preset weighting factors ,Will Time-based optimization with variable step size With the The target step size at any given time is variable. Perform weighted fusion to obtain The target step size at any given time is variable. , represented as: .

[0014] Preferably, based on The input signal vector at time step, the nonlinear error factor, and the target variable step size, for The adaptive weight vector at time step is updated to obtain... 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, express The target step size at any given time is variable. express Nonlinear error factor at time step express The input signal vector at time t.

[0015] This embodiment provides a filter network based on the variable step-size robust adaptive filter described above, including: Connect multiple adaptive filters to obtain the filter network; For each adaptive filter in the filter network, based on this adaptive filter The input signal vector at time step, the nonlinear error factor, and the target variable step size, for The adaptive weight vector at time step is updated to obtain... The intermediate estimated adaptive weight vector at time step; For each adaptive filter in the filter network, based on the preset joint coefficient, each neighbor adaptive filter directly connected with it is weightedly summed with the intermediate estimated adaptive weight vector of the neighbor adaptive filter at the moment to obtain the target adaptive weight vector of each adaptive filter in the filter network at the moment .

[0016] Preferably, the target adaptive weight vector of each adaptive filter in the filter network at the moment is expressed as: ; wherein, denotes the target adaptive weight vector of the th adaptive filter in the filter network at the moment ; denotes the set of neighbor adaptive filters directly connected with the th adaptive filter in the filter network; denotes the preset joint coefficient of the th neighbor adaptive filter of the th adaptive filter in the filter network, , , denotes the number of neighbor adaptive filters in ; denotes the intermediate estimated adaptive weight vector of the th neighbor adaptive filter of the th adaptive filter at the moment ; for any adaptive filter in the filter network, the intermediate estimated adaptive weight vector of the adaptive filter at the moment is expressed as , denotes the target adaptive weight vector of the th adaptive filter at the moment , denotes the target variable step size of the th adaptive filter at the moment , denotes the nonlinear error factor of the th adaptive filter at the moment , denotes the input signal vector of the th adaptive filter at the moment .

[0017] The above technical solution of the present application has the following beneficial effects compared with the prior art:

[0018] The variable step robust adaptive filter provided by the application introduces a nonlinear error factor by performing nonlinear transformation on the estimation error signal to compensate for the filtering deviation caused by the existence of impulse noise, so that the adaptive filtering process is more robust, and a filtering result with faster convergence speed and better robust performance is obtained; meanwhile, based on the nonlinear error factor, the mean square deviation minimization is used to construct the target variable step, so that the filter uses a larger step in the initial stage to accelerate convergence, and automatically reduces the step when approaching the steady state to reduce the steady state misadjustment, thereby achieving a good compromise between convergence speed and steady state accuracy.

[0019] The application obtains the target variable step at the moment t+1 based on the outer product and trace minimization of the mean square deviation at the moment t+1. The application obtains the candidate variable step at the moment t+1 by online estimation of the effective error estimate, correlation coefficient, average error estimate and nonlinear error estimate at the moment t+1. The application obtains the target variable step at the moment t+1 by truncation and time smoothing.The application is based on the optimal criterion of minimizing the mean square deviation at the moment t+1, online real-time estimates the key statistics such as effective error and correlation coefficient, calculates the theoretically optimal candidate step, and finally obtains the target step which is safe and smooth through truncation and time smoothing. The design makes the filter automatically use a larger step to realize fast tracking in the initial stage of convergence, and automatically switch to a small step to realize fine adjustment when approaching the steady state, thereby intelligently balancing the core contradiction between convergence speed and steady state accuracy. At the same time, the mechanism works with the nonlinear error factor to ensure the excellent robustness and stability of the filter in complex environments such as impulse noise.

