Constrained Robust Adaptive Filters and Filter Networks Based on Conjugate Gradient Method
By combining linear constraints and nonlinear weighting functions with a constrained robust adaptive filter based on the conjugate gradient method, the robustness and convergence speed of the adaptive filter in the context of impulse noise are solved, achieving faster convergence and stronger robustness, which is applicable to fields such as smart healthcare, environmental monitoring, and precision agriculture.
Patent Information
- Authority / Receiving Office
- CN · China
- Patent Type
- Patents(China)
- Current Assignee / Owner
- SUZHOU UNIV
- Filing Date
- 2026-04-21
- Publication Date
- 2026-07-17
AI Technical Summary
Existing adaptive filters have poor robustness and slow convergence speed in impulse noise environments.
A constraint-robust adaptive filter based on the conjugate gradient method is adopted. By combining linear constraints and nonlinear weighting functions, the adaptive weights are updated through the conjugate gradient optimization method to construct a filter network to improve robustness and convergence speed.
Faster convergence speed and better robustness were achieved in impulse noise environments. The constructed filter network has self-correction capability in the event of node failure, ensuring the stability and robustness of the system.
Smart Images
Figure CN122068876B_ABST
Abstract
Description
Technical Field
[0001] This invention relates to the field of telephone communication technology, and in particular to a constrained robust adaptive filter and filter network based on the conjugate gradient method. Background Technology
[0002] System identification is an important branch of adaptive signal processing. Many problems, such as traditional adaptive noise cancellation, adaptive echo cancellation, and active noise control, can be reduced to system identification problems. Traditional least mean square (LMS) and normalized least mean square (NLMS) adaptive filters are easy to implement, but in certain special scenarios, the output signal of an unknown system may be affected by impulse noise, leading to a sharp decline in performance. To enhance the robustness of adaptive filters in impulse noise environments, engineers have designed a series of impulse noise-resistant adaptive filters, such as least mean square error symbols adaptive filters, maximum correlation entropy-based adaptive filters, and logical distance-based adaptive filters.
[0003] In certain application scenarios, the filter weight vector is subject to a linear constraint. In such scenarios, it is necessary to design appropriate linearly constrained adaptive filters to improve performance. This linear constraint often includes prior information from the actual application, such as the direction of signal arrival in adaptive beamforming. Based on the linearly constrained minimum variance (LCMV) filter in array signal processing, engineers have designed a linearly constrained minimum mean square (CLMS) filter. For cases where the input signal has specific correlations, engineers have designed constrained minimum recursive least squares filters and constrained affine projection filters.
[0004] Traditional constrained filters suffer significant performance degradation when encountering non-Gaussian impulse noise. To address this issue, researchers have designed robust linear constrained adaptive filters based on criteria such as minimum error entropy and maximum correlation entropy. To further enhance the performance of constrained filters in scenarios affected by non-Gaussian impulse noise, constrained minimum logarithmic hyperbolic cosine filters and constrained minimum mean M-estimation filters have been developed. However, these robust constrained filters suffer from slow convergence speeds or excessive coefficient parameters. Newton's method offers faster convergence, but the conjugate gradient method requires significantly less data storage compared to it, making it more suitable for solving large-scale problems. The conjugate gradient method offers a balance between convergence speed and computational complexity, and some researchers have designed constrained filters based on it; however, these filters exhibit poor robustness. Summary of the Invention
[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problems of poor filtering robustness and slow convergence speed of the adaptive filter in the prior art.
[0006] To address the aforementioned technical problems, this invention provides a constrained robust adaptive filter based on the conjugate gradient method, comprising:
[0007] Get Time and Before the moment The sampled values of the input signal input to the system to be estimated at each time point constitute... The input signal vector at time t is obtained by projection. The projected input signal vector at time t;
[0008] Obtaining the adaptive filter in Moment An adaptive weight set under linear constraints is formed. Adaptive weight vector at time step; 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. Output signal at time; calculation The difference between the expected signal and the output signal at time t is used to obtain... The estimation error signal at time;
[0009] based on The estimated error signal at time step is used to construct a nonlinear weighted function shape control parameter to... The nonlinear weighting function at time points;
[0010] based on The forgetting factor, nonlinear weighting function, projected input signal vector, and its transpose vector at each time step are obtained recursively through updates. The autocorrelation matrix at time step;
[0011] Initialize the conjugate search direction, residual vector, and update step size, based on The conjugate search direction at time step, residual vector, projected input signal vector, estimation error signal, and nonlinear weighting function are all present in the input signal vector. The autocorrelation matrix at time step 1 is obtained. The update step size at any given moment;
[0012] calculate The product of the update step size and the conjugate search direction at each time step, the pre-defined linear constraint correlation matrix, and The product of the adaptive weight vectors at each time step, and the sum of the vectors related to the preset linear constraints, are used to obtain the result. The adaptive weight vector at time step;
[0013] Among them, based on The update step size, conjugate search direction, residual vector, projected input signal vector, estimation error signal, and nonlinear weighting function at each time step are specified. The autocorrelation matrix at time t, for The residual vector and conjugate search direction are updated at each time step to obtain... The residual vector at each time step and the conjugate search direction are used to obtain... The update step size at any given moment.
