Variable step-size robust adaptive filter and filter network

Abstract

The application relates to the technical field of adaptive filtering, and discloses a variable-step-size robust adaptive filter and a filter network, which are aimed at solving the technical problem that a traditional adaptive filter cannot effectively balance convergence speed, steady-state accuracy and anti-pulse noise interference. A nonlinear error factor is introduced, a large error caused by pulse noise is effectively suppressed through a generalized function form of the nonlinear error factor, and the robustness of a filtering process is significantly improved; meanwhile, a variable step-size mechanism is proposed, a theoretically optimal candidate step size is calculated online by minimizing a mean square deviation at a next moment, and an adaptive target variable step size is generated through truncation and time smoothing processing, so that a dynamic balance between fast convergence and low steady-state misadjustment is realized. The filter is expanded to a distributed network, each node follows a diffusion strategy of first updating and then combining, and a joint coefficient is used to realize global information sharing and performance collaborative optimization.

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 different norms of error 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 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:

[0008] 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;

[0009] Obtaining the adaptive filter in Multiple adaptive weights at time points constitute The adaptive weight vector at time step;

[0010] 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;

[0011] based on The preset expected signal and output signal at time are obtained. The estimation error signal at time;

[0012] 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;

[0013] 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.

[0014] 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, and the adaptive weight vector at the time instant is obtained.

[0015] 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, expressed as:

[0016] ;

[0017] wherein, denotes the output signal of the adaptive filter at the time instant; denotes the adaptive weight vector 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 adaptive weight value in 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 , denotes the sample value of the input signal at the time instant denotes the sample value of the input signal at the time instant ,

[0018] Preferably, the estimated error signal at the time instant is subjected to nonlinear transformation, and then adjusted by using a preset shape parameter to construct the nonlinear error factor at the time instant, expressed as:

[0019] ;

[0020] wherein, denotes the nonlinear error factor at the time instant denotes the preset size parameter denotes the estimated error signal at the time instant , denotes the preset expected signal at the time instant denotes the output signal of the adaptive filter at the time instant denotes the output signal of the adaptive filter at the time instant denotes the preset expected signal at the time instant denotes the output signal of the adaptive filter 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, denotes a positive shape parameter, denotes an absolute value operation.

[0021] Preferably, based on the input signal vector, the estimation error signal and the nonlinear error factor at the time instant, the candidate variable step size at the time instant is obtained by using the least mean square deviation minimization, the target variable step size at the time instant is obtained by truncating and time smoothing the candidate variable step size at the time instant,

[0022] based on the effective error estimation at the time instant, the estimation error signal and the nonlinear error factor at the time instant are exponentially smoothed by using the exponential moving average method to obtain the effective error estimation at the time instant,

[0023] based on the average error estimation at the time instant, the square of the estimation error signal at the time instant is exponentially smoothed by using the exponential moving average method to obtain the average error estimation at the time instant,

[0024] the correlation coefficient at the time instant is obtained by normalizing the effective error estimation at the time instant by using the average error estimation at the time instant,

[0025] based on the correlation coefficient, the average error estimation, the nonlinear error estimation and the noise variance value at the time instant, and the trace of the correlation matrix of the input signal vector, the candidate variable step size at the time instant is obtained,

[0026] the optimized variable step size at the time instant is obtained by truncating the candidate variable step size at the time instant by using the preset safety step size,

[0027] the target variable step size at the time instant is obtained by weightedly fusing the optimized variable step size at the time instant and the target variable step size at the time instant,

[0028] the target variable step size at the time instant is obtained by weightedly fusing the optimized variable step size at the time instant and the target variable step size at the time instant.​​​​​​​​​​​​​​​​​​​​​

[0029] Preferably, The correlation coefficient at time k is obtained by:

[0030] Based on the effective error estimate at time k, the estimation error signal at time k is obtained by: The effective error estimate at time k is obtained by exponentially smoothing the estimation error signal at time k with an exponential moving average method, and is represented as: The estimation error signal at time k is obtained by: Exponentially smoothing the nonlinear error factor at time k with an exponential moving average method, the effective error estimate at time k is obtained by: The effective error estimate at time k is obtained by exponentially smoothing the estimation error signal at time k with an exponential moving average method, and is represented as: The average error estimate at time k is obtained by:

[0031] Based on the average error estimate at time k, the estimation error signal at time k is obtained by: Exponentially smoothing the square of the estimation error signal at time k with an exponential moving average method, the average error estimate at time k is obtained by: The average error estimate at time k is obtained by exponentially smoothing the square of the estimation error signal at time k with an exponential moving average method, and is represented as: The correlation coefficient at time k is obtained by: The correlation coefficient at time k is obtained by:

[0032] The correlation coefficient at time k is obtained by: The correlation coefficient at time k is obtained by: The correlation coefficient at time k is obtained by:

[0033] ;

[0034] wherein, denotes a preset forgetting factor, is a regularization factor to prevent the denominator from being zero.

[0035] Preferably, the candidate variable step size at time k is obtained based on the correlation coefficient at time k, the average error estimate at time k, the nonlinear error estimate at time k, the noise variance value, and the trace of the correlation matrix of the input signal vector, and includes: The nonlinear error estimate at time k is obtained by:

[0036] The nonlinear error estimate at time k is obtained by: Exponentially smoothing the square of the nonlinear error factor at time k with an exponential moving average method, the nonlinear error estimate at time k is obtained by: The nonlinear error estimate at time k is obtained by exponentially smoothing the square of the nonlinear error factor at time k with an exponential moving average method, and is represented as: The nonlinear error estimate at time k is obtained by exponentially smoothing the square of the nonlinear error factor at time k with an exponential moving average method, and is represented as: The nonlinear error estimate at time k is obtained by exponentially smoothing the square of the nonlinear error factor at time k with an exponential moving average method, and is represented as:

[0037] The nonlinear error estimate at time k is obtained by exponentially smoothing the square of the nonlinear error factor at time k with an exponential moving average method, and is represented as: ​​​​​​​​​​​​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 , represented as: ;

[0038] 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.

[0039] Preferably, based on Acquisition of candidate variable step size at time step The target step size at any given time is variable, including:

[0040] Using preset safety step size ,right Candidate variable step size at time Truncate and obtain Time-based optimization with variable step size , represented as: ;

[0041] 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: .

[0042] 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:

[0043] ;

[0044] 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.

[0045] This embodiment provides a filter network based on the variable step-size robust adaptive filter described above, including:

[0046] Connect multiple adaptive filters to obtain the filter network;

[0047] 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;

[0048] For each adaptive filter in the filter network, based on preset joint coefficients, the adaptive filters directly connected to it are... The intermediate estimated adaptive weight vectors at time points are weighted and summed to obtain the values ​​of each adaptive filter in the filter network. The target adaptive weight vector at time step.

[0049] Preferably, each adaptive filter in the filter network is in The target adaptive weight vector at time t is expressed as:

[0050] ;

[0051] 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 at time an intermediate estimate adaptive weight vector at time an intermediate estimate adaptive weight vector at time , an objective adaptive weight vector of the th adaptive filter at time an objective adaptive weight vector of the th adaptive filter at time an objective variable step-size of the th adaptive filter at time a non-linear error factor of the th adaptive filter at time a non-linear error factor of the th adaptive filter at time an input signal vector of the th adaptive filter at time

[0052] The above technical solutions of the present application have the following beneficial effects compared with the prior art:

[0053] The variable step-size robust adaptive filter has the following beneficial effects: the non-linear error factor is introduced by performing non-linear 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 the filtering result has faster convergence speed and better robust performance; and based on the non-linear error factor, the objective variable step-size is constructed by using the minimum mean square deviation, so that the filter uses a larger step-size in the initial stage to accelerate convergence, and automatically reduces the step-size when approaching the steady state to reduce the steady-state deviation, thereby achieving a good compromise between convergence speed and steady-state accuracy.

[0054] The present application obtains the objective variable step-size at time based on the outer product and the trace minimization of the mean square deviation at next time, and obtains the effective error estimate, the correlation coefficient, the average error estimate and the non-linear error estimate at time by online estimation, to obtain the candidate variable step-size at time , and then obtains the objective variable step-size at time The target variable step size at each moment. Based on the optimal criterion of minimizing the mean square error at the next moment, the present application estimates the 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 after truncation and time smoothing processing. This design enables the filter to automatically adopt a larger step size to achieve rapid tracking at the initial 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.