[0020] The filter network constructed based on the variable step robust adaptive filter is based on the mechanism that each adaptive filter is updated first and then combined with its neighbor adaptive filter, based on information sharing and knowledge diffusion, so that the adaptive filter can quickly converge to accurate weights, and can effectively utilize the dispersed information in the filter network, thereby accelerating the identification process of the entire network to the real system and improving the identification efficiency; at the same time, the filter network will not collapse due to the failure of a few nodes, even if the data of a certain node is temporarily completely wrong, it will be corrected by the correct information of other normal nodes in the joint step, further ensuring the robustness of the filtering. BRIEF DESCRIPTION OF DRAWINGS

[0021] In order to make the content of the application more easily understood, the application will be further described in detail below according to specific embodiments of the application and in conjunction with the drawings, in which: Figure 1 is a step flow chart of the variable step robust adaptive filter provided by the application; Figure 2 ​is a structural block diagram of a variable step size robust adaptive filter; Figure 3 is a comparison diagram of normalized mean square deviation curves of different adaptive filters in a system identification scenario; Figure 4 is a comparison diagram of normalized mean square deviation curves of different adaptive filter networks in a distributed system identification scenario. DETAILED DESCRIPTION

[0022] The present application will be further described below with reference to the drawings and specific embodiments, so that those skilled in the art can better understand the present application and implement it.

[0023] Referring to Figure 1 , a step flow chart of the variable step size robust adaptive filter of the present application, the specific steps include: S101: obtaining , and , the sampling values of the input signal input to the system to be estimated at a plurality of time instants before , to form an input signal vector of the adaptive filter at , denoted as: , , wherein represents the sampling value of the input signal at , represents the sampling value of the input signal at the th time instant before , and represents a transposition operation; S102: obtaining a plurality of adaptive weights of the adaptive filter at , to form an adaptive weight vector at , denoted as: , , wherein represents the th adaptive weight in the adaptive weight vector at , represents the total number of adaptive weights; S103: obtaining the inner product of the adaptive weight vector at and the input signal vector as the output signal of the adaptive filter at , denoted as ; S104: based on the preset expected signal and the output signal at , obtaining the estimation error signal at ; , represented as , express The preset expected signal at a given time; S105: Yes After performing a nonlinear transformation on the time-estimation error signal, it is adjusted using preset shape parameters to construct... Nonlinear error factor at time , represented as: ; in, Indicates the preset size parameters; Represents a symbolic function. and These represent the negative shape parameters and the positive shape parameters, respectively. This indicates the absolute value operation; S106: Based on The input signal vector at time step 1, the estimation error signal, and the nonlinear error factor are obtained by minimizing the mean square deviation. Candidate variable step sizes for each time step are determined, and truncation and time smoothing are performed to obtain... The target step size can be changed at any given time. S107: Based on The input signal vector at time step, the nonlinear error factor, and the target variable step size, for The adaptive weight vector at time step is updated to obtain... The adaptive weight vector at time step.

[0024] The variable step-size robust adaptive filter described in this invention introduces a nonlinear error factor by performing a nonlinear transformation on the estimation error signal to compensate for the filtering deviation caused by the presence of impulse noise. This makes the adaptive filtering process more robust, resulting in filtering results with faster convergence speed and better robust performance. At the same time, based on the nonlinear error factor, the target variable step size is constructed by minimizing the mean square deviation. The filter uses a larger step size in the initial stage to accelerate convergence, and automatically reduces the step size to reduce steady-state misalignment when approaching steady state. This achieves a good trade-off between convergence speed and steady-state accuracy.

[0025] Specifically, in step S106, The acquisition of the target variable step size at each time step includes: S106-1: Based on Effective error estimation at time point Using the exponential moving average method, for Time estimation error signal With nonlinear error factor Perform exponential smoothing to obtain Effective error estimation at time point , is represented as: , Indicates a preset forgetting factor; S106-2: Based on Mean error estimation at time Using the exponential moving average method, for The square of the estimation error signal at time [time] Perform exponential smoothing to obtain Mean error estimation at time , is represented as: ; S106-3: Utilization The average error estimate at time t is The effective error estimate at time step is standardized to obtain Correlation coefficient at time , is represented as: , To prevent regularization factors with a denominator of 0; S106-4: Based on Nonlinear error estimation at time step Using the exponential moving average method, for The square of the nonlinear error factor at time step Perform exponential smoothing to obtain Nonlinear error estimation at time step , is represented as: ; S106-5: Based on Correlation coefficient at time Mean error estimation Nonlinear error estimation Noise variance and the correlation matrix of the input signal vector traces , obtain Candidate variable step size at time , is represented as: , , This represents the expectation operation. and They represent The input signal vector at time t and its corresponding transpose; 106-6: Utilizing a preset safety step size ,right Candidate variable step size at time Truncate and obtain Time-based optimization with variable step size denotes: ; S106-7: using preset weighting factor , the target variable step size at time t is obtained by optimizing the variable step size at time t and the target variable step size at time t is weighted and fused, and the target variable step size at time t is obtained . the target variable step size at time t denotes: .