[0014] Preferably, the adaptive filter is obtained in Moment An adaptive weight set under linear constraints is formed. Adaptive weight vector at time step , is represented as:
[0015] ;
[0016] The linear constraint condition is expressed as follows: ;
[0017] Indicates that the adaptive filter is in The first moment Each adaptive weight; Represented as size The constraint matrix, Indicates size is The constraint vector, Indicates the total number of constraints. , T represents transpose.
[0018] Preferably, based on The estimated error signal at time step is used to construct a nonlinear weighted function shape control parameter to... Nonlinear weighting function at time step , is represented as:
[0019] ;
[0020] in, express The estimation error signal at time t is expressed as follows: , express Expected signal at time, express Output signal at time; This represents the shape control parameter of the nonlinear weighted function.
[0021] Preferably, based on The forgetting factor, nonlinear weighting function, projected input signal vector, and its transpose vector at each time step are obtained recursively through updates. Autocorrelation matrix at time step , is represented as:
[0022] ;
[0023] in, express The forgetting factor of time; and express The projected input signal vector and its transpose vector at time t are denoted as: , express The input signal vector at time t, The predefined linear constraint correlation matrix, which is related to the linear constraint conditions, is represented as follows: ; Indicates size is The identity matrix, Represented as size The constraint matrix, where N represents the total number of constraints; express Projected input signal vector at any time The autocorrelation matrix.
[0024] Preferably, based on The conjugate search direction at time step, residual vector, projected input signal vector, estimation error signal, and nonlinear weighting function are all present in the input signal vector. The autocorrelation matrix at time step 1 is obtained. Update step size , is represented as:
[0025] ;
[0026] in, Represents the regularization term. express The residual vector at time step, and express The conjugate search direction at time and its transpose.
[0027] Preferably, calculation The product of the update step size and the conjugate search direction at each time step, the pre-defined linear constraint correlation matrix, and The product of the adaptive weight vectors at each time step and the sum of the vectors related to the preset linear constraints are used to obtain the result. Adaptive weight vector at time step , is represented as:
[0028] ;
[0029] in, express The adaptive weight vector at time step; The vector representing the predefined linear constraint related to the linear constraint is denoted as: , Indicates size is The constraint vector.
[0030] Preferably, Residual vector at time step , is represented as:
[0031] ;
[0032] in, express The forgetting factor of time, express The residual vector at time step, express The update step size at any moment, express The autocorrelation matrix at time t, and express The conjugate search direction at time step and its transpose. express The nonlinear weighting function at time t, express The projected input signal vector at time t, express The estimation error signal at time.
[0033] Preferably, Conjugate search direction at time , is represented as:
[0034] ;
[0035] in, express The residual vector at time step, express The conjugate search direction at any given moment. Indicates matrix transpose. express The autocorrelation matrix at time t, This represents the regularization term.
[0036] This embodiment provides a filter network, including:
[0037] Multiple constrained robust adaptive filters based on the conjugate gradient method, as described above, are connected to construct a filter network;
[0038] For each adaptive filter in the filter network, based on this adaptive filter The update step size and conjugate search direction at each moment, for The adaptive weight vector is updated at each time step; based on preset joint coefficients, the adaptive weights corresponding to each neighboring adaptive filter directly connected to the current adaptive filter are weighted and summed to obtain the adaptive weights of each adaptive filter in the filter network. The adaptive weight vector at time step.
