Robust recursive least squares adaptive filter based on inverse qr decomposition and storage medium

Abstract

The application relates to the technical field of telephone communication, and discloses a robust recursive least square adaptive filter based on inverse QR decomposition and a storage medium, which comprises the following steps: calculating the inner product of an adaptive weight vector at a moment and an input signal vector, and obtaining an output signal of the adaptive filter at the moment; calculating the difference between an expected signal at the moment and the output signal, obtaining an estimated error signal, and constructing a nonlinear weighting function; based on the input signal vector at the moment, a transpose of the input signal vector, the nonlinear weighting function, an inverse correlation matrix of the input signal vector, and a covariance of the estimated error signal, recursively updating the inverse correlation matrix of the input signal vector at the moment, and constructing a block matrix containing the inverse correlation matrix of the input signal vector at the moment; performing inverse QR matrix decomposition and unit rotation operation on the block matrix in sequence, obtaining an inverse QR decomposition front array and a rear array at the moment, constructing a gain vector at the moment, and updating the adaptive weight vector at the moment.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of telephone communication, in particular to a robust recursive least square adaptive filter based on inverse QR decomposition and a storage medium. BACKGROUND

[0002] System identification is an important branch of adaptive signal processing, and many problems such as traditional adaptive channel equalization, adaptive noise cancellation, adaptive echo cancellation, active noise control, etc. can be attributed to system identification. The traditional least mean square (LMS) and normalized least mean square (NLMS) adaptive filter is easy to implement, but in some special environments, the performance will decrease sharply. For example, in some scenarios, the output signal of an unknown system can be disturbed by impulse noise. In order to enhance the robustness of the adaptive filter in the impulse noise environment, a series of adaptive filters resistant to impulse noise are designed by the technical personnel, such as error symbol least mean square adaptive filter, adaptive filter based on maximum correlation entropy, adaptive filter based on logical distance metric, etc.

[0003] In the design process of adaptive filter, it is usually assumed that an infinite word length (i.e. infinite precision) model is used to generate the analog sample values of the input data, and all internal operations are performed. However, in actual digital implementation, the input data and the data generated during iteration must be quantized to a finite precision, and this quantization process will affect the actual performance of the filter. For RLS type filters, the advantage is that the convergence speed is fast, and the eigenvalue distribution of the input data autocorrelation matrix is not sensitive when converging, so it has good identification ability for colored input signals; but the RLS filter has numerical instability problem due to the dependence on Riccati equation.

[0004] At present, the technical personnel have designed an RLS based on QR decomposition (QR-RLS), which relies on the QR decomposition with good numerical properties in matrix algebra in the construction process. Although this method has numerical stability, the QR-RLS filter converts the original problem into a triangular system that is easier to solve when calculating the weight vector, but still needs to be substituted to get the final solution, that is, the calculation of each weight vector depends on the result of the previous one, and it is impossible to efficiently obtain the weight of the filter at each moment, so this limits the application of the QR-RLS filter to adaptive beamforming and echo cancellation, etc., and cannot effectively cope with scenarios that need to continuously monitor or use the weight vector. SUMMARY

[0005] Therefore, the technical problem to be solved by the present application is to overcome the numerical instability and poor filtering robustness of the adaptive filter in the prior art.

[0006] To solve the above technical problems, the application provides a robust recursive least square adaptive filter based on inverse QR decomposition, which comprises:

[0007] Obtain the sampling value of the input signal input to the system to be estimated at the continuous time points before the time point, to form an input signal vector at the time point; Obtain the adaptive weight of the adaptive filter at the time point, to form an adaptive weight vector at the time point; Obtain the inner product of the adaptive weight vector at the time point and the input signal vector, to obtain the output signal of the adaptive filter at the time point; Obtain the inner product of the adaptive weight vector at the time point and the input signal vector, to obtain the output signal of the adaptive filter at the time point; Obtain the inner product of the adaptive weight vector at the time point and the input signal vector, to obtain the output signal of the adaptive filter at the time point; Obtain the inner product of the adaptive weight vector at the time point and the input signal vector, to obtain the output signal of the adaptive filter at the time point; Obtain the inner product of the adaptive weight vector at the time point and the input signal vector, to obtain the output signal of the adaptive filter at the time point; Obtain the inner product of the adaptive weight vector at the time point and the input signal vector, to obtain the output signal of the adaptive filter at the time point;