[0026] The application obtains the target variable step size at time t by adaptively updating the target variable step size at time t based on the outer product and the trace minimization of the mean square error at next time, and by online estimating the effective error estimate, the correlation coefficient, the average error estimate and the nonlinear error estimate at time t , the candidate variable step size at time t is obtained, and then the target variable step size at time t is obtained by truncation and time smoothing. The application is based on the optimal criterion of minimizing the mean square error at next time, and online estimates the key statistics such as effective error and correlation coefficient in real time, calculates the theoretically optimal candidate step size, and finally obtains the target step size which is safe and smooth through truncation and time smoothing processing. The design makes the filter automatically adopt a larger step size to realize fast tracking in the early stage of convergence, and automatically switch to a small step size to realize fine adjustment when approaching steady state, thereby intelligently balancing the core contradiction between convergence speed and steady state accuracy. At the same time, the mechanism works together with the nonlinear error factor to ensure the excellent robustness and stability of the filter in complex environments such as pulse noise.

[0027] Specifically, after obtaining the target variable step size at time t , the adaptive weight vector at time t is updated by combining the input signal vector at time t , the nonlinear error factor , and the target variable step size at time t , and the adaptive weight vector at time t is obtained , denoted as: .The adaptive filter calculates the inner product of the adaptive weight vector at time t and the input signal vector, and obtains the output signal of the adaptive filter at time t .

[0028] ​​Based on the above embodiments, in this embodiment of the invention, an adaptive filter network is constructed using the aforementioned adaptive filter. An adaptive network refers to multiple nodes connected through a certain topology, which perform adaptive signal processing through self-learning and inter-node information interaction. Each node estimates parameters through an adaptive process, while nodes exchange data according to a certain cooperative strategy, enabling each node to transmit and share network information, thereby better approximating the network parameters. Therefore, adaptive networks have wide applications in industries such as wireless sensor networks, smart healthcare, video communication, tracking and positioning, and environmental monitoring. Distributed networks can more fully utilize the communication cooperation of network nodes, possessing better scalability and robustness.