[0055] The filter network constructed based on the variable step size robust adaptive filter, 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 accurate weights, 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. BRIEF DESCRIPTION OF DRAWINGS

[0056] In order to make the content of the present application more easily understood, the present application will be further described in detail below according to specific embodiments of the present application and in conjunction with the drawings, in which:

[0057] Figure 1 is a step flow chart of the variable step size robust adaptive filter provided by the present application;

[0058] Figure 2 is a structural block diagram of the variable step size robust adaptive filter;

[0059] Figure 3 is a comparison chart of normalized mean square error curves of different adaptive filters in a system identification scenario;

[0060] Figure 4 is a comparison chart of normalized mean square error curves of different adaptive filter networks in a distributed system identification scenario. DETAILED DESCRIPTION

[0061] The present application will be further described below in conjunction with the drawings and specific embodiments, so that those skilled in the art can better understand the present application and implement it, but the embodiments are not limiting to the present application.

[0062] Referring to Figure 1 the step flow chart of the variable step size robust adaptive filter of the present application, the specific steps include:

[0063] S101: Obtain 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. Input signal vector at time 1 , represented as:

[0064] , express The sampled value of the input signal at time t. express The moment before The sampled value of the input signal at each moment. Indicates the transpose operation;

[0065] S102: Obtain the adaptive filter in Multiple adaptive weights at time points constitute Adaptive weight vector at time step , represented as:

[0066] , express The first time in the adaptive weight vector at time step An adaptive weight, , Indicates the total number of adaptive weights;

[0067] S103: Acquisition 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 , represented as ;

[0068] S104: Based on The preset expected signal and output signal at time are obtained. Time estimation error signal , represented as , express The preset expected signal at a given time;

[0069] 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:

[0070] ;

[0071] wherein, denotes a preset dimension parameter; denotes a sign function, denotes a negative shape parameter and a positive shape parameter, denotes an absolute value operation;

[0072] S106: based on the input signal vector at the moment, the estimation error signal and the nonlinear error factor, the candidate variable step size at the moment is obtained by using the least mean square deviation, and the truncation and time smoothing are performed to obtain the target variable step size at the moment; S106: based on the input signal vector at the moment, the estimation error signal and the nonlinear error factor, the candidate variable step size at the moment is obtained by using the least mean square deviation, and the truncation and time smoothing are performed to obtain the target variable step size at the moment; S106: based on the input signal vector at the moment, the estimation error signal and the nonlinear error factor, the candidate variable step size at the moment is obtained by using the least mean square deviation, and the truncation and time smoothing are performed to obtain the target variable step size at the moment; S106: based on the input signal vector at the moment, the estimation error signal and the nonlinear error factor, the candidate variable step size at the moment is obtained by using the least mean square deviation, and the truncation and time smoothing are performed to obtain the target variable step size at the moment;

[0073] S107: based on the input signal vector at the moment, the nonlinear error factor and the target variable step size, the adaptive weight vector at the moment is updated to obtain the adaptive weight vector at the moment. S107: based on the input signal vector at the moment, the nonlinear error factor and the target variable step size, the adaptive weight vector at the moment is updated to obtain the adaptive weight vector at the moment. S107: based on the input signal vector at the moment, the nonlinear error factor and the target variable step size, the adaptive weight vector at the moment is updated to obtain the adaptive weight vector at the moment. S107: based on the input signal vector at the moment, the nonlinear error factor and the target variable step size, the adaptive weight vector at the moment is updated to obtain the adaptive weight vector at the moment.

[0074] The variable step size 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 least mean square deviation is used to construct a target variable step size, so that the filter uses a larger step size in the initial stage to accelerate convergence, and automatically reduces the step size when approaching a steady state to reduce steady-state distortion, thereby achieving a good compromise between convergence speed and steady-state accuracy.

