Deviation compensation constraint adaptive filtering method and system based on error nonlinearity

Abstract

The invention relates to the technical field of adaptive filtering, and discloses a method and system for adaptive filtering with deviation compensation constraint based on error nonlinearity. The method comprises the following steps: when the weight of an adaptive filter is subject to linear constraints, an adaptive weight vector and a noisy input signal vector are constructed according to the adaptive weight and a noisy speech signal sampling value, an output signal is generated by an inner product, an estimated error signal is generated, and a median of square errors is calculated; after an error signal variance estimate and an adaptive weight vector power estimate are calculated according to the median of square errors and an adaptive weight vector, an input noise variance estimate is calculated; a deviation compensation term is calculated according to the adaptive weight vector and the input noise variance estimate, and the adaptive weight vector is updated with the noisy input signal vector and the estimated error signal; and the inner product of the adaptive weight vector affected by the updated low-efficiency input noise and the noisy input signal vector is calculated to obtain an output signal compensated for input noise deviation.

Description

Technical Field

[0001] The invention relates to the field of filter design, and in particular to a deviation compensation constraint adaptive filtering method and system based on error nonlinearity. Background Art

[0002] In the field of adaptive filtering, the adaptive filter can estimate the transmission characteristics of the unknown system, such as frequency response and delay spread, and then compensate for the channel distortion by adjusting its own coefficients, so that the output signal of the estimated system can better restore the characteristics of the original input signal. The two main application directions of adaptive filtering are system identification and adaptive beamforming.

[0003] System identification is an important branch of adaptive signal processing. Many problems such as traditional adaptive channel equalization, adaptive noise elimination, adaptive echo cancellation, active noise control, etc. can be attributed to system identification problems. Traditional least mean square (LMS) and normalized least mean square (NLMS) adaptive filtering methods are easy to implement, but their performance will drop sharply in some special environments. For example, in some cases, the output signal of the unknown system may be contaminated by impulse noise. In order to enhance the ability of adaptive filters to resist impulse interference, a series of adaptive filtering methods that resist impulse noise have been proposed, such as the error sign least mean square adaptive filtering method, the mixed norm adaptive filtering method, and the adaptive filtering method based on maximum correlation entropy.

[0004] Adaptive beamforming is an important application in constrained adaptive filters and is also a major research issue in the field of array signal processing. Adaptive beamforming technology can adaptively adjust the weight coefficients of each element in the antenna array through a given optimization criterion to achieve beam gain and nulling in the direction of the desired signal and the interference signal, thereby selectively receiving or suppressing signals from different spatial directions. In actual engineering applications, adaptive beamforming methods are often affected by various interferences or errors, resulting in problems such as main lobe position offset, side lobe level amplitude increase, and pattern model mismatch. Therefore, under complex environmental conditions, it is necessary to deeply study and improve the robust constrained adaptive filtering method and its engineering implementation to improve its beamforming performance.

[0005] In the above two application scenarios, the commonly used adaptive filtering systems are designed based on the standard regression model, that is, it is assumed that the input signal is the same as the unknown system. However, due to sampling errors and other reasons in practical applications, the input signal is mixed with noise, which greatly affects the performance of the traditional adaptive filtering system, and then leads to a large error in the output signal of the system. At present, the error is usually eliminated by using the deviation compensation method and the total least squares method; scholars have proposed the deviation compensation maximum correlation entropy method (BC-MCC) and the deviation compensation minimum error entropy method (BC-MEE). Although these methods have good anti-impulse noise effects under error variable models, they focus more on error elimination. Their cost functions and update mechanisms do not consider the linear constraints of adaptive weights. When applied to scenarios where adaptive weights are subject to linear constraints, the weight vector may exceed the range specified by the linear constraints during the update process. Therefore, the existing methods cannot be applied to application scenarios where adaptive weights are subject to linear constraints. At the same time, their cost functions can also be further optimized to improve the robustness of the methods. Summary of the invention

[0006] Therefore, the technical problem to be solved by the present invention is to overcome the problem that the adaptive method in the prior art cannot be applied to the application scenario where the adaptive weights are subject to linear constraints and the filtering robustness is poor.