[0029] The variable step-size robust adaptive filter network (VSS-DRGA) proposed in this invention employs model-driven real-time adjustment of the step size for updating filter coefficients, thereby further improving performance in impulse noise environments. In the filter network of this embodiment, the adaptive filter at each node has the same filtering process; specifically, for any adaptive filter in the filter network... All include: S201: Obtain Time and preceding consecutive The sampled value of the input signal input to the system to be estimated at time 1 , forming the input signal vector , represented as: ; S202: Obtain the adaptive filter exist Moment Adaptive weights To form an adaptive weight vector , represented as: ; S203: Calculate the dot product of the adaptive weight vector and the input signal vector, which serves as the adaptive filter. exist Output signal at time , represented as ; S204: Calculation Preset expected signal at time The difference between the output signal and the output signal is obtained. Time estimation error signal , represented as: ; S205: Based on The estimated error signal at time step is used to calculate the nonlinear error factor of the robust generalized adaptive filter. , is denoted as: ; wherein, is a shape parameter which can be negative, is a shape parameter which is positive, is a scale parameter; denotes a sign function operation, which returns 1 when the input is positive, -1 when the input is negative, and 0 when the input is 0; denotes taking the absolute value; S206: based on the adaptive weight vector at time k, calculate the exponential smoothing online estimation of the variable step-size related term at time k, based on the outer product and trace, the candidate variable step-size is obtained by minimizing the mean square error, including: calculating the estimation formula of the term related to the error signal and the nonlinear error factor in the candidate variable step-size value at time k ; ; ; ; ; by smoothing the estimation of at time k and ; ; ; ; ; ; ; ; wherein, is a regularization factor to prevent the denominator from being zero, which is a very small positive number; is a forgetting factor; denotes the trace operation of a matrix, denotes the correlation matrix of the input signal vector, defined as , denotes the variance value of the noise; S207: truncate and time smooth the candidate variable step-size to obtain the final target variable step-size, including: S207-1: based on the set maximum step-size value , the maximum value , the minimum value , the candidate variable step-size is truncated to obtain the optimized variable step-size , denoted as: ; S207-2: based on the pre-set weighting factor ,right Time-based optimization with variable step size With the The target step size at any given time is variable. Perform time smoothing to obtain The target step size at any given time is variable. , represented as: ; S208: For the first filter network An adaptive filter, based on The input signal vector at each time step, the estimation error signal, and the target variable step size are updated using error nonlinearity. The adaptive weight vector at time step 1 is used to obtain the weight vector of the filter network at time step 2. An adaptive filter in intermediate estimated adaptive weight vector at time step , represented as: ; in, Indicates the first An adaptive filter in The target adaptive weight vector at time step. Indicates the first An adaptive filter in The target step size at any given time is variable. Indicates the first An adaptive filter in Nonlinear error factor at time step Indicates the first An adaptive filter in The input signal vector at time t; S209: The first filter network An adaptive filter in The intermediate estimated adaptive weight vector at time step 1 is combined with the intermediate estimated adaptive weight vectors of its neighbors to update its parameter estimates, thus obtaining the _th ... An adaptive filter in The target adaptive weight vector at time step , represented as: ; in, Represents the first filter in the filter network. The set of neighboring adaptive filters directly connected to an adaptive filter; In the filter network, the first The first adaptive filter The preset joint coefficients of the neighbor adaptive filter, , , denotes the number of neighbor adaptive filters in the adaptive filter network; denotes the th adaptive filter in the adaptive filter network; denotes the intermediate estimated adaptive weight vector of the th neighbor adaptive filter of the th adaptive filter at time S210: for each adaptive filter in the adaptive filter network, calculate the inner product of its adaptive weight vector at time and the input signal vector, and obtain the output signal of the system to be estimated at time

[0030] In the embodiments of the present application, the joint coefficient can be designed using uniform weight, Metropolis, Laplacian, etc. Based on the joint coefficient designed by uniform weight, all neighbors have equal weights, which is suitable for scenarios where all nodes are equal, the network topology is relatively uniform, and the data reliability of all nodes is similar; based on the joint coefficient designed by Metropolis, the weight of each neighbor is inversely proportional to its own connection degree, and then the weight vector of all nodes converges to the same value; based on the joint coefficient designed by Laplacian, the weight of each neighbor is designed depending on the topology structure of the filter network, which can naturally capture the spatial relationship between nodes. Users can select the most suitable cooperation rule according to specific application requirements, such as pursuing fairness, fast consensus or using graph structure, and the topology structure of the filter network and node reliability, so as to formulate the joint coefficient of each node.

[0031] In the filter network of the present application, each adaptive filter constructs an adaptive weight vector and a regression vector according to the adaptive weight and the input signal sample value, and the inner product generates an output signal and obtains an estimation error signal; based on the estimation error signal, a nonlinear response factor of a robust generalized adaptive filter is calculated and combined with an input vector to update the adaptive weight vector; further based on the outer product and the trace of the robust generalized adaptive filter minimization framework, the estimation statistics are recursively estimated and the step size varying with time is calculated; the optimal step size is truncated and smoothed to obtain a variable step size value; the filter is further extended to a distributed network, and each node exchanges information with all its neighboring nodes; it can have faster convergence speed and lower steady-state deviation, and has strong anti-impulse performance.