[0008] Obtain the inner product of the adaptive weight vector at the time point and the input signal vector, to obtain the output signal of the adaptive filter at the time point; Obtain the inner product of the adaptive weight vector at the time point and the input signal vector, to obtain the output signal of the adaptive filter at the time point; Obtain the inner product of the adaptive weight vector at the time point and the input signal vector, to obtain the output signal of the adaptive filter at the time point;

[0009] Based on the estimation error signal at the time point, a nonlinear weighting function at the time point is constructed; Based on the estimation error signal at the time point, a nonlinear weighting function at the time point is constructed; Based on the estimation error signal at the time point, a nonlinear weighting function at the time point is constructed;

[0010] Based on the input signal vector at the time point and its transpose, the nonlinear weighting function at the time point, the inverse correlation matrix of the input signal vector at the time point, and the covariance of the estimation error signal at the time point, the inverse correlation matrix of the input signal vector at the time point is recursively updated to obtain; Based on the update of the inverse correlation matrix of the input signal vector at the time point, a block matrix containing the inverse correlation matrix of the input signal vector at the time point is constructed;

[0011] Based on the update of the inverse correlation matrix of the input signal vector at the time point, a block matrix containing the inverse correlation matrix of the input signal vector at the time point is constructed; Based on the update of the inverse correlation matrix of the input signal vector at the time point, a block matrix containing the inverse correlation matrix of the input signal vector at the time point is constructed;

[0012] Based on the update of the inverse correlation matrix of the input signal vector at the time point, a block matrix containing the inverse correlation matrix of the input signal vector at the time point is constructed; Based on the update of the inverse correlation matrix of the input signal vector at the time point, a block matrix containing the inverse correlation matrix of the input signal vector at the time point is constructed; Based on the update of the inverse correlation matrix of the input signal vector at the time point, a block matrix containing the inverse correlation matrix of the input signal vector at the time point is constructed; Based on the update of the inverse correlation matrix of the input signal vector at the time point, a block matrix containing the inverse correlation matrix of the input signal vector at the time point is constructed;

[0013] Based on the update of the inverse correlation matrix of the input signal vector at the time point, a block matrix containing the inverse correlation matrix of the input signal vector at the time point is constructed; Based on the update of the inverse correlation matrix of the input signal vector at the time point, a block matrix containing the inverse correlation matrix of the input signal vector at the time point is constructed; Based on the update of the inverse correlation matrix of the input signal vector at the time point, a block matrix containing the inverse correlation matrix of the input signal vector at the time point is constructed;

[0014] Based on the update of the inverse correlation matrix of the input signal vector at the time point, a block matrix containing the inverse correlation matrix of the input signal vector at the time point is constructed; ​​The product of the gain vector at time step and the estimation error signal, and... The adaptive weight vectors at each time step are summed to obtain... The adaptive weight vector at time step.

[0015] Preferably, the adaptive filter is obtained in The output signal at time includes:

[0016] Get 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 ;

[0017] Obtaining the adaptive filter in Moment Each adaptive weight is composed of Adaptive weight vector at time step ;

[0018] calculate 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 ;

[0019] in, Indicates the input signal at The sampled value at time 10:00. , This represents the total number of weights in the adaptive filter. Indicates matrix transpose; Indicates that the adaptive filter is in The first moment An adaptive weight.

[0020] Preferably, based on The estimation error signal at time t, construct The nonlinear weighting function at time t is expressed as:

[0021] ;

[0022] 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.