[0007] In order to solve the above technical problems, the present invention provides a deviation compensation constraint adaptive filtering method based on error nonlinearity, comprising:

[0008] Get in Time and The sampling values ​​of the noisy input signal input to the estimated system at multiple consecutive moments before the moment constitute The noisy input signal vector at time t;

[0009] Get the adaptive filter in Multiple linearly constrained adaptive weights at the moment, composed of The adaptive weight vector at the moment;

[0010] calculate The inner product of the adaptive weight vector at time and the noisy input signal vector is used as the adaptive filter Output signal at the moment;

[0011] calculate The difference between the noisy expected signal and the output signal at time , we get The estimated error signal at time t;

[0012] based on Time and Continuous before time The estimated error signal at the moment is calculated The median square error at time, is a positive integer representing the length of the median filter; based on The median square error at the moment is calculated The estimated value of the variance of the error signal at time instant;

[0013] based on The adaptive weight vector at time , calculate The adaptive weight vector variance power estimate at time t, combined with The estimated variance of the error signal at time t is obtained The estimated value of the input noise variance at time t;

[0014] based on The adaptive weight vector at the moment and the input noise variance estimate are obtained Deviation compensation item at the moment;

[0015] based on The deviation compensation term at the moment, the noisy input signal vector and the estimated error signal are updated using the error nonlinearity The adaptive weight vector at the moment is obtained The adaptive weight vector at the moment;

[0016] calculate The inner product of the adaptive weight vector at time t and the noisy input signal vector is used to obtain the estimated system at Output signal at the time.

[0017] Preferably, The acquisition of the deviation compensation item at the moment includes:

[0018] based on The adaptive weight vector at time and the input noise variance estimate ,calculate Deviation compensation term at time , expressed as:

[0019] ;

[0020] in, is a kernel width parameter with a positive value; express An estimate of the variance of the error signal at time instant .

[0021] Preferably, based on The deviation compensation term at the moment, the noisy input signal vector and the estimated error signal are updated using the error nonlinearity The adaptive weight vector at the moment is obtained The adaptive weight vector at the moment is expressed as:

[0022] ;

[0023] in, express The adaptive weight vector at time , express The adaptive weight vector at time , Indicates a positive step size parameter. represents the constraint matrix, and the calculation formula is ; Indicates size The identity matrix of Indicates size The constraint matrix of represents the noisy input signal vector, express The estimated error signal at time t; Indicates size The constraint vector.

[0024] Preferably, the calculation The inner product of the adaptive weight vector at time and the noisy input signal vector is used as the adaptive filter The output signals at each moment include:

[0025] Get Time and its previous continuous The sampled value of the noisy input signal at the time instant composition The noisy input signal vector at time , expressed as: ;

[0026] Get the adaptive filter in M adaptive weights subject to linear constraints at time composition The adaptive weight vector at time , expressed as: ;

[0027] Computing adaptive filters Output signal at time , expressed as: ;

[0028] in, express The adaptive weight vector at time Adaptive weights, , Represents a transpose operation.

[0029] Preferably, the calculation The difference between the noisy expected signal and the output signal at time , we get The estimated error signal at time t is expressed as:

[0030] ;

[0031] in, express The estimated error signal at time t, express The noisy expected signal at time , express Output signal at the time.

[0032] Preferably, based on Time and Continuous before time The estimated error signal at the moment is calculated The median square error at the moment is expressed as:

[0033] ;

[0034] in, express The median square error at time, It means taking the median, express The square value of the estimated error signal at time , , is a positive integer representing the length of the median filter.

[0035] Preferably, based on The median square error at the moment is calculated The estimated variance of the error signal at time t is expressed as:

[0036] ;

[0037] in, express The estimated variance of the error signal at time , Represents a positive smoothing factor.

[0038] Preferably, based on The adaptive weight vector at time , calculate The adaptive weight vector variance power estimate at time t, combined with The estimated variance of the error signal at time t is obtained The estimated value of the input noise variance at time , including:

[0039] based on The adaptive weight vector at time and The adaptive weight vector variance power estimate at time ,calculate The adaptive weight vector variance power estimate at time , expressed as:

[0040] ;

[0041] based on The adaptive weight vector variance power estimate at time , and combined with The estimated variance of the error signal at time , get The estimated value of the input noise variance at time , expressed as:

[0042] ;

[0043] in, It represents the variance ratio of output noise to input noise, and the expression is , represents the measurement noise variance without impulse noise, represents the variance of the input noise.