[0039] Preferably, each adaptive filter in the filter network is in The adaptive weight vector at time step is expressed as:
[0040] ;
[0041] in, In the filter network, the first An adaptive filter in The adaptive weight vector at time step; 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 Each neighbor adaptive filter in The adaptive weight vector at time step, This represents the predefined linear constraint correlation matrix related to the linear constraint conditions. This represents the preset linear constraint-related vector. Indicates the first Each neighbor adaptive filter in The update step size at any moment, Indicates the first Each neighbor adaptive filter in The conjugate search direction at any given moment.
[0042] Compared with the prior art, the above-described technical solution of the present invention has the following advantages:
[0043] The constraint-robust adaptive filter based on the conjugate gradient method described in this invention integrates linear constraints into the entire adaptive filtering calculation process, utilizing the conjugate gradient optimization method combined with... The projected input signal vector and its transpose, the autocorrelation matrix of the input signal vector, the residual vector, the conjugate search direction, and the estimation error signal at each time step are used to obtain the optimal update step size. The adaptive weights subject to linear constraints are then updated to achieve adaptive filtering of the output signal of the system to be estimated. Next, the residual vector and conjugate search direction at the next time step are calculated to obtain the subsequent optimal step size and the update of the adaptive weights. This invention constructs a nonlinear cost function based on the estimation error signal, which can achieve faster convergence and better robust filtering results even when the desired signal is superimposed with impulse interference. Simultaneously, the conjugate gradient optimization method provides a balance between convergence speed and computational complexity, further improving the filter performance.
[0044] This invention constructs a filter network based on a constrained robust adaptive filter using the conjugate gradient method. Based on a mechanism where each adaptive filter updates first and then joins with its neighboring adaptive filters, and leveraging data sharing and information diffusion, the adaptive filter can quickly estimate the parameters of interest and fully utilize the information from each node in the network. Furthermore, the entire adaptive filter network system will not be paralyzed or fail due to the failure of individual nodes in the diffusion strategy; even if the data of a certain node temporarily becomes abnormal, it will be corrected in the joint step, further ensuring the robustness of the filtering. Attached Figure Description
[0045] To make the content of this invention easier to understand, the invention will be further described in detail below with reference to specific embodiments and accompanying drawings, wherein:
[0046] Figure 1 This is a flowchart of the constrained robust adaptive filter based on the conjugate gradient method of the present invention.
[0047] Figure 2 This is a block diagram of a constrained robust adaptive filter based on the conjugate gradient method.
[0048] Figure 3 This is a comparison chart of the normalized mean square deviation curves of the adaptive filtering system in the constrained system identification scenario;
[0049] Figure 4 This is a comparison chart of the normalized mean square deviation curves of the adaptive filtering system in the identification scenario of the distributed constraint system. Detailed Implementation
[0050] The present invention will be further described below with reference to the accompanying drawings and specific embodiments, so that those skilled in the art can better understand and implement the present invention. However, the embodiments described are not intended to limit the present invention.
[0051] Reference Figure 1As shown, the filtering flowchart of the constrained robust adaptive filter based on the conjugate gradient method of the present invention includes specific steps S101 to S106.
[0052] S101: Obtain Time and Before the moment The sampled values of the input signal input to the system to be estimated at each time point constitute... The input signal vector at time t is obtained by projection. The projected input signal vector at time t.
[0053] in, The input signal vector at time t is denoted as ; Indicates the input signal at The sampled value at time 10:00. , This represents the total number of weights in the adaptive filter.
[0054] in, The projected input signal vector at time t is represented as: ; The predefined linear constraint correlation matrix, which is related to the linear constraint conditions, is represented as follows: ; Indicates size is The identity matrix, Represented as size The constraint matrix, Indicates the total number of constraints. , T represents transpose.
[0055] S102: Obtain the adaptive filter in Moment An adaptive weight set under linear constraints is formed. Adaptive weight vector at time step; 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. Output signal at time; calculation The difference between the expected signal and the output signal at time t is used to obtain... The estimation error signal at time.
[0056] S102-1: Adaptive weight vector at time step , is represented as:
[0057] ;
[0058] The linear constraint condition is expressed as follows: ;
[0059] Indicates that the adaptive filter is in The first moment Each adaptive weight; Indicates size is The constraint vector, This indicates the matrix transpose.
[0060] S102-2: The output signal at time t is represented as: .
[0061] S102-3: The estimation error signal at time t is expressed as: , express The expected signal at any given moment.
[0062] S103: Based on The estimation error signal at time and the shape control parameters of the nonlinear weighting function , build The nonlinear weighting function at time t is expressed as: .