[0023] Preferably, based on Input signal vector at time 1 and its transpose , Nonlinear weighting function at time step , Inverse correlation matrix of the input signal vector at time step ,as well as Estimate the covariance of the error signal at each time step, and recursively update to obtain it. Input signal vector at time inverse correlation matrix , is represented as:

[0024] ;

[0025] in, express The forgetting factor of time, express Input signal vector at time 1 The inverse correlation matrix; express The covariance of the time-estimation error signal is expressed as follows: .

[0026] Preferably, based on Input signal vector at time inverse correlation matrix The update, build includes Block matrix of the inverse correlation matrix of the input signal vector at time step , is represented as:

[0027] .

[0028] Preferably, for block matrices Perform inverse QR matrix decomposition to obtain Inverse QR decomposition of the array before time step , is represented as:

[0029] .

[0030] Preferably, for Inverse QR decomposition of the array before time step Perform unitary rotation operation to obtain The array after inverse QR decomposition at time t is represented as:

[0031] ;

[0032] in, express The unitary rotation at time t; denotes the block elements of the array at time ; denotes the gain vector at time denotes the inverse QR-decomposed covariance negative square root of the estimation error.

[0033] Preferably, based on the block elements of the array at time , a nonlinear weighting function and the covariance of the estimation error signal , the gain vector at time is constructed and is expressed as:

[0034] .

[0035] Preferably, the product of the gain vector at time and the estimation error signal is calculated, and the adaptive weight vector at time is added to obtain the adaptive weight vector at time , which is expressed as:

[0036] .

[0037] The embodiment provides a computer readable storage medium, and a computer program is stored on the computer readable storage medium, and the computer program is executed by a processor to implement the steps of the robust recursive least square adaptive filter based on inverse QR decomposition.

[0038] Compared with the prior art, the above technical scheme of the application has the following beneficial effects:

[0039] The robust recursive least square adaptive filter based on inverse QR decomposition constructs a nonlinear weighting function of an error function, combines the input signal vector at time and its transpose, the inverse correlation matrix of the input signal vector, and the covariance of the estimation error signal, and recursively updates to obtain ​​​The inverse correlation matrix of the input signal vector at the moment is obtained; the inverse QR matrix decomposition and the unit rotation calculation are performed on the block matrix of the inverse correlation matrix, the gain vector is obtained, the adaptive weight is updated, and the adaptive filtering of the system output signal to be estimated is realized. The nonlinear cost function based on the estimation error signal is constructed, the filtering result with faster convergence speed and better robust performance can be obtained in the case that the expected signal is superimposed with pulse interference, the inverse QR decomposition method is used, the direct update is performed through a simple recursive formula, the good numerical characteristics of the QR decomposition are possessed, the stability of the numerical recursion is ensured, and the filtering robustness is further ensured. BRIEF DESCRIPTION OF DRAWINGS

[0040] In order to make the content of the present application more easily understood, the present application is further described in detail below according to specific embodiments of the present application and in combination with the drawings, in which:

[0041] Figure 1 is a filtering flow chart of the robust recursive least square adaptive filter based on inverse QR decomposition of the present application;

[0042] Figure 2 is a structural block diagram of the robust adaptive filter based on inverse QR decomposition;

[0043] Figure 3 is a normalized mean square error curve comparison diagram of the adaptive filtering system in the system identification scene. DETAILED DESCRIPTION

[0044] The present application is further described below in combination with the drawings and specific embodiments, so that those skilled in the art can better understand the present application and implement the present application, but the embodiments are not used as the limitation of the present application.

[0045] Referring to Figure 1 Fig. 1, the filtering flow chart of the robust recursive least square adaptive filter based on inverse QR decomposition of the present application is shown, and the specific steps are shown as S101 to S108.

[0046] S101: obtaining the sampling value of the input signal input to the system to be estimated at the moment and the moments before the moment, to form the input signal vector at the moment; obtaining the adaptive weight of the adaptive filter at the moment, to form the adaptive weight vector at the moment; calculating the inner product of the adaptive weight vector at the moment and the input signal vector, to obtain the output signal of the adaptive filter at the moment: ​​​​​​​​

[0047] S101-1: Obtain 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 ;

[0048] S101-2: Obtaining the adaptive filter in Moment Each adaptive weight is composed of Adaptive weight vector at time step ;

[0049] S101-3: 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 ;

[0050] in, Indicates the input signal at The sampled value at time 10:00. , This represents the total number of weights in the adaptive filter. Indicates matrix transpose; Indicates that the adaptive filter is in The first moment An adaptive weight.

