Robust recursive least square adaptive filter based on inverse QR decomposition and storage medium

Abstract

The invention 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, and the method comprises the steps: calculating an inner product of an adaptive weight vector at a moment and an input signal vector, and obtaining an output signal at the moment of the adaptive filter; calculating a difference value between the expected signal and the output signal at the moment, obtaining an estimation error signal, and constructing a nonlinear weighting function; recursively updating and acquiring an inverse correlation matrix of the moment input signal vector based on the moment input signal vector and transpose thereof, a nonlinear weighting function, the inverse correlation matrix of the input signal vector and the covariance of the estimated error signal, and constructing a block matrix containing the inverse correlation matrix of the moment input signal vector; inverse QR matrix decomposition and unitary rotation operation are sequentially carried out on the block matrix, an array before inverse QR decomposition and an array after inverse QR decomposition at the moment are obtained, a gain vector at the moment is constructed, and a self-adaptive weight vector at the moment is updated and obtained.

Description

Technical Field

[0001] This invention relates to the field of telephone communication technology, and in particular to a robust recursive least squares adaptive filter and storage medium based on inverse QR decomposition. Background Technology

[0002] System identification is an important branch of adaptive signal processing. Many problems, such as traditional adaptive channel equalization, 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 their performance degrades sharply in certain special environments. For example, in some scenarios, the output signal of an unknown system may be affected by impulse noise. 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 adaptive filter design, it is typically assumed that an infinite word length (i.e., infinite precision) model is used to generate analog sampled values ​​of the input data and perform all internal operations. However, in actual digital implementations, both the input data and the data generated during iteration must be quantized to finite precision, and this quantization process affects the actual performance of the filter. RLS-type filters have the advantage of fast convergence and insensitivity to the eigenvalue distribution of the input data's autocorrelation matrix during convergence, thus exhibiting good recognition capabilities for colored input signals; however, RLS filters suffer from numerical instability due to their reliance on the Riccati equation.

[0004] Currently, engineers have designed a QR-RLS-based RLS (QR-RLS), which relies on the QR decomposition method in matrix algebra for its construction. While this method offers numerical stability, the QR-RLS filter transforms the original problem into a more easily solvable triangular system when calculating the weight vectors. However, it still requires back-substitution to obtain the final solution; that is, the calculation of each weight vector depends on the result of the previous one. This makes it difficult to efficiently obtain the filter weights at each time step. Therefore, this limits the application of QR-RLS filters to adaptive beamforming and echo cancellation, and it cannot effectively handle scenarios requiring continuous monitoring or use of weight vectors. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problems of unstable values ​​and poor filtering robustness of adaptive filters in the prior art.

[0006] To address the aforementioned technical problems, this invention provides a robust recursive least squares adaptive filter based on inverse QR decomposition, comprising: 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... The input signal vector at time t; obtaining the adaptive filter at... Moment Each adaptive weight is composed of 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; calculate 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 estimation error signal at time t, construct The nonlinear weighting function at time points; based on The input signal vector at time t and its transpose, Nonlinear weighting function at time step The inverse correlation matrix of the input signal vector at time step, and Estimate the covariance of the error signal at each time step, and recursively update to obtain it. The inverse correlation matrix of the input signal vector at each time step; based on The update of the inverse correlation matrix of the input signal vector at each time step constructs a matrix containing... The block matrix of the inverse correlation matrix of the input signal vector at each time step; Perform inverse QR matrix decomposition on the block matrix to obtain The inverse QR decomposition of the array before time step; for Before the inverse QR decomposition at time 1, the array undergoes a unitary rotation operation to obtain... The array after inverse QR decomposition at time t; based on The covariance of the block elements of the array after inverse QR decomposition at time step 1, the nonlinear weighting function, and the estimated error signal is used to construct... Gain vector at time step; calculate 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.

[0007] Preferably, the adaptive filter is obtained in The output signal at time includes: 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 ; Obtaining the adaptive filter in Moment Each adaptive weight is composed of Adaptive weight vector at time step ; 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 ; 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.

[0008] Preferably, based on The estimation error signal at time t, construct The nonlinear weighting function at time t is expressed 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.

[0009] 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: ; in, 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: .

[0010] 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: .

[0011] Preferably, for block matrices Perform inverse QR matrix decomposition to obtain Inverse QR decomposition of the array before time step , is represented as: .

[0012] 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: ; 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.

[0013] Preferably, 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 , is represented as: .

[0014] Preferably, 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 , is represented as: .

[0015] This embodiment provides a computer-readable storage medium storing a computer program thereon. 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.

[0016] Compared with the prior art, the above-described technical solution of the present invention has the following advantages: 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. Attached Figure Description

[0017] 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: Figure 1 This is a flowchart of the filtering process of the robust recursive least squares adaptive filter based on inverse QR decomposition of the present invention. Figure 2 This is a block diagram of a robust adaptive filter based on inverse QR decomposition; Figure 3 This is a comparison chart of the normalized mean square deviation curves of the adaptive filtering system in the system identification scenario. Detailed Implementation

[0018] 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.

[0019] Reference Figure 1 The flowchart of the robust recursive least squares adaptive filter based on inverse QR decomposition of the present invention is shown in S101 to S108.