[0063] S104: Based on The forgetting factor, nonlinear weighting function, projected input signal vector, and its transpose vector at each time step are obtained recursively through updates. The autocorrelation matrix at time t is expressed as:
[0064] ;
[0065] in, express The forgetting factor of time, express Projected input signal vector at any time The autocorrelation matrix.
[0066] S105: Initialize the conjugate search direction, residual vector, and update step size, based on... The conjugate search direction at time step, residual vector, projected input signal vector, estimation error signal, and nonlinear weighting function are all present in the input signal vector. The autocorrelation matrix at time step 1 is obtained. The update step size at each moment is represented as:
[0067] ;
[0068] in, Represents the regularization term. express The residual vector at time step, express The conjugate search direction at any given moment.
[0069] S106: Calculation The product of the update step size and the conjugate search direction at each time step, the pre-defined linear constraint correlation matrix, and The product of the adaptive weight vectors at each time step and the sum of the vectors related to the preset linear constraints are used to obtain the result. The adaptive weight vector at time step is expressed as:
[0070] ;
[0071] in, The vector representing the predefined linear constraint related to the linear constraint is denoted as: , Indicates size is The constraint vector.
[0072] In this embodiment, based on The forgetting factor of time residual vector Update step size Conjugate search direction Nonlinear weighting function Estimation error signal Projected input signal vector ,as well as Autocorrelation matrix at time step ,renew Residual vector at time step , is represented as: .
[0073] In this embodiment, based on the regularization term, Residual vector at time step Conjugate search direction ,as well as Autocorrelation matrix at time step ,renew Conjugate search direction at time , is represented as: .
[0074] Specifically, in acquiring After obtaining the residual vector and conjugate search direction at time step, update to obtain The update step size is updated in real time, and then the data is updated accordingly. Adaptive weight vector at time step This enables adaptive filtering.
[0075] The constrained robust adaptive filter based on the conjugate gradient method described in this invention integrates linear constraints into the entire adaptive filtering calculation process. It uses the conjugate gradient optimization method to update the adaptive weights subject to linear constraints, thereby achieving adaptive filtering of the output signal of the system to be estimated. At the same time, it integrates nonlinear functions into the entire adaptive filtering calculation process to suppress abnormal interference caused by impulse noise, so as to achieve stronger robustness in scenarios where the desired signal contains impulse noise.
[0076] Based on the above embodiments, in this embodiment of the invention, an adaptive filter network is constructed using the aforementioned adaptive filter. The adaptive network is composed of multiple network nodes with adaptive signal processing capabilities interconnected according to a specific topology. Each network node can perform preliminary iterative estimation of the target parameters based on local data, and jointly optimize the final estimation result through information exchange with neighboring nodes. The diffusion strategy exhibits better stability and accuracy. Adaptive networks have shown wide application value in many fields such as smart healthcare, environmental monitoring, precision agriculture, and disaster relief management. The constrained robust conjugate gradient adaptive filter network (DCR-CG) proposed in this invention has good robustness in constrained adaptive networks. In the filter network of this embodiment, the adaptive filter at each node has the same filtering process; specifically, taking any adaptive filter in the filter network... Taking this as an example, the specific filtering process of the filter network is illustrated in steps S201 to S211.
[0077] S201: Obtain in Time and consecutive moments before The sampled values of the input signal input to the system to be estimated at each time point constitute... Input signal vector at time 1 , is represented as:
[0078] ;
[0079] in, Indicates the first The input signal of each adaptive filter is The sampled value at time 10:00. , This represents the total number of weights in the adaptive filter.
[0080] S202: Obtain the adaptive filter exist Moment An adaptive weight set under linear constraints is formed. Adaptive weight vector at time step , is represented as:
[0081] ;
[0082] The linear constraint condition imposed on the adaptive weight vector is expressed as follows: ; Represented as size The constraint matrix, Indicates size is The constraint vector, Indicates the total number of constraints. .
[0083] S203: Calculation The dot product of the adaptive weight vector and the input signal vector at each time step is used as the adaptive filter. exist Output signal at time , is represented as: .
[0084] S204: Calculation The difference between the preset expected signal and the output signal at a given time is obtained. Time estimation error signal , is represented as: .