[0044] This embodiment provides a system using the above-mentioned error nonlinearity-based deviation compensation constraint adaptive filtering method, including:

[0045] The data acquisition module is used to obtain Time and The sampling values ​​of the noisy input signal input to the estimated system at multiple consecutive moments before the moment constitute The noisy input signal vector at time t;

[0046] Output signal calculation module, used to obtain the adaptive filter Multiple linearly constrained adaptive weights at the moment, composed of The adaptive weight vector at time ; Calculate The inner product of the adaptive weight vector at time and the noisy input signal vector is used as the adaptive filter Output signal at the moment;

[0047] Input noise variance estimation calculation module, used to calculate The difference between the noisy expected signal and the output signal at time , we get The estimated error signal at time ; based on Time and Continuous before time The estimated error signal at the moment is calculated The median square error at time, is a positive integer representing the length of the median filter; based on The median square error at the moment is calculated The estimated variance of the error signal at time ; based on The adaptive weight vector at time , calculate The adaptive weight vector variance power estimate at time t, combined with The estimated variance of the error signal at time t is obtained The estimated value of the input noise variance at time t;

[0048] Deviation compensation calculation module, used for The adaptive weight vector at the moment and the input noise variance estimate are obtained Deviation compensation item at the moment;

[0049] Update output module for The deviation compensation term at the moment, the noisy input signal vector and the estimated error signal are updated using the error nonlinearity The adaptive weight vector at the moment is obtained The adaptive weight vector at time ; Calculate The inner product of the adaptive weight vector at time t and the noisy input signal vector is used to obtain the estimated system at Output signal at the time.

[0050] The above technical solution of the present invention has the following beneficial effects compared with the prior art:

[0051] The error nonlinearity-based deviation compensation constraint adaptive filtering method of the present invention integrates linear constraints into the entire adaptive filtering calculation process, calculates the deviation compensation term by using the error signal variance estimate based on the estimated error signal and the noise variance estimate, updates the adaptive weights subject to linear constraints, and realizes adaptive filtering of the output signal of the estimated system. The present invention calculates the variance estimate by integrating the error signals at multiple moments, which can avoid the excessive adjustment of the weight vector due to the abnormal error at a single moment, and improves the compensation accuracy; and comprehensively considers the adaptive weight and the error signal variance estimate to estimate the noise variance, which can more accurately grasp the noise situation in the system, and in the subsequent weight update and signal processing process, can better compensate or suppress the noise, and improve the filtering accuracy; at the same time, the present invention introduces the deviation compensation term based on the error nonlinear term in the scene where there is noise at the input end to compensate for the filtering deviation caused by the presence of input noise in the system, so that the adaptive filtering process is more robust, and a filtering result with faster convergence speed and better robust performance is obtained; the present invention enables the expected signal to achieve stronger robustness in the scene containing impulse noise, and can effectively reduce the adverse effects of input noise. BRIEF DESCRIPTION OF THE DRAWINGS

[0052] In order to make the content of the present invention more clearly understood, the present invention is further described in detail below according to specific embodiments of the present invention in conjunction with the accompanying drawings, wherein:

[0053] Figure 1 It is a flowchart of the steps of the error nonlinearity-based bias compensation constraint adaptive filtering method provided by the present invention;

[0054] Figure 2 It is the structural frame of the adaptive filter with noisy input;

[0055] Figure 3 It is a comparison diagram of the normalized mean square deviation curve of the adaptive filtering system in the system identification scenario;

[0056] Figure 4 It is a comparison diagram of the amplitude-frequency characteristic curves of the adaptive filtering system in the beamforming scenario. DETAILED DESCRIPTION

[0057] The present invention is further described below in conjunction with the accompanying drawings and specific embodiments so that those skilled in the art can better understand the present invention and implement it, but the embodiments are not intended to limit the present invention.

[0058] Reference Figure 1 As shown, the flowchart of the step of the deviation compensation constraint adaptive filtering method based on error nonlinearity provided by the present invention includes the following specific steps:

[0059] S101: Get Time and The sampling values ​​of the noisy input signal input to the estimated system at multiple consecutive moments before the moment constitute The noisy input signal vector at time t;

[0060] S102: Obtaining the adaptive filter Multiple linearly constrained adaptive weights at the moment, composed of The adaptive weight vector at the moment;

[0061] S103: Calculation The inner product of the adaptive weight vector at time and the noisy input signal vector is used as the adaptive filter Output signal at the moment;

[0062] S104: Calculation The difference between the noisy expected signal and the output signal at time , we get The estimated error signal at time t is expressed as:

[0063] ;

[0064] in, express The estimated error signal at time t, express The noisy expected signal at time , express Output signal at the time.