[0032] The variable step robust adaptive filter provided by the application introduces a model-driven variable step design, calculates a candidate step based on the outer product and trace minimization of the mean square deviation at the next moment, and obtains a target variable step at each moment through truncation and time smoothing, so that the adaptive filter can adopt a larger step in the initial stage to accelerate convergence, and automatically reduce the step to reduce steady-state misadjustment when approaching the steady state, thereby achieving a good compromise between convergence speed and steady-state accuracy; meanwhile, the application introduces an error nonlinear term to compensate for the filtering deviation caused by the existence of impulse noise in the system, so that the adaptive filtering process is more robust, and a filtering result with faster convergence speed and better robust performance is obtained.

[0033] Based on the above embodiment, in order to prove the effectiveness of the application, the performance of the variable step robust adaptive filter (VSS-RGA) and the filter network (VSS-DRGA) provided by the application is verified by computer experiment. The experiment estimates an unknown system in a system identification application scene containing impulse noise interference, and compares the experimental results with those of the least mean square (LMS) adaptive filter, the sign error (SA) adaptive filter, the generalized maximum correlation entropy (GMCC) adaptive filter, the robust generalized adaptive (RGA) filter, and the filter network corresponding to each adaptive filter.

[0034] Referring to Figure 2 , it is a structural block diagram of the variable step robust adaptive filter. The noise signal of the embodiment is Gaussian noise plus impulse noise; the system identification scene experiment adopts normalized mean square deviation (NMSD) as a performance measure, that is, , in dB, wherein represents taking the logarithm, is the weight value of the actual system.

[0035] The noise signal used in the experiment contains a zero-mean Gaussian white noise with a variance of and an impulse noise , that is, . The impulse noise is generated by a Bernoulli Gaussian process, that is, , wherein is a Bernoulli process, and the probability of taking 0 is 0.95 and the probability of taking 1 is 0.05, is a zero-mean Gaussian white noise.

[0036] Referring to Figure 3 , it is a comparison diagram of the normalized mean square deviation curves of different adaptive filters in the system identification scene; the parameters of each method are LMS( ), SA ( ), GMCC , ), RGA( , , , VSS-RGA , , , , ).

[0037] Reference Figure 4 The figure shows a comparison of normalized mean square deviation curves for different adaptive filter networks in a distributed system identification scenario; the parameters of each method are DLMS ( DSA ), DGMCC , ),DRGA( , , , VSS-DRGA , , , ).

[0038] Depend on Figure 3 and Figure 4 As can be seen, whether it is a system identification scenario of a single-node adaptive filter or a distributed filter network, the VSS-RGA adaptive filter and VSS-DRGA adaptive filter network of the present application have good anti-impulse performance and can take into account both low steady-state offset and fast convergence speed.

[0039] The variable step-size robust adaptive filter described in this invention introduces a nonlinear error factor by performing a nonlinear transformation on the estimation error signal to compensate for the filtering deviation caused by impulse noise. This makes the adaptive filtering process more robust, resulting in filtering results with faster convergence and better robust performance. Simultaneously, based on the nonlinear error factor, the target variable step size is constructed by minimizing the mean square deviation. The filter uses a larger step size initially to accelerate convergence, and automatically reduces the step size near steady state to reduce steady-state misalignment, thus achieving a good trade-off between convergence speed and steady-state accuracy. This invention achieves this by adaptively updating the filter... When the target step size is variable, the mean square error of the next time step is minimized based on the outer product and trace taking, and then estimated online. To obtain the effective error estimate, correlation coefficient, average error estimate, and nonlinear error estimate at each time step. The candidate variable step size of the time instant, and then the target variable step size is obtained through truncation and time smoothing The target variable step size of the time instant. Based on the optimal criterion of minimizing the mean square deviation of the next time instant, the present application estimates key statistics such as effective error and correlation coefficient in real time online, calculates the theoretically optimal candidate step size, and finally obtains the target step size which is both safe and smooth through truncation and time smoothing. This design enables the filter to automatically adopt a larger step size to achieve fast tracking in the early stage of convergence, and automatically switch to a small step size to achieve fine adjustment when approaching the steady state, thereby intelligently balancing the core contradiction between convergence speed and steady-state accuracy. At the same time, this mechanism works together with the nonlinear error factor to ensure the excellent robustness and stability of the filter in complex environments such as pulse noise. The filter network constructed based on the variable step size robust adaptive filter of the present application is based on the mechanism of updating each adaptive filter first and then jointly with its neighbor adaptive filter, based on information sharing and knowledge diffusion, so that the adaptive filter can quickly converge to the accurate weight, and can effectively utilize the dispersed information in the filter network, thereby speeding up the identification process of the entire network to the real system and improving the identification efficiency; at the same time, the filter network will not collapse due to the failure of a few nodes, even if the data of a certain node is temporarily completely wrong, it will be corrected by the correct information of other normal nodes in the joint step, further ensuring the robustness of the filter.