[0051] S102: Calculation The difference between the expected signal and the output signal at time t is used to obtain... Time estimation error signal The expression is: , express The expected signal at any given moment.

[0052] S103: Based on The estimation error signal at time t, construct Nonlinear weighting function at time step The expression is: , This represents the shape control parameter of the nonlinear weighted function.

[0053] S104: Based on Input signal vector at time 1 and its transpose , Nonlinear weighting function at time step , Inverse correlation matrix of the input signal vector at time step ,as well as Estimate the covariance of the error signal at each time step, and recursively update to obtain it. Input signal vector at time inverse correlation matrix , represented as: , express The forgetting factor of time, express Input signal vector at time The inverse correlation matrix; express The covariance of the time-estimation error signal is expressed as follows: .

[0054] S105: Based on Input signal vector at time inverse correlation matrix The update, build includes Block matrix of the inverse correlation matrix of the input signal vector at time step , represented as: .

[0055] S106: Block Matrix Perform inverse QR matrix decomposition to obtain Inverse QR decomposition of the array before time step , represented as: ;right Inverse QR decomposition of the array before time step Perform unitary rotation operation to obtain The array after inverse QR decomposition at time t is represented as:

[0056] ;

[0057] in, express The unitary rotation at time t; express The block elements of the array after time step 1 are expressed as follows: ; express Gain vector at time step This represents the negative square root of the covariance of the estimation error after inverse QR decomposition.

[0058] S107: Based on Block elements of the array after inverse QR decomposition at time 1 Nonlinear weighting function Covariance with the estimated error signal , build Gain vector at time step , represented as: .

[0059] S108: Calculation Gain vector at time step With estimation error signal The product of, and Adaptive weight vector at time step Add to get Adaptive weight vector at time step , represented as: .

[0060] The robust recursive least squares adaptive filter based on inverse QR decomposition described in this invention constructs a nonlinear weighting function for the error function, combined with... The input signal vector at time step (i.e., its transpose), the inverse correlation matrix of the input signal vector, and the covariance of the estimation error signal are recursively updated to obtain... The inverse correlation matrix of the input signal vector is obtained at each time step. Inverse QR matrix decomposition and unitary rotation are performed on the block matrix of the inverse correlation matrix to obtain the gain vector. The adaptive weights are then updated to achieve adaptive filtering of the output signal of the system to be estimated. This invention constructs a nonlinear cost function based on the estimation error signal, which can obtain filtering results with faster convergence and better robustness even when the desired signal is superimposed with impulse interference. Simultaneously, by utilizing the inverse QR decomposition method, updates are directly performed through a simple recursive formula, and the good numerical characteristics of QR decomposition are maintained, ensuring the stability of the numerical recursion and further guaranteeing the robustness of the filtering.

[0061] Based on the above embodiments, in this embodiment of the invention, the step of system identification in a scenario where the desired signal contains impulse noise, using the robust recursive least squares adaptive filter based on inverse QR decomposition provided by the present invention, specifically includes:

[0062] 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 , represented as:

[0063] ;

[0064] S202: Obtain the adaptive filter in Moment Each adaptive weight is composed of Adaptive weight vector at time step , represented as: ;

[0065] in, Indicates the input signal at The sampled value at time 10:00. express The adaptive weight vector at time t is the first An adaptive weight, , Indicates the transpose operation;

[0066] S203: Calculation The dot product of the adaptive weight vector and the input signal vector at time step 1 is used as the adaptive filter. The output signal at time t is represented as: ;

[0067] S204: Calculation The difference between the preset expected signal and the output signal at a given time is obtained. The estimation error signal at time t is expressed as: ;

[0068] S205: Using nonlinear functions to... The estimated error signals at each time point are weighted and recursively updated to obtain... Robust weighted autocorrelation matrix of the input signal at each time step , represented as:

[0069] ;

[0070] in, express The forgetting factor of time, express Input signal vector at time The autocorrelation matrix, Representing nonlinear function pairs The estimation error signals at time 1 are weighted and represented as follows: , These are parameters that control the shape of the nonlinear function;

[0071] S206: Based on Input signal vector at time 1 and its transpose and Nonlinear weighting function at time step ,as well as Inverse correlation matrix of the input signal vector at time step ,as well as Estimate the covariance of the error signal at each time step and update the obtained value. Input signal vector at time The inverse correlation matrix is ​​expressed as:

[0072] ;

[0073] wherein, is based on the input signal vector at time after recursive update the inverse correlation matrix at time , i.e., the inverse of is expressed as the inverse of is expressed as the covariance of the estimation error, and ;

[0074] S207: Based on the update of the inverse correlation matrix, a block matrix containing all information of the inverse correlation matrix at time is constructed, which is expressed as:

[0075] ;

[0076] wherein, is expressed as the weighted square root of the estimation error signal at time

[0077] S208: Based on the block matrix containing all information of the inverse correlation matrix at time , a matrix decomposition operation is performed to obtain the front array of the inverse QR decomposition, which is expressed as:

[0078] ;

[0079] wherein, is expressed as the square root inverse matrix at time

[0080] S209: Based on the front array of the inverse QR decomposition, a unitary rotation operation is performed to obtain the back array of the inverse QR decomposition, which is expressed as:

[0081] ;

[0082] wherein, is expressed as the unitary rotation quantity at time is expressed as the gain vector at time is expressed as the block element of the back array at time ;

[0083] The weight vector of inverse QR-RLS can be directly updated using a simple recursive formula and possesses the favorable numerical properties of QR decomposition. This filter is well-suited for scenarios requiring continuous monitoring or use of the weight vector, such as system identification, spectral estimation, and adaptive equalization. Furthermore, its cost function can be further optimized to improve the robustness of the filtering method.

[0084] S210: Calculate the block elements of the post-array based on inverse QR decomposition. Gain vector at time step , represented as:

[0085] ;

[0086] in, It can be obtained from the first row of the first column of the array after inverse QR decomposition;

[0087] S211: Based on The gain vector at time step is obtained. Adaptive weight vector at time step , represented as: .

[0088] The robust recursive least squares adaptive filter based on inverse QR decomposition described in this invention uses the inverse QR decomposition method to calculate the gain vector and update the adaptive weights to achieve adaptive filtering of the output signal of the system to be estimated. At the same time, nonlinear functions are incorporated 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.

[0089] To demonstrate the effectiveness of this invention, this embodiment employs computer experiments to verify the performance of the robust recursive least squares (R-IQR-RLS) adaptive filter based on inverse QR decomposition provided by this invention. The experiment was conducted in an environment with impulse noise interference and a noisy input signal to identify the application scenario and estimate the unknown system. The results were compared with those of an RLS (IQR-RLS) filter based on inverse QR decomposition and a recursive minimum M-estimation (QR-RLM) adaptive filter based on QR decomposition.

[0090] Reference Figure 2 The diagram shown is a block diagram of a robust adaptive filter based on inverse QR decomposition. 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.

[0091] 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 process, i.e. ,in It is a Bernoulli process, and its probability of taking the value 0 is 0.99, and its probability of taking the value 1 is 0.01. It is Gaussian white noise with zero mean and variance of . . Reference Figure 3 The figure shows a comparison of the normalized mean square deviation curves of the adaptive filtering system in the system identification scenario. The parameters of each method are IQR-RLS (…). ), QR-RLM ( ), R-IQR-RLS ( In system identification scenarios, the R-IQR-RLS adaptive filtering system of this application embodiment all exhibits good anti-pulse performance.