[0020] S101: 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... The input signal vector at time t; obtaining the adaptive filter at... Moment Each adaptive weight is composed of 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: 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 ; S101-2: Obtaining the adaptive filter in Moment Each adaptive weight is composed of Adaptive weight vector at time step ; 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 ; 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.

[0021] 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.

[0022] 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.

[0023] 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 , is 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: .

[0024] 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 , is represented as: .

[0025] S106: Block Matrix Perform inverse QR matrix decomposition to obtain Inverse QR decomposition of the array before time step , is 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: ; 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.

[0026] 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 , is represented as: .

[0027] 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 , is represented as: .

[0028] 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.

[0029] 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: 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: ; S202: Obtain the adaptive filter in Moment Each adaptive weight is composed of Adaptive weight vector at time step , is represented as: ; 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; 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. The output signal at time t is represented as: ; 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: ; 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 , is represented as: ; 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; 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: ; in, Indicates based on Input signal vector at time After recursive update The inverse correlation matrix at time t, i.e. The reverse; Represented as The reverse, The covariance, representing the estimation error, is expressed as: ; S207: Based on the inverse correlation matrix update, construct a system containing... The block matrix containing all information of the inverse correlation matrix at time t is represented as: ; in, Represented as The estimated error signal at time t is weighted and squared. S208: Based on inclusion The block matrix containing all information of the inverse correlation matrix at time t is subjected to matrix decomposition to obtain the front array of the inverse QR decomposition, represented as: ; in, express The inverse matrix of the square root at time step; S209: Based on the front array of the inverse QR decomposition, perform a unitary rotation operation to obtain the back array of the inverse QR decomposition, represented as: ; in, express The unitary rotation at time t, express Gain vector at time step express The block elements of the array after time step 1 are expressed as follows: ; 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. S210: Calculate the block elements of the post-array based on inverse QR decomposition. Gain vector at time step , is represented as: ; in, It can be obtained from the first row of the first column of the array after inverse QR decomposition; S211: Based on The gain vector at time step is obtained. Adaptive weight vector at time step , is represented as: .

[0030] 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.

[0031] 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.

[0032] 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.

[0033] 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 the probability of it taking the value 0 is 0.99 and the probability of it taking the value 1 is 0.01. It is Gaussian white noise with zero mean and variance. . 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.

[0034] 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.

[0035] 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.

[0036] 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.

[0037] 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.

[0038] 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.

[0039] 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.

[0040] 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.

[0041] 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 robust recursive least squares adaptive filter based on inverse QR decomposition, characterized in that, include: 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... The input signal vector at time t; obtaining the adaptive filter at... Moment Each adaptive weight is composed of 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; calculate 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 estimation error signal at time t, construct The nonlinear weighting function at time points; based on The input signal vector at time t and its transpose, Nonlinear weighting function at time step The inverse correlation matrix of the input signal vector at time step, and Estimate the covariance of the error signal at each time step, and recursively update to obtain it. The inverse correlation matrix of the input signal vector at each time step; based on The update of the inverse correlation matrix of the input signal vector at each time step constructs a matrix containing... The block matrix of the inverse correlation matrix of the input signal vector at each time step; Perform inverse QR matrix decomposition on the block matrix to obtain The array before the inverse QR decomposition at time t; right Before the inverse QR decomposition at time 1, the array undergoes a unitary rotation operation to obtain... The array after inverse QR decomposition at time t; based on The covariance of the block elements of the array after inverse QR decomposition at time step 1, the nonlinear weighting function, and the estimated error signal is used to construct... Gain vector at time step; calculate 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.

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: 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 ; Obtaining the adaptive filter in Moment Each adaptive weight is composed of Adaptive weight vector at time step ; 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 ; 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.

3. The robust recursive least squares adaptive filter based on inverse QR decomposition according to claim 1, characterized in that, based on The estimation error signal at time t, construct The nonlinear weighting function at time t is expressed 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 robust recursive least squares adaptive filter based on inverse QR decomposition according to claim 1, characterized in that, 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 1 inverse correlation matrix , represented as: ； 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: .

5. The robust recursive least squares adaptive filter based on inverse QR decomposition according to claim 4, characterized in that, based on Input signal vector at time 1 inverse correlation matrix The update, build includes Block matrix of the inverse correlation matrix of the input signal vector at time step , represented as: 。 6. The robust recursive least squares adaptive filter based on inverse QR decomposition according to claim 5, characterized in that, block matrix Perform inverse QR matrix decomposition to obtain Inverse QR decomposition of the array before time step , represented as: 。 7. The robust recursive least squares adaptive filter based on inverse QR decomposition according to claim 6, characterized in that, 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: ； 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.

8. The robust recursive least squares adaptive filter based on inverse QR decomposition according to claim 7, characterized in that, 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: 。 9. The robust recursive least squares adaptive filter based on inverse QR decomposition according to claim 1, characterized in that, calculate 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: 。 10. A computer-readable storage medium having a computer program stored thereon, characterized in that, When the computer program is executed by the processor, it implements the steps of the robust recursive least squares adaptive filter based on inverse QR decomposition as described in any one of claims 1 to 9.

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