[0085] S205: Using a nonlinear function to... An adaptive filter in The estimation error signal at time step is weighted and recursively updated to obtain the first time step. An adaptive filter in Robust weighted autocorrelation matrix of the input signal at each time step , is represented as:
[0086] ;
[0087] in, express The forgetting factor of time, the first An adaptive filter in Projected input signal vector at time 1 Represented as , The matrix representing the linear constraints is denoted as follows: ; Indicates size is The identity matrix, Represented as size The constraint matrix; Represents the nonlinear function with respect to the first... An adaptive filter in The estimation error signals at time 1 are weighted and represented as follows: , It is represented as a parameter that controls the shape of the nonlinear function.
[0088] S206: Based on the first An adaptive filter in Projected input signal vector at time 1 , Time estimation error signal , Nonlinear weighting function at time step as well as Autocorrelation matrix at time step , obtain the An adaptive filter in Update the required update step size continuously. , is represented as:
[0089] ;
[0090] in, It is a regularization term. It is the first An adaptive filter in The residual vector at time step, It is the first An adaptive filter in The conjugate search direction at any given moment.
[0091] S207: Calculate the... An adaptive filter in Step size of time With conjugate search direction The product of, and Adaptive weight vector at time step Add them together and update to get the result. An adaptive filter in Intermediate estimate of time , is represented as:
[0092] ;
[0093] in, The vector representing the linear constraint is denoted as: , Indicates size is The constraint vector.
[0094] S208: Based on the first An adaptive filter in Projected input signal vector at time 1 , Residual vector at time step , Step size of time , Conjugate search direction at time , Time estimation error signal , Nonlinear weighting function at time step as well as Autocorrelation matrix at time step , obtain the An adaptive filter in Residual vector at time step , is represented as:
[0095] .
[0096] S209: Based on the first An adaptive filter in Residual vector at time step , Coefficient parameters at time as well as Conjugate search direction at time , obtain the An adaptive filter in Conjugate search direction at time , is represented as: .
[0097] S210: The first filter network An adaptive filter in The intermediate estimate at time step is combined with the intermediate estimates of its neighbors to update its parameter estimates, thus obtaining the intermediate estimate at time step step 1 in the filter network. An adaptive filter in Adaptive weights at time points , is represented as:
[0098] ;
[0099] 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, , This coefficient can be designed using rules such as uniform weighting, Metropolis, and Laplacian. express The number of middle-neighbor adaptive filters; Indicates the first The first adaptive filter Each neighbor adaptive filter in Intermediate estimate of time.
[0100] S211: 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.
[0101] In this invention, each linearly constrained adaptive filter in the filter network constructs an adaptive weight vector and a regression vector based on the adaptive weights and the sampled values of the input signal. The inner product generates the output signal and obtains the estimation error signal. The adaptive weight vector is updated by combining nonlinear functions and conjugate gradient optimization methods. The filter is further extended to a distributed network, where each node exchanges information with all its neighboring nodes. In network environments where the desired signal contains impulse noise, it achieves stronger robustness, effectively reduces the adverse effects of input noise, and has a faster convergence speed.
[0102] To demonstrate the effectiveness of this invention, this embodiment employs computer experiments to verify the performance of the constrained robust adaptive filter (CR-CG) and filter network (DCR-CG) based on the conjugate gradient method provided by this invention. The experiment was conducted in an environment with impulse noise interference and noisy input signals to estimate unknown systems in an application scenario. The results were compared with those of the constrained (CCG) adaptive filter based on the conjugate gradient method, the constrained minimum M-estimation (CLMM) adaptive filter, and the corresponding filter networks for each adaptive filter.
[0103] Reference Figure 2 The diagram shows the structural block diagram of a constrained robust adaptive filter based on the conjugate gradient method. In this embodiment, the noise signal is Gaussian noise plus impulse noise; the normalized mean square deviation (NMSD) is used as the performance metric for the system's scene identification experiment. The unit is dB, where Indicates taking the logarithm. These are the weights of the actual system.
[0104] Noise signals used in system identification experiments It contains a mean of zero and a variance of . Gaussian white noise and a pulse noise ,Right now Gaussian noise and the desired noise-free signal are preserved. signal-to-noise ratio in dB, impulse noise Produced by Bernoulli Gaussian processes, i.e. ,in It is a Bernoulli process, and the probability of it taking the value 0 is 0.99 and the probability of it taking the value 1 is 0.01. Gaussian white noise with zero mean.