[0075] Specifically, in step S106, the target variable step size at the moment is obtained, including:

[0076] S106-1: based on the effective error estimation at the moment, the exponential smoothing is performed on the estimation error signal at the moment and the nonlinear error factor at the moment by using the exponential moving average method to obtain the effective error estimation at the moment, denoted as: , denotes a preset forgetting factor; S106-2: based on the average error estimation at the moment, the exponential smoothing is performed on the estimation error signal at the moment and the nonlinear error factor at the moment by using the exponential moving average method to obtain the effective error estimation at the moment, denotes a preset forgetting factor;

[0077] S106-2: based on the average error estimation at the moment, the exponential smoothing is performed on the estimation error signal at the moment and the nonlinear error factor at the moment by using the exponential moving average method to obtain the effective error estimation at the moment, ​​​​Square of the estimation error signal of the time instant Exponential smoothing is performed on the square of the nonlinear error factor of the time instant Average error estimation of the time instant , is expressed as: ;

[0078] S106-3: The average error estimation of the time instant is standardized on the effective error estimation of the time instant to obtain the correlation coefficient of the time instant Average error estimation of the time instant , To prevent the denominator from being 0, a regularization factor is added;

[0079] S106-4: Based on the nonlinear error estimation of the time instant , the exponential moving average method is used to perform exponential smoothing on the square of the nonlinear error factor of the time instant Nonlinear error estimation of the time instant , is expressed as: ; ;

[0080] S106-5: Based on the correlation coefficient of the time instant , the average error estimation , the nonlinear error estimation , the noise variance value , and the trace of the correlation matrix of the input signal vector , the candidate variable step size of the time instant , is expressed as: , , , , represents the expected operation, , and , respectively, represent the input signal vector of the time instant and its corresponding transpose;

[0081] 106-6: The candidate variable step size of the time instant is truncated using a preset safe step size , to obtain the optimized variable step size of the time instant , is expressed as: ; S106-7: The optimized variable step size of the time instant is multiplied by a preset weighting factor

[0082] , to obtain the final variable step size of the time instant .​​​​​​​​​​​ 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: .

[0083] This invention acquires adaptive updates 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 at time point is then truncated and time-smoothed to obtain... The target step size is variable. Based on the optimal criterion of minimizing the mean square deviation at the next time step, this invention estimates key statistics such as effective error and correlation coefficient online in real time, calculates the theoretically optimal candidate step size, and then performs truncation and time smoothing to finally obtain a safe and smooth target step size. This design enables the filter to automatically use a larger step size for fast tracking in the early stages of convergence, and automatically switches to a smaller step size for fine adjustment as it approaches steady state, thus intelligently balancing the core contradiction between convergence speed and steady-state accuracy. Simultaneously, this mechanism works in conjunction with the nonlinear error factor to ensure the filter's excellent robustness and stability under complex environments such as impulse noise.

[0084] Specifically, in acquiring The target step size at any given time is variable. Afterwards, combined Input signal vector at time 1 Nonlinear error factor ,right Adaptive weight vector at time step Update and obtain Adaptive weight vector at time step , represented as: Adaptive filter calculation The dot product of the adaptive weight vector and the input signal vector at time t is used to obtain the adaptive filter's performance at time t. The output signal at any given time.

[0085] 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.

[0086] 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:

[0087] 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:

[0088] ;

[0089] S202: Obtain the adaptive filter exist Moment Adaptive weights To form an adaptive weight vector , represented as:

[0090] ;

[0091] 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 ;

[0092] 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: ;

[0093] S205: Based on the estimation error signal of the time instant, the non-linear error factor of the robust generalized adaptive filter is calculated , denoted as:

[0094] ;

[0095] 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, returning 1 when the input is positive, -1 when the input is negative, and 0 when the input is 0; denotes taking the absolute value;

[0096] S206: Based on the adaptive weight vector of the time instant, the variable step size related item of the time instant is calculated , the exponential smoothing online estimation of the variable step size related item is obtained based on the outer product and trace, and the candidate variable step size is obtained by minimizing the mean square deviation , including:

[0097] The estimation formula of the candidate variable step size value of the time instant related to the error signal and the non-linear error factor is calculated, denoted as: ;

[0098] The estimation formula of the candidate variable step size of the time instant is smoothed to obtain and , the estimation formula of which is:

[0099] ; ; ;

[0100] The candidate variable step size of the time instant is constructed, denoted as: ;

[0101] 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;