[0065] S105: Based on Time and Continuous before time The estimated error signal at the moment is calculated The median square error at time, is a positive integer representing the length of the median filter; based on The median square error at the moment is calculated The estimated value of the variance of the error signal at time instant;

[0066] S106: Based on The adaptive weight vector at time , calculate The adaptive weight vector variance power estimate at time t, combined with The estimated variance of the error signal at time t is obtained The estimated value of the input noise variance at time t;

[0067] S107: Based on The adaptive weight vector at the moment and the input noise variance estimate are obtained Deviation compensation item at the moment;

[0068] S108: Based on The deviation compensation term at the moment, the noisy input signal vector and the estimated error signal are updated using the error nonlinearity The adaptive weight vector at the moment is obtained The adaptive weight vector at the moment;

[0069] S109: Calculation The inner product of the adaptive weight vector at time t and the noisy input signal vector is used to obtain the estimated system at Output signal at the time.

[0070] The error nonlinearity-based bias compensation constrained adaptive filtering method described in the present invention integrates linear constraints into the entire adaptive filtering calculation process, calculates the bias compensation term using the error signal variance estimate based on the estimated error signal and the noise variance estimate, updates the adaptive weights subject to linear constraints, and realizes adaptive filtering of the output signal of the estimated system.

[0071] Specifically, in steps S101 to S103, the calculation The inner product of the adaptive weight vector at time and the noisy input signal vector is used as the adaptive filter The output signals at each moment include:

[0072] Get Time and its previous continuous The sampled value of the noisy input signal at the time instant composition The noisy input signal vector at time , expressed as: ;

[0073] Get the adaptive filter in Moment Adaptive weights subject to linear constraints composition The adaptive weight vector at time , expressed as: ;

[0074] Computing adaptive filters Output signal at time , expressed as: ;

[0075] in, express The adaptive weight vector at time Adaptive weights, , Represents a transpose operation.

[0076] Specifically, in step S105, The acquisition of the error signal variance estimate at the moment includes:

[0077] S105-1: Based on Time and Continuous before time The estimated error signal at the moment is calculated The median square error at the moment is expressed as:

[0078] ;

[0079] in, express The median square error at time, It means taking the median, express The square value of the estimated error signal at time , , is a positive integer representing the length of the median filter;

[0080] S105-2: Based on The median square error at the moment is calculated The estimated variance of the error signal at time t is expressed as:

[0081] ;

[0082] in, express The estimated variance of the error signal at time , Represents a positive smoothing factor.

[0083] The present invention calculates the variance estimation value by integrating the error signals at multiple moments, thereby avoiding excessive adjustment of the weight vector due to an abnormal error at a single moment and improving the compensation accuracy.

[0084] Specifically, in step S106, The acquisition of the estimated value of the input noise variance at the moment includes:

[0085] S106-1: Based on The adaptive weight vector at time and The adaptive weight vector variance power estimate at time ,calculate The adaptive weight vector variance power estimate at time , expressed as:

[0086] ;

[0087] S106-2: Based on The adaptive weight vector variance power estimate at time , and combined with The estimated variance of the error signal at time , get The estimated value of the input noise variance at time , expressed as:

[0088] ;

[0089] in, It represents the variance ratio of output noise to input noise, and the expression is , represents the measurement noise variance without impulse noise, represents the variance of the input noise.

[0090] The present invention estimates the noise variance by comprehensively considering the adaptive weights and the error signal variance estimation value, which can more accurately grasp the noise situation in the system. In the subsequent weight update and signal processing process, the noise can be better compensated or suppressed, thereby improving the filtering accuracy.

[0091] Specifically, in step S107, The acquisition of the deviation compensation item at the moment includes:

[0092] based on The adaptive weight vector at time and the input noise variance estimate ,calculate Deviation compensation term at time , expressed as:

[0093] ;

[0094] in, is a kernel width parameter with a positive value.

[0095] Specifically, in step S108, The calculation of the adaptive weight vector at the moment is expressed as:

[0096] ;

[0097] in, express The adaptive weight vector at time , express The adaptive weight vector at time , Indicates a positive step size parameter. represents the constraint matrix, and the calculation formula is ; Indicates size The identity matrix of Indicates size The constraint matrix of Indicates size The constraint vector.

[0098] In the scenario where there is noise at the input end, the present invention introduces a deviation compensation term based on the error nonlinear term to compensate for the model deviation that may exist in the system, thereby making the adaptive filtering process more robust and obtaining a filtering result with faster convergence speed and better robust performance; the present invention enables the expected signal to achieve stronger robustness in scenarios containing impulse noise, and can effectively reduce the adverse effects of input noise.