[0092] The robust recursive least squares adaptive filter based on inverse QR decomposition described in this invention incorporates nonlinear functions into the entire adaptive filtering calculation process. Utilizing the inverse QR decomposition method, it calculates the gain vector and updates the adaptive weights, making the adaptive filtering process more stable and resulting in filtering results with faster convergence and better robustness. This invention enables the desired signal to achieve stronger robustness in scenarios containing impulse noise and effectively reduces the adverse effects of input noise.

[0093] Based on the above embodiments, the present invention provides a computer-readable storage medium storing a computer program thereon, wherein when the computer program is executed by a processor, it implements the steps of the robust recursive least squares adaptive filter based on inverse QR decomposition as described above.

[0094] The robust recursive least squares adaptive filter based on inverse QR decomposition described in this invention constructs a nonlinear weighting function for the error function, combined with... The input signal vector at time step (i.e., its transpose), the inverse correlation matrix of the input signal vector, and the covariance of the estimation error signal are recursively updated to obtain... The inverse correlation matrix of the time input signal vector is obtained; the inverse QR matrix decomposition and the unit rotation calculation are performed on the block matrix of the inverse correlation matrix, the gain vector is obtained, the adaptive weight is updated, and the adaptive filtering of the system output signal to be estimated is realized.

[0095] Those skilled in the art will understand that the embodiments of the present application can be provided as methods, systems or computer program products. Therefore, the present application can take the form of an entirely hardware embodiment, an entirely software embodiment or an embodiment combining software and hardware aspects. Moreover, the present application can take the form of a computer program product implemented on one or more computer-usable storage media (including, but not limited to, disk storage, CD-ROMs, optical storage devices, etc.) containing computer-usable program code.

[0096] The present application is described with reference to flowcharts and / or block diagrams according to the methods, devices (systems) and computer program products of the embodiments of the present application. It should be understood that each flow and / or block in the flowcharts and / or block diagrams, and the combination of flows and / or blocks in the flowcharts and / or block diagrams can be implemented by computer program instructions. These computer program instructions can be provided to a general-purpose computer, a special-purpose computer, an embedded processor or other programmable data processing devices to produce a machine, so that the instructions executed by the computer or other programmable data processing devices generate a device that implements the functions specified in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 an apparatus that carries out the functions specified in one or more flows and / or blocks.

[0097] These computer program instructions can also be stored in a computer-readable memory that can direct the computer or other programmable data processing devices to work in a specific manner, so that the instructions stored in the computer-readable memory produce a manufactured product including instruction devices that implement the functions specified in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocks Figure 1 an apparatus that carries out the functions specified in one or more flows and / or blocks.

[0098] These computer program instructions can also be loaded into a computer or other programmable data processing device, so that a series of operation steps are performed on the computer or other programmable device to produce a computer-implemented process, so that the instructions executed on the computer or other programmable device provide a process for implementing the functions specified in the flowcharts and / or block diagrams. Figure 1 one or more flows and / or blocksFigure 1 the steps of the functions specified in the one or more blocks.

[0099] Obviously, the above-described embodiments are only examples for the purpose of clarity and are not intended to limit the implementation. Based on the above description, other different forms of changes or variations can also be made by those of ordinary skill in the art. Here, it is not necessary and impossible to exhaust all the implementations. The obvious changes or variations derived therefrom are still within the protection scope of the present application.