[0105] Reference Figure 3 The figure shows a comparison of the normalized mean square deviation curves of the adaptive filtering system in the constrained system identification scenario. The parameters of each method are CCG ( ), CLMM ( ), CR-CG ( In constraint system identification scenarios, the CR-CG adaptive filtering system of this application embodiments all exhibit good anti-pulse performance.
[0106] Reference Figure 4 The figure shows a comparison of the normalized mean square deviation curves of the adaptive filtering system in the identification scenario of the distributed constraint system. The parameters of each method are DCCG ( ), DCLMM ( ), DCR-CG ( In distributed constraint system identification scenarios, the DCR-CG adaptive filtering system of this application exhibits good anti-impulse performance.
[0107] The constraint-robust adaptive filter based on the conjugate gradient method described in this invention integrates linear constraints into the entire adaptive filtering calculation process, utilizing the conjugate gradient optimization method, combined with... The projected input signal vector and its transpose, the autocorrelation matrix of the input signal vector, the residual vector, the conjugate search direction, and the estimation error signal at each time step are used to obtain the optimal step size required for updating. The adaptive weights subject to linear constraints are then updated to achieve adaptive filtering of the output signal of the system to be estimated. Next, the residual vector and conjugate search direction at the next time step are calculated to obtain the subsequent optimal step size and the updated adaptive weights. This invention constructs a nonlinear cost function based on the estimation error signal, which can achieve faster convergence and better robust filtering results even when the desired signal is superimposed with impulse interference. Simultaneously, the conjugate gradient optimization method provides a balance between convergence speed and computational complexity, further improving filter performance.
[0108] 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.
[0109] This application is described with reference to flowchart illustrations and / or block diagrams of methods, apparatus (systems), and computer program products according to embodiments of this application. It will be understood that each block of the flowchart illustrations and / or block diagrams, and combinations of blocks in the flowchart illustrations and / or block diagrams, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, special-purpose computer, embedded processor, or other programmable data processing apparatus to produce a machine, such that the instructions, which execute via the processor of the computer or other programmable data processing apparatus, generate instructions for implementing the flowchart... Figure 1 One or more processes and / or boxes Figure 1 A device that provides the functions specified in one or more boxes.
[0110] These computer program instructions may also be stored in a computer-readable storage medium that can direct a computer or other programmable data processing device to function in a particular manner, such that the instructions stored in the computer-readable storage medium produce an article of manufacture including instruction means, which are implemented in a process Figure 1 One or more processes and / or boxes Figure 1 The function specified in one or more boxes.
[0111] These computer program instructions may also be loaded onto a computer or other programmable data processing equipment to cause a series of operational steps to be performed on the computer or other programmable equipment to produce a computer-implemented process, thereby providing instructions that execute on the computer or other programmable equipment for implementing the process. Figure 1 One or more processes and / or boxes Figure 1 The steps of the function specified in one or more boxes.
[0112] Obviously, the above embodiments are merely illustrative examples for clear explanation and are not intended to limit the implementation. Those skilled in the art will recognize that other variations or modifications can be made based on the above description. It is neither necessary nor possible to exhaustively list all possible implementations here. However, obvious variations or modifications derived therefrom are still within the scope of protection of this invention.
Claims
1. A constrained robust adaptive filter based on the conjugate gradient method, characterized in that, include: Get Time and Before the moment The sampled values of the input signal input to the system to be estimated at each time point constitute... The input signal vector at time t is obtained by projection. The projected input signal vector at time t; Obtaining the adaptive filter in Moment An adaptive weight set under linear constraints is formed. Adaptive weight vector at time step; 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. Output signal at time; calculation The difference between the expected signal and the output signal at time t is used to obtain... The estimation error signal at time; based on The estimated error signal at time step is used to construct a nonlinear weighted function shape control parameter to... The nonlinear weighting function at time points; based on The forgetting factor, nonlinear weighting function, projected input signal vector, and its transpose vector at each time step are obtained recursively through updates. Autocorrelation matrix at time step , is represented as: ;in, express The forgetting factor of time; and express The projected input signal vector and its transpose vector at time t are denoted as: , express The input signal vector at time t, The predefined linear constraint correlation matrix, which is related to the linear constraint conditions, is represented as follows: ; Indicates size is The identity matrix, Represented as size The constraint matrix, where N represents the total number of constraints; express Projected input signal vector at any time The autocorrelation matrix; Initialize the conjugate search direction, residual vector, and update step size, based on The conjugate search direction at time step, residual vector, projected input signal vector, estimation error signal, and nonlinear weighting function are all present in the input signal vector. The autocorrelation matrix at time step 1 is obtained. The update step size at any given moment; calculate The product of the update step size and the conjugate search direction at each time step, the pre-defined linear constraint correlation matrix, and The product of the adaptive weight vectors at each time step, and the sum of the vectors related to the preset linear constraints, are used to obtain the result. The adaptive weight vector at time step; Among them, based on The update step size, conjugate search direction, residual vector, projected input signal vector, estimation error signal, and nonlinear weighting function at each time step are specified. The autocorrelation matrix at time t, for The residual vector and conjugate search direction are updated at each time step to obtain... The residual vector at each time step and the conjugate search direction are used to obtain... The update step size at any given moment.