[0099] Based on the above embodiment, in an embodiment of the present invention, using the error nonlinearity-based deviation compensation adaptive filter provided by the present invention, in a scenario where the expected signal contains impulse noise, the steps of performing system identification specifically include:

[0100] S201: Obtaining adaptive weights of an adaptive filter subject to linear constraints and sampling values ​​of a noisy input signal, and constructing corresponding adaptive weight vectors and noisy input signal vectors;

[0101] Depend on Time adaptive filter Adaptive weights , composed of the adaptive weight vector , expressed as: ; , Represents the transpose operation;

[0102] Among them, the linear constraints on the adaptive weight vector are expressed as: ; Indicates size The constraint matrix, Indicates size The constraint vector, Represents the total number of constraints, ;

[0103] Depend on Time and its previous continuous The sampled value of the noisy input signal at the time instant , which is composed of a noisy input signal vector , expressed as: ;

[0104] S202: Yes The adaptive weight vector at the time is inner-producted with the noisy input signal vector to generate The output signal at time is expressed as: ;

[0105] S203: Based on The noisy expected signal at time and Output signal at time The difference generation The estimated error signal at time , expressed as: ;

[0106] according to Time and before The estimated error signal at time ,generate The median square error at time , expressed as: ; Indicates the median filter length;

[0107] S204: Based on The median square error at time ,calculate The estimated variance of the error signal at time , expressed as: ;in, Represents the smoothing factor, ranging from 0.99 to 0.999, used for smoothing estimation;

[0108] S205: Based on The adaptive weight vector at time and The adaptive weight vector variance power estimate at time ,calculate The adaptive weight vector variance power estimate at time , expressed as: ;

[0109] S206: Based on The estimated variance of the error signal at time Power estimate with adaptive weight vector ,calculate The estimated value of the input noise variance at time , expressed as:

[0110] ;

[0111] in, It represents the variance ratio of output noise to input noise, and the expression is , represents the measurement noise variance without impulse noise, represents the variance of the input noise;

[0112] S207: Based on The adaptive weight vector at time and the input noise variance estimate ,calculate The deviation compensation term at time is expressed as:

[0113] ;

[0114] in, Represents a kernel width parameter with a positive value;

[0115] S208: Based on Deviation compensation term at time , noisy input signal vector and the estimated error signal , using the error nonlinear update to obtain Time-Adaptive Weight Vector , expressed as:

[0116] ;

[0117] in, Indicates the preset step size parameter whose value is an integer. represents the constraint matrix, expressed as ; Indicates size The identity matrix of Indicates size The constraint matrix of Indicates size The constraint vector.

[0118] The error nonlinearity-based deviation compensation constrained adaptive filtering method described in the present invention calculates the deviation compensation term and then updates the adaptive weight vector subject to linear constraints through the deviation compensation term, so as to achieve stronger robustness in the scenario where the expected signal contains impulse noise and effectively reduce the adverse effects of input noise.

[0119] In order to prove the effectiveness of the present invention, this embodiment uses a computer experiment method to verify the performance of the error nonlinearity-based bias compensation (BC-CSLDM) adaptive filter provided by the present invention. The experiment estimates the unknown system in two application scenarios of system identification and beamforming in an environment with pulse noise interference and noisy input signals, and compares the experimental results with those of the constrained least mean square (LMS) adaptive filtering method, the bias compensation constrained least mean square (BC-CLMS) adaptive filtering method, the constrained maximum correlation entropy (CMCC) adaptive filtering method, and the constrained minimum error entropy (CMEE) adaptive filtering method.

[0120] Reference Figure 2 As shown in FIG. 1 , the structural block diagram of the adaptive filter with input noise. The noise signal of this embodiment is Gaussian noise plus impulse noise; the system recognition scene experiment uses the normalized mean square deviation (NMSD) as the performance measure, that is, , in dB, where represents taking the logarithm, is the weight of the actual system. The beamforming simulation diagram consists of the direction angle (in degrees) and the amplitude-frequency characteristic (in dB).