[0102] ​​​​S207: Truncate and time-smooth the candidate variable step size to obtain the final target variable step size, including:

[0103] S207-1: Based on the set maximum step size value Using the maximum value Take the minimum value For candidate variable step size Perform truncation to obtain the optimized variable step size. , represented as: ;

[0104] S207-2: Based on preset weighting factors ,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: ;

[0105] 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:

[0106] ;

[0107] 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;

[0108] 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 1 , represented as:

[0109] ;

[0110] 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, , , 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;

[0111] S210: For each adaptive filter in the filter network, calculate its... The dot product of the adaptive weight vector and the input signal vector at time step 1 is used to obtain the system under estimation at time step 2. The output signal at any given time.

[0112] In this embodiment of the invention, the joint coefficient Joint coefficients can be designed using rules such as uniform weight, Metropolis, and Laplacian. Uniform weight-based joint coefficients assign equal weights to all neighbors, suitable for scenarios where all nodes are of equal status, the network topology is relatively uniform, and the data reliability of all nodes is similar. Metropolis-based joint coefficients ensure that the weight of each neighbor is inversely proportional to its own degree of connectivity, thus causing the weight vectors of all nodes to eventually converge to the same value. Laplacian-based joint coefficients design the weights of each neighbor based on the topology of the filter network, naturally capturing the spatial relationships between nodes. Users can choose the most suitable cooperation rule to formulate the joint coefficients of each node based on specific application requirements, such as pursuing fairness, fast consensus, or utilizing graph structures, as well as the topology and node reliability of the filter network.

[0113] Each adaptive filter in the filter network of the application constructs an adaptive weight vector and a regressor vector according to adaptive weights and input signal sample values, and generates an output signal by inner product and obtains an estimated error signal; a non-linear response factor of a robust generalized adaptive filter is calculated based on the estimated error signal and combined with an input vector to update the adaptive weight vector; further based on an outer product and a trace of the robust generalized adaptive filter minimization framework, an estimation statistic is recursively estimated and a time-varying step size 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, each node exchanges information with all adjacent nodes; the filter can have a faster convergence speed and a lower steady-state misadjustment, and has a strong anti-impulse performance.

[0114] The variable step size robust adaptive filter of the application introduces a model-driven variable step size design, estimates key statistics online and calculates a candidate step size based on the outer product and the trace minimization of the mean square deviation at the next time, and then obtains the target variable step size at each time through truncation and time smoothing, so that the adaptive filter can use a larger step size in the initial stage to speed up the convergence, and automatically reduce the step size when approaching the steady state to reduce the steady-state misadjustment, thereby achieving a good compromise between convergence speed and steady-state accuracy; at the same time, the application introduces an error non-linear term to compensate for the filtering deviation caused by the existence of impulse noise in the system in the presence of impulse noise, so that the adaptive filtering process is more robust, and the filter result has faster convergence speed and better robust performance.

[0115] Based on the above embodiment, in order to prove the effectiveness of the application, the performance of the variable step size 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 scenario containing impulse noise interference, and compares the experimental results with those of the least mean square (LMS) adaptive filter, the signed 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.

[0116] Referring to Figure 2 , the structure block diagram of the variable step size robust adaptive filter is shown. The noise signal of the embodiment is Gaussian noise plus impulse noise; the system identification scene experiment uses normalized mean square deviation (NMSD) as a performance measure, i.e. , in dB, where represents taking the logarithm, is the weight value of the actual system.

[0117] The noise signal used in the experiment It contains a mean of zero and a variance of . Gaussian white noise and a pulse noise ,Right now Impulse noise Produced by Bernoulli Gaussian process, i.e. ,in It is a Bernoulli process, and the probability of it taking the value 0 is 0.95 and the probability of it taking the value 1 is 0.05. Gaussian white noise with zero mean.

[0118] Reference Figure 3 The figure shows a comparison of the normalized mean square deviation (MSD) curves of different adaptive filters in the system identification scenario; the parameters of each method are LMS ( ), SA ( ), GMCC , ), RGA( , , , VSS-RGA , , , , ).

[0119] 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 , , , ).