[0040] Those skilled in the art will appreciate that embodiments of the present application can be provided as methods, systems, or computer program products. Accordingly, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment, or an embodiment combining software and hardware aspects. Furthermore, the present 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-ROMs, optical storage, etc.) having computer usable program code embodied thereon.

[0041] The present application is described with reference to flowcharts and / or block diagrams according to the methods, devices (systems), and computer program products of the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, as well as combinations of flows and / or blocks in the flowcharts 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, a special-purpose computer, an embedded processor, or other programmable data processing apparatus to produce a machine, so that the instructions executed by the processor of the computer or other programmable data processing apparatus produce a means for implementing the functions specified in the flowcharts and / or block diagrams. Figure 1 The means for implementing one or more functions specified in one or more flows and / or blocks. Figure 1 The means for implementing one or more functions specified in one or more flows and / or blocks.

[0042] These computer program instructions can also be stored in a computer readable memory that can direct a computer or other programmable data processing apparatus to function in a particular manner, such that the instructions stored in the computer readable memory produce an article of manufacture including instructions which implement the Figure 1 function specified in the flow or flows and / or blocks Figure 1 of the block or blocks.

[0043] These computer program instructions can also be loaded onto a computer or other programmable data processing apparatus to cause a series of operational steps to be performed on the computer or other programmable apparatus to produce a computer implemented process such that the instructions that are executed on the computer or other programmable apparatus provide steps for implementing the Figure 1 function specified in the flow or flows and / or blocks Figure 1 of the block or blocks.

[0044] Obviously, the above-described embodiments are only examples and are not intended to limit the present application. Based on the above description, one of ordinary skill in the art can make other variations and changes without departing from the present application. It is not necessary to recite all of the embodiments, and obvious changes or variations are not included herein. However, such obvious changes or variations are still within the scope of the present application.

Claims

1. A variable step-size robust adaptive filter, characterized by, Comprising: acquisition the time instant and the sampling values of the input signal to the system to be estimated, which are input to the adaptive filter at the time instant the input signal vector of the adaptive filter at the time instant The adaptive filter obtains a plurality of adaptive weights at a time instant, and forms an adaptive weight vector at the time instant. The adaptive filter obtains a plurality of adaptive weights at a time instant, and forms an adaptive weight vector at the time instant. The adaptive filter obtains a plurality of adaptive weights at a time instant, and forms an adaptive weight vector at the time instant. acquiring the inner product of the adaptive weight vector at the time instant and the input signal vector as the output signal of the adaptive filter at the time instant ​ based on a preset desired signal and the output signal at the time instant, obtaining an estimation error signal at the time instant; right After performing a nonlinear transformation on the time-estimation error signal, it is adjusted using preset shape parameters to construct... The nonlinear error factor at time step; Based on the input signal vector at the time instant, the estimation error signal and the non-linear error factor, the mean square deviation minimization is used to obtain the candidate variable step size at the time instant, and the truncation and time smoothing are performed to obtain the target variable step size at the time instant; based on The input signal vector at time step, the nonlinear error factor, and the target variable step size, for The adaptive weight vector at time step is updated to obtain... The adaptive weight vector at time step.