[0121] The noise signal used in the experiment contains a zero mean and a variance of Gaussian white noise and an impulse noise ,Right now . Impulse noise Produced by a Bernoulli Gaussian process, that is ,in is a Bernoulli process, and the probability of taking 0 is 0.95 and the probability of taking 1 is 0.05. is a zero-mean Gaussian white noise. Figure 3 As shown in the figure, it is a comparison of the normalized mean square deviation curve of the adaptive filtering system in the system identification scenario; the parameters of each method are CLMS ( ), BC-CLMS( ), CMCC( , ),CLMM( ), BC-CSLDM( , ). Reference Figure 4 As shown in Figure 1, the amplitude-frequency characteristic curve comparison of the adaptive filtering system in the beamforming scenario, where the incident angle of the useful signal is set to 0°, there are three interference signals, and the incident angles are set to -35°, 25°, and 60° respectively; the parameters of each method are CLMS ( ), BC-CLMS( ), CMCC( , ),CLMM( ), BC-CSLDM( , ).Depend on Figure 3 and Figure 4 It can be seen that, no matter in the system identification scenario or the beamforming scenario, the BC-CSLDM adaptive filtering system of the implementation mode of the present application has good anti-pulse performance, and has the lowest steady-state imbalance in the scenario where there is noise in the input signal.

[0122] Based on the above embodiment, the embodiment of the present invention further provides a system for applying the above-mentioned error nonlinearity-based deviation compensation constraint adaptive filtering method, including:

[0123] The data acquisition module is used to obtain Time and The sampling values ​​of the noisy input signal input to the system to be estimated at multiple consecutive moments before the moment constitute a noisy input signal vector;

[0124] Output signal calculation module, used to obtain the adaptive filter The adaptive weight vector is composed of multiple linearly constrained adaptive weights at the time instant; the inner product of the adaptive weight vector and the noisy input signal vector is calculated as the adaptive filter Output signal at the moment;

[0125] Input noise variance estimation calculation module, used to calculate The difference between the noisy expected signal and the output signal at time , we get The estimated error signal at time ; based on Time and Continuous before time The estimated error signal at the moment is calculated The median square error at time, is a positive integer representing the length of the median filter; based on The median square error at the moment is calculated The estimated variance of the error signal at time ; based on The adaptive weight vector at time , calculate The adaptive weight vector variance power estimate at time t, combined with The estimated variance of the error signal at time t is obtained The estimated value of the input noise variance at time t;

[0126] Deviation compensation calculation module, used for The adaptive weight vector at the moment and the input noise variance estimate are obtained Deviation compensation item at the moment;

[0127] Update output module for The deviation compensation term at the moment, the noisy input signal vector and the estimated error signal are updated using the error nonlinearity The adaptive weight vector at the moment is obtained The adaptive weight vector at time ; Calculate The inner product of the adaptive weight vector at time t and the noisy input signal vector is used to obtain the estimated system at Output signal at the time.

[0128] The error-nonlinear-based bias-compensation-constrained adaptive filtering system of this embodiment is used to implement the aforementioned error-nonlinear-based bias-compensation-constrained adaptive filtering method, so the specific implementation method of the error-nonlinear-based bias-compensation-constrained adaptive filtering system can be seen in the implementation method of the error-nonlinear-based bias-compensation-constrained adaptive filtering method in the previous text, for example, a data acquisition module, used to implement step S101 in the aforementioned error-nonlinear-based bias-compensation-constrained adaptive filtering method; an output signal calculation module, used to implement steps S102 and S103 in the aforementioned error-nonlinear-based bias-compensation-constrained adaptive filtering method; an input noise variance estimation value calculation module, used to implement steps S104, S105 and S106 in the aforementioned error-nonlinear-based bias-compensation-constrained adaptive filtering method; a deviation compensation item calculation module, used to implement step S107 in the aforementioned error-nonlinear-based bias-compensation-constrained adaptive filtering method; an update output module, used to implement steps S108 and S109 in the aforementioned error-nonlinear-based bias-compensation-constrained adaptive filtering method; therefore, its specific implementation method can refer to the description of the corresponding embodiments of each part, which will not be repeated here.