2. The constrained robust adaptive filter based on the conjugate gradient method according to claim 1, characterized in that, Obtaining the adaptive filter in Moment An adaptive weight set under linear constraints is formed. Adaptive weight vector at time step , is represented as: ； The linear constraint condition is expressed as follows: ; Indicates that the adaptive filter is in The first moment Each adaptive weight; Represented as size The constraint matrix, Indicates size is The constraint vector, Indicates the total number of constraints. , T represents transpose.
3. The constrained robust adaptive filter based on the conjugate gradient method according to claim 1, characterized in that, based on The estimated error signal at time step is used to construct a nonlinear weighted function shape control parameter to... Nonlinear weighting function at time step , is represented as: ； in, express The estimation error signal at time t is expressed as follows: , express Expected signal at time, express Output signal at time; This represents the shape control parameter of the nonlinear weighted function.
4. The constrained robust adaptive filter based on the conjugate gradient method according to claim 1, characterized in that... ,based on The conjugate search direction at time step, residual vector, projected input signal vector, estimation error signal, and nonlinear weighting function are all present in the input signal vector. The autocorrelation matrix at time step 1 is obtained. Update step size , is represented as: ； in, Represents the regularization term. express The residual vector at time step, and express The conjugate search direction at time and its transpose.
5. The constrained robust adaptive filter based on the conjugate gradient method according to claim 4, characterized in that, calculate The product of the update step size and the conjugate search direction at each time step, the pre-defined linear constraint correlation matrix, and The product of the adaptive weight vectors at each time step and the sum of the vectors related to the preset linear constraints are used to obtain the result. Adaptive weight vector at time step , is represented as: ； in, express The adaptive weight vector at time step; The vector representing the predefined linear constraint related to the linear constraint is denoted as: , Indicates size is The constraint vector.
6. The constrained robust adaptive filter based on the conjugate gradient method according to claim 1, characterized in that, Residual vector at time step , is represented as: ； in, express The forgetting factor of time, express The residual vector at time step, express The update step size at any moment, express The autocorrelation matrix at time t, express The conjugate search direction at any given moment. express The nonlinear weighting function at time t, express The projected input signal vector at time t, express The estimation error signal at time.
7. The constrained robust adaptive filter based on the conjugate gradient method according to claim 1, characterized in that, Conjugate search direction at time , is represented as: ； in, express The residual vector at time step, and express The conjugate search direction at time step and its transpose. Indicates matrix transpose. express The autocorrelation matrix at time t, This represents the regularization term.
8. A filter network, characterized in that, include: A filter network is constructed by connecting multiple constrained robust adaptive filters based on the conjugate gradient method as described in any one of claims 1 to 7. For each adaptive filter in the filter network, based on this adaptive filter The update step size and conjugate search direction at each moment, for The adaptive weight vector is updated at each time step; based on preset joint coefficients, the adaptive weights corresponding to each neighboring adaptive filter directly connected to the current adaptive filter are weighted and summed to obtain the adaptive weights of each adaptive filter in the filter network. The adaptive weight vector at time step.
9. The filter network according to claim 8, characterized in that, Each adaptive filter in the filter network The adaptive weight vector at time step is expressed as: ； in, In the filter network, the first An adaptive filter in The adaptive weight vector at time step; 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 Each neighbor adaptive filter in The adaptive weight vector at time step, This represents the predefined linear constraint correlation matrix related to the linear constraint conditions. This represents the preset linear constraint-related vector. Indicates the first A neighbor adaptive filter in The update step size at any moment, Indicates the first Each neighbor adaptive filter in The conjugate search direction at any given moment.