2. The variable step-size robust adaptive filter of claim 1, wherein, Get The dot product of the adaptive weight vector and the input signal vector at time t is used as the adaptive filter's... The output signal at time t is represented as: ； wherein denotes the output signal of the adaptive filter at the time instant ; denotes the transpose of the adaptive weight vector at the time instant ; , denotes the th adaptive weight of the adaptive weight vector at the time instant ; , denotes the total number of adaptive weights; denotes the input signal vector at the time instant , , denotes the sample value of the input signal at the time instant ; denotes the sample value of the input signal at the time instant ; denotes the sample value of the input signal at the time instant 3. The variable step-size robust adaptive filter of claim 1, wherein, On After the estimation error signal of the time instant is nonlinearly transformed, a preset shape parameter is used for adjustment to construct The nonlinear error factor of the time instant is expressed as: ； wherein denotes a non-linear error factor at time instant denotes a preset size parameter; denotes an estimation error signal at time instant , denotes a preset desired signal at time instant denotes an output signal of the adaptive filter at time instant ; denotes a sign function, and denote a negative shape parameter and a positive shape parameter, respectively, denotes an absolute value operation.

4. The variable step-size robust adaptive filter of claim 1, wherein, Based on the input signal vector at the time instant, the estimation error signal and the non-linear error factor, the target variable step size at the time instant is obtained by using the minimum mean square error the candidate variable step size at the time instant, and the target variable step size at the time instant is obtained by truncating and time smoothing the target variable step size at the time instant, comprising: Based on The effective error estimation of the moment is obtained by using the exponential moving average method on The effective error estimation of the moment is obtained by using the exponential moving average method on The effective error estimation of the moment is obtained by using the exponential moving average method on Based on The average error estimate of the time instant is obtained by using the exponential moving average method to perform exponential smoothing on the square of the estimated error signal of the time instant The average error estimate of the time instant is obtained by using the exponential moving average method to perform exponential smoothing on the square of the estimated error signal of the time instant The average error estimate of the time instant is obtained by using the exponential moving average method to perform exponential smoothing on the square of the estimated error signal of the time instant Utilizing the average error estimate of the time instant the effective error estimate of the time instant is standardized to obtain the correlation coefficient of the time instant; Based on The nonlinear error estimation at the time t is obtained by using the exponential moving average method to perform exponential smoothing on the square of the nonlinear error factor at the time t. The nonlinear error estimation at the time t is obtained by using the exponential moving average method to perform exponential smoothing on the square of the nonlinear error factor at the time t. The nonlinear error estimation at the time t is obtained by using the exponential moving average method to perform exponential smoothing on the square of the nonlinear error factor at the time t. Based on the correlation coefficient, the average error estimate, the nonlinear error estimate, the noise variance value at the time instant, and the trace of the correlation matrix of the input signal vector, a candidate variable step size at the time instant is obtained the correlation coefficient, the average error estimate, the nonlinear error estimate, the noise variance value at the time instant, and the trace of the correlation matrix of the input signal vector, a candidate variable step size at the time instant is obtained Using a preset safety step size, for The candidate variable step size at time step is truncated to obtain Optimization of timing with variable step size; Will Optimization of time step size and the first step The target at each time step is weighted and fused to obtain the result. The target step size can be changed at any given time.

5. The variable step-size robust adaptive filter of claim 4, wherein, The obtaining of the correlation coefficient of the time instant comprises: Based on the effective error estimation at the time instant , the estimation error signal at the time instant is exponentially smoothed with a non-linear error factor to obtain the effective error estimation at the time instant , denoted as: ;​ Based on the average error estimation at the time instant , the estimation error signal at the time instant is exponentially smoothed to obtain the average error estimation at the time instant , denoted as: ;​​ Utilizing the average error estimate of the time instant the effective error estimate of the time instant is standardized to obtain the correlation coefficient of the time instant is expressed as: ； wherein, represents a preset forgetting factor, is a regularization factor to prevent the denominator from being 0.