[0129] The error nonlinearity-based deviation compensation constraint adaptive filtering method of the present invention integrates linear constraints into the entire adaptive filtering calculation process, calculates the deviation compensation term by using the error signal variance estimate based on the estimated error signal and the noise variance estimate, updates the adaptive weights subject to linear constraints, and realizes adaptive filtering of the output signal of the estimated system. The present invention calculates the variance estimate by integrating the error signals at multiple moments, which can avoid the excessive adjustment of the weight vector due to the abnormal error at a single moment, and improves the compensation accuracy; and comprehensively considers the adaptive weight and the error signal variance estimate to estimate the noise variance, which can more accurately grasp the noise situation in the system, and in the subsequent weight update and signal processing process, can better compensate or suppress the noise, and improve the filtering accuracy; at the same time, the present invention introduces the deviation compensation term based on the error nonlinear term to compensate for the model deviation that may exist in the system in the scene where there is noise at the input end, so that the adaptive filtering process is more robust, and a filtering result with faster convergence speed and better robust performance is obtained; the present invention enables the expected signal to achieve stronger robustness in the scene containing impulse noise, and can effectively reduce the adverse effects of input noise.

[0130] Those skilled in the art will appreciate that the embodiments of the present application may be provided as methods, systems, or computer program products. Therefore, the present application may adopt the form of a complete hardware embodiment, a complete software embodiment, or an embodiment combining software and hardware. Moreover, the present application may adopt the form of a computer program product implemented on one or more computer-usable storage media (including but not limited to disk storage, CD-ROM, optical storage, etc.) containing computer-usable program codes.

[0131] The present application is described with reference to the flowcharts and / or block diagrams of the methods, devices (systems), and computer program products according to the embodiments of the present application. It should be understood that each process and / or box in the flowchart and / or block diagram, as well as the combination of the processes and / or boxes in the flowchart and / or block diagram, can be implemented by computer program instructions. These computer program instructions can be provided to a processor of a general-purpose computer, a special-purpose computer, an embedded processor, or other programmable data processing device to generate a machine, so that the instructions executed by the processor of the computer or other programmable data processing device generate instructions for implementing the processes in the flowchart and / or block diagram. Figure 1 A process or multiple processes and / or boxes Figure 1 A device that provides the functions specified in a block or multiple blocks.

[0132] These computer program instructions may also be stored in a computer-readable memory capable of directing a computer or other programmable data processing device to operate in a specific manner, so that the instructions stored in the computer-readable memory produce an article of manufacture comprising an instruction device, which implements the process Figure 1 A process or multiple processes and / or boxes Figure 1 A function specified in one or more boxes.

[0133] These computer program instructions can also be loaded onto a computer or other programmable data processing device so that a series of operating steps are executed on the computer or other programmable device to produce a computer-implemented process, thereby providing instructions for implementing the process. Figure 1 A process or multiple processes and / or boxes Figure 1 The steps for the functions specified in one or more boxes.

[0134] Obviously, the above embodiments are merely examples for the purpose of clear explanation and are not intended to limit the implementation methods. For those skilled in the art, other different forms of changes or modifications can be made based on the above description. It is not necessary and impossible to list all the implementation methods here. The obvious changes or modifications derived therefrom are still within the scope of protection of the present invention.

Claims

1. A bias compensation constrained adaptive filtering method based on error nonlinearity, characterized in that: include: Get in Time and The sampling values ​​of the noisy input signal input to the estimated system at multiple consecutive moments before the moment constitute The noisy input signal vector at time t; Get the adaptive filter in Multiple linearly constrained adaptive weights at the moment, composed of The adaptive weight vector at the moment; calculate The inner product of the adaptive weight vector at time and the noisy input signal vector is used as the adaptive filter Output signal at the moment; calculate The difference between the noisy expected signal and the output signal at time , we get The estimated error signal at time t; based on Time and Continuous before time The estimated error signal at the moment is calculated The median square error at time, is a positive integer representing the length of the median filter; based on The median square error at the moment is calculated The estimated value of the variance of the error signal at time instant; based on The adaptive weight vector at time , calculate The adaptive weight vector variance power estimate at time t, combined with The estimated variance of the error signal at time t is obtained The estimated value of the input noise variance at time t; based on The adaptive weight vector at the moment and the input noise variance estimate are obtained Deviation compensation item at the moment; based on The deviation compensation term at the moment, the noisy input signal vector and the estimated error signal are updated using the error nonlinearity The adaptive weight vector at the moment is obtained The adaptive weight vector at the moment; calculate The inner product of the adaptive weight vector at time t and the noisy input signal vector is used to obtain the estimated system at Output signal at the time.

2. The error nonlinearity-based bias compensation constrained adaptive filtering method according to claim 1, characterized in that: The acquisition of the deviation compensation item at the moment includes: based on The adaptive weight vector at time and the input noise variance estimate ,calculate Deviation compensation term at time , expressed as: ； in, is a kernel width parameter with a positive value; express An estimate of the variance of the error signal at time instant .