[0120] Depend on Figure 3 and Figure 4 It is evident that, regardless of whether it is a single-node adaptive filter or a distributed filter network system identification scenario, the VSS-RGA adaptive filter and VSS-DRGA adaptive filter network of the present application implementation have good anti-impulse performance and can balance low steady-state offset and fast convergence speed.

[0121] 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 robustness. 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 at time point is then truncated and time-smoothed to obtain... The target step size is variable. Based on the optimal criterion of minimizing the mean square deviation at the next time step, this invention estimates key statistics such as effective error and correlation coefficient online in real time, calculates the theoretically optimal candidate step size, and then performs truncation and time smoothing to finally obtain a safe and smooth target step size. This design enables the filter to automatically use a larger step size for fast tracking in the early stages of convergence, and automatically switches to a smaller step size for fine adjustment as it approaches steady state, thus intelligently balancing the core contradiction between convergence speed and steady-state accuracy. Simultaneously, this mechanism works in conjunction with the nonlinear error factor to ensure the filter's excellent robustness and stability under complex environments such as impulse noise. This invention relates to a filter network constructed based on a variable step-size robust adaptive filter. Based on a mechanism where each adaptive filter is updated first and then combined with its neighboring adaptive filters, and leveraging information sharing and knowledge diffusion, the adaptive filters can quickly converge to accurate weights and effectively utilize the dispersed information within the filter network. This accelerates the entire network's identification process of the real system and improves identification efficiency. Furthermore, 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 incorrect, it will be corrected by the correct information from other normal nodes during the combination step, further ensuring the robustness of the filtering.

[0122] 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.

[0123] The 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 which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 one or more flow or blocks

[0124] The 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 which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 one or more flow or blocks

[0125] The 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 which execute on the computer or other programmable apparatus provide steps for implementing the functions specified in the flowchart block or blocks. Figure 1 one or more flow or blocks Figure 1 one or more flow or blocks

[0126] Obviously, the above-described embodiments are only examples for clarity of description and are not limiting on the embodiments. Based on the above description, one of ordinary skill in the art can further make other different forms of changes or modifications. Here, all the embodiments are not required to be enumerated, and the obvious changes or modifications derived therefrom are still within the protection 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 t is expressed as: ;in, express The nonlinear error factor at time; Indicates the preset size parameters; express The estimation error signal at time t is expressed as follows: , express The preset expected signal at a given time. Indicates that the adaptive filter is in Output signal at time; Represents a symbolic function. and These represent the negative shape parameters and the positive shape parameters, respectively. This indicates the absolute value operation; 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 time instant ; denotes the input signal vector at time instant ; denotes the transpose of the adaptive weight vector , denotes the th adaptive weight of the adaptive weight vector at time instant ; , denotes the total number of adaptive weights; denotes the input signal vector at time instant ; , denotes the sample value of the input signal at time instant ; denotes the sample value of the input signal at time instant ; denotes the sample value of the input signal at time instant 3. 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 truncation and time smoothing the target variable step size at the time instant, comprising: Based on the effective error estimate at the time instant , the estimation error signal is exponentially smoothed with a non-linear error factor to obtain the effective error estimate at the time instant , which is expressed as: ; Based on the average error estimation at time , the square of the estimation error signal at time is exponentially smoothed to obtain the average error estimation at time , denoted as: ;​​ Utilizing the average error estimate of the time instant the effective error estimate of the time instant is standardized, obtaining the correlation coefficient of the time instant , expressed as: ; Based on nonlinear error estimation at time , the square of the nonlinear error factor at time is exponentially smoothed using the exponential moving average method, to obtain the nonlinear error estimation at time , expressed as: ;​​ 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 , represented as: ; 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 length at the moment is obtained by the target variable step length at the moment is obtained by the target variable step length at the moment is obtained by ; wherein denotes a preset forgetting factor, is a regularization factor to prevent the denominator from being zero; the correlation matrix of the input signal vector denotes , denotes an expectation operation, and denote the input signal vector at the time instant and its corresponding transpose, respectively.

4. 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, which is expressed as: the adaptive weight vector at the time instant, which is expressed 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 5. A filter network based on the variable step-size robust adaptive filter according to any one of claims 1 to 4, 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 .

6. The filter network of claim 5, wherein, Each adaptive filter in the filter network The target adaptive weight vector at time t is expressed 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 Each 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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