6. The variable step-size robust adaptive filter of claim 5, wherein, Based on the correlation coefficient, the average error estimate, the nonlinear error estimate, the noise variance value at the time instant, and the trace of the correlation matrix of the input signal vector, a candidate variable step size at the time instant is obtained the correlation coefficient, the average error estimate, the nonlinear error estimate, the noise variance value at the time instant, and the trace of the correlation matrix of the input signal vector, a candidate variable step size at the time instant is obtained Based on nonlinear error estimation at time t , the square of the nonlinear error factor at time t is exponentially smoothed using an exponential moving average method to obtain the nonlinear error estimation at time t , which is expressed as: ;​​​ Based on the correlation coefficient of the time instant , the average error estimate , the nonlinear error estimate , the noise variance value , and the trace of the correlation matrix of the input signal vector , a candidate variable step size for the time instant is obtained , denoted as: ;​ Wherein, the correlation matrix of the input signal vector , represented as , This represents the expectation operation. and They represent The input signal vector at time t and its corresponding transpose.

7. The variable step-size robust adaptive filter of claim 4, wherein, based on candidate variable step size acquisition target variable step size Using a preset safety step size , the candidate variable step size at the time instant is truncated to obtain the optimized variable step size at the time instant ; Utilizing preset weighting factors , the optimization variable step size at the moment is determined by the target variable step size at the moment , and the weighting factor at the moment , and is expressed as: .

8. The variable step-size robust adaptive filter of claim 1, wherein, Based on the input signal vector at the time instant, the nonlinear error factor and the target variable step size, the adaptive weight vector at the time instant is updated to obtain the adaptive weight vector at the time instant, denoted as: the adaptive weight vector at the time instant, denoted as: ； wherein denotes an adaptive weight vector at time instant denotes an adaptive weight vector at time instant denotes a target variable step size at time instant denotes a non-linear error factor at time instant denotes an input signal vector at time instant 9. A filter network based on the variable step-size robust adaptive filter according to any one of claims 1 to 8, characterized in that, Comprising: connecting the plurality of adaptive filters to obtain a filter network; For each adaptive filter in the filter network, based on the input signal vector at the current time instant, a non-linear error factor and a target variable step size, the adaptive weight vector at the current time instant is updated to obtain an intermediate estimated adaptive weight vector at the current time instant. For each adaptive filter in the filter network, based on the input signal vector at the current time instant, a non-linear error factor and a target variable step size, the adaptive weight vector at the current time instant is updated to obtain an intermediate estimated adaptive weight vector at the current time instant. For each adaptive filter in the filter network, based on the input signal vector at the current time instant, a non-linear error factor and a target variable step size, the adaptive weight vector at the current time instant is updated to obtain an intermediate estimated adaptive weight vector at the current time instant. For each adaptive filter in For each adaptive filter in the filter network, based on a preset joint coefficient, each neighbor adaptive filter directly connected with the adaptive filter is weighted and summed based on an intermediate estimation adaptive weight vector at the moment to obtain a target adaptive weight vector of each adaptive filter in the filter network at the moment .

10. The filter network of claim 9, wherein, The target adaptive weight vector at the time instant t for each adaptive filter in the filter network is denoted as: The target adaptive weight vector at the time instant t for each adaptive filter in the filter network is denoted as: ； in, In the filter network, the first An adaptive filter in The target adaptive weight vector at any given time; Represents the first filter in the filter network. The set of neighboring adaptive filters directly connected to an adaptive filter; In the filter network, the first The first adaptive filter The preset joint coefficients of the neighbor adaptive filter, , , express The number of middle-neighbor adaptive filters; Indicates the first The first adaptive filter A neighbor adaptive filter in The intermediate estimated adaptive weight vector at time step; for any adaptive filter in the filter network, its... The intermediate estimated adaptive weight vector at time step is represented as follows: , Indicates the first An adaptive filter in The target adaptive weight vector at time step. Indicates the first An adaptive filter in The target step size at any given time is variable. Indicates the first An adaptive filter in Nonlinear error factor at time step Indicates the first An adaptive filter in The input signal vector at time t.

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