3. The error nonlinearity-based bias compensation constrained adaptive filtering method according to claim 2, characterized in that: based on The deviation compensation term at the moment, the noisy input signal vector and the estimated error signal are updated using the error nonlinearity The adaptive weight vector at the moment is obtained The adaptive weight vector at the moment is expressed as: ； in, express The adaptive weight vector at time , express The adaptive weight vector at time , Indicates a positive step size parameter. represents the constraint matrix, and the calculation formula is ; Indicates size The identity matrix of Indicates size The constraint matrix of represents the noisy input signal vector, express The estimated error signal at time t; Indicates size The constraint vector.

4. The error nonlinearity-based bias compensation constrained adaptive filtering method according to claim 1, characterized in that: calculate The inner product of the adaptive weight vector at time and the noisy input signal vector is used as the adaptive filter The output signals at each moment include: Get Time and its previous continuous The sampled value of the noisy input signal at time composition The noisy input signal vector at time , expressed as: ; Get the adaptive filter in M adaptive weights subject to linear constraints at time composition The adaptive weight vector at time , expressed as: ; Computing adaptive filters Output signal at time , expressed as: ; in, express The adaptive weight vector at time Adaptive weights, , Represents a transpose operation.

5. The error nonlinearity-based bias compensation constrained adaptive filtering method according to claim 4, characterized in that: calculate The difference between the noisy expected signal and the output signal at time , we get The estimated error signal at time t is expressed as: ； in, express The estimated error signal at time t, express The noisy expected signal at time , express Output signal at the time.

6. The error nonlinearity-based bias compensation constrained adaptive filtering method according to claim 5, characterized in that: based on Time and Continuous before time The estimated error signal at the moment is calculated The median square error at the moment is expressed as: ； in, express The median square error at time, It means taking the median, express The square value of the estimated error signal at time , , is a positive integer representing the length of the median filter.

7. The error nonlinearity-based bias compensation constrained adaptive filtering method according to claim 6, characterized in that: based on The median square error at the moment is calculated The estimated variance of the error signal at time t is expressed as: ； in, express The estimated variance of the error signal at time , Represents a positive smoothing factor.

8. The error nonlinearity-based bias compensation constrained adaptive filtering method according to claim 7, characterized in that: based on The adaptive weight vector at time , calculate The adaptive weight vector variance power estimate at time t, combined with The estimated variance of the error signal at time t is obtained The estimated value of the input noise variance at time , including: based on The adaptive weight vector at time and The adaptive weight vector variance power estimate at time ,calculate The adaptive weight vector variance power estimate at time , expressed as: ； based on The adaptive weight vector variance power estimate at time , and combined with The estimated variance of the error signal at time , get The estimated value of the input noise variance at time , expressed as: ； in, It represents the variance ratio of output noise to input noise, and the expression is , represents the measurement noise variance without impulse noise, represents the variance of the input noise.

9. A system using the error nonlinearity-based bias compensation constrained adaptive filtering method according to any one of claims 1 to 8, characterized in that: include: The data acquisition module is used to obtain Time and The sampling values ​​of the noisy input signal input to the estimated system at multiple consecutive moments before the moment constitute The noisy input signal vector at time t; Output signal calculation module, used to obtain the adaptive filter Multiple linearly constrained adaptive weights at the moment, composed of The adaptive weight vector at time ; Calculate The inner product of the adaptive weight vector at time and the noisy input signal vector is used as the adaptive filter Output signal at the moment; Input noise variance estimation calculation module, used to calculate The difference between the noisy expected signal and the output signal at time , we get The estimated error signal at time ; based on Time and Continuous before time The estimated error signal at the moment is calculated The median square error at time, is a positive integer representing the length of the median filter; based on The median square error at the moment is calculated The estimated variance of the error signal at time ; based on The adaptive weight vector at time , calculate The adaptive weight vector variance power estimate at time t, combined with The estimated variance of the error signal at time t is obtained The estimated value of the input noise variance at time t; Deviation compensation calculation module, used for The adaptive weight vector at the moment and the input noise variance estimate are obtained Deviation compensation item at the moment; Update output module for The deviation compensation term at the moment, the noisy input signal vector and the estimated error signal are updated using the error nonlinearity The adaptive weight vector at the moment is obtained The adaptive weight vector at time ; Calculate The inner product of the adaptive weight vector at time t and the noisy input signal vector is used to obtain the estimated system at Output signal at the time.

Images