Claims

1. A robust recursive least squares adaptive filter based on inverse QR decomposition, characterized in that, Comprising: acquiring the time instant and successively before the time instant sample values of an input signal input to the system to be estimated at the time instant, to form an input signal vector at the time instant; acquiring adaptive weights of the adaptive filter at the time instant, to form an adaptive weight vector at the time instant; calculating an inner product of the adaptive weight vector at the time instant and the input signal vector, to acquire an output signal of the adaptive filter at the time instant;​ Computing the difference between the expected signal and the output signal at the time instant, obtaining an estimation error signal at the time instant; Based on an estimate error signal of the time instant, a nonlinear weighting function is constructed of the time instant, expressed as: ; wherein, represents an estimate error signal of the time instant, expressed as , represents an expected signal of the time instant, represents an output signal of the time instant; represents a nonlinear weighting function shape control parameter; based on the input signal vector at time instant n and its transpose, a non-linear weighting function of time instant n, the inverse correlation matrix of the input signal vector at time instant n, and the covariance of the estimation error signal at time instant n, recursively update the inverse correlation matrix of the input signal vector at time instant n; Based on the update of the inverse correlation matrix of the input signal vector at the moment, the block matrix containing the inverse correlation matrix of the input signal vector at the moment is constructed, and is expressed as: ; wherein, represents the forgetting factor at the moment, represents the transpose of the input signal vector at the moment , and represents the inverse correlation matrix of the input signal vector at the moment . An inverse QR matrix decomposition is performed on the block matrix to obtain The inverse QR decomposition pre-array at the time instant is denoted as: ; On the basis of the above-mentioned method, the present application further provides a method for obtaining a QR decomposition of a matrix. A unitary rotation operation is performed on the inverse QR decomposition pre-array at the time point to obtain an inverse QR decomposition post-array at the time point. A unitary rotation operation is performed on the inverse QR decomposition pre-array at the time point to obtain an Based on the block elements of the inverse QR decomposition of the array at time t, the nonlinear weighting function, and the covariance of the estimation error signal, construct the gain vector at time t; Computing the product of the gain vector at the time instant and the estimation error signal, and adding the product to the adaptive weight vector at the time instant to obtain the adaptive weight vector at the time instant the product of the gain vector at the time instant and the estimation error signal, and adding the product to the adaptive weight vector at the time instant to obtain the adaptive weight vector at the time instant the product of the gain vector at the time instant and the estimation error signal, and adding the product to the adaptive weight vector at the time 2. The robust recursive least squares adaptive filter based on inverse QR decomposition according to claim 1, characterized in that, Obtaining the adaptive filter in The output signal at time includes: acquiring the time instant and the time instant before sample values of an input signal input to the system to be estimated at the time instant, to form an input signal vector at the time instant ; An adaptive filter is acquired at a time instant of the adaptive weights, constituting an adaptive weights vector at a time instant ; Computing the inner product of the adaptive weight vector at the time instant and the input signal vector, obtaining the output signal of the adaptive filter at the time instant ; and ; wherein, represents a sample value of the input signal at time , , represents a total number of weights of the adaptive filter, represents a matrix transpose; represents an adaptive weight of the adaptive filter at time , th adaptive weight.

3. The robust recursive least squares adaptive filter based on inverse QR decomposition of claim 1, wherein, based on the input signal vector at time instant and its transpose , the non-linear weighting function at time instant , the inverse correlation matrix of the input signal vector at time instant , and the covariance of the estimation error signal at time instant , recursively updated as the inverse correlation matrix of the input signal vector at time instant is denoted by ； wherein denotes a forgetting factor at time instant denotes the inverse correlation matrix of the input signal vector at time instant denotes the covariance of the estimation error signal at time instant .

4. The robust recursive least squares adaptive filter based on inverse QR decomposition of claim 1, wherein, To the inverse QR decomposition of the array at time t Perform a unitary rotation operation to obtain the inverse QR decomposition of the array at time t, denoted as ； where denotes a unitary rotation at time denotes a block element of the array after time ; denotes a gain vector at time denotes the inverse QR-decomposed covariance negative square root of the estimation error.

5. The robust recursive least squares adaptive filter based on inverse QR decomposition of claim 4, wherein, based on block elements of the inverse QR decomposition of the array at time instant , a non-linear weighting function covariance of the estimation error signal , constructing gain vector at time instant is expressed as: 。 6. The robust recursive least squares adaptive filter based on inverse QR decomposition of claim 1, wherein, Computing the gain vector at time instant the product of the estimation error signal and the adaptive weight vector at time instant the adaptive weight vector at time instant is obtained by adding the adaptive weight vector at time instant is expressed as 。 7. A computer-readable storage medium having stored thereon a computer program, characterized in that, The computer program, when executed by a processor, implements the steps of the robust recursive least squares adaptive filter based on inverse QR decomposition according to any one of claims 1 to 6.

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