Robust gradient adaptive lattice filter

Abstract

The application relates to the technical field of adaptive filter, and discloses a robust gradient adaptive lattice filter, which constructs an input vector by using input signals at current and historical moments, calculates forward and backward prediction errors of each order through a lattice structure recursion, and updates reflection coefficients by using a normalized gradient descent method; a transformation matrix formed based on the obtained reflection coefficients is used to perform linear orthogonal transformation on the input vector to generate a backward prediction error vector, and the backward prediction error vector is used as the input of a transverse filter; inner product operation is performed on the current adaptive weight vector to obtain a filtering output, and the filtering output is compared with an expected signal to generate an estimation error; a nonlinear cost function in the form of a rational fraction is constructed based on the error, a gradient of the cost function with respect to the weight is further calculated, a normalization factor of the backward prediction error vector is introduced to robustly and iteratively update the adaptive weight; and finally, the updated weight and the backward prediction error vector are subjected to inner product operation to output a filtering result resistant to impulse noise.

Description

Technical Field

[0001] This invention relates to the field of adaptive filter technology, and in particular to a robust gradient adaptive lattice filter. Background Technology

[0002] In the field of adaptive filter technology, system identification is a fundamental and crucial task. Its goal is to construct an adaptive filter to approximate the dynamic characteristics of an unknown system by observing its input and output signals. Many problems, such as adaptive channel equalization, adaptive noise cancellation, adaptive echo cancellation, and active noise control, can be reduced to the problem of system identification.

[0003] When the input signals are highly correlated (e.g., speech and communication signals), traditional Least Mean Square (LMS) or Normalized Least Mean Square (NLMS) filters for system identification suffer from slow convergence. To accelerate convergence, researchers have designed various acceleration strategies, including subband segmentation, affine projection, and observation model-based decorrelation. Subband segmentation achieves approximate whitening through frequency band division, but may introduce reconstruction distortion and additional delay. Affine projection effectively improves convergence speed but introduces high computational complexity due to matrix inversion. Observation model-based decorrelation relies on accurate modeling of the statistical characteristics of the input signals; once the model mismatches, the filter's performance degrades.

[0004] On the other hand, in some environments, the system output can be affected by impulse noise. Adaptive filters based on the mean square error (MSE) criterion are extremely sensitive to this type of noise, easily generating large filtering errors and even causing the filter to diverge. To address this, a series of robust adaptive methods have been proposed, such as error sign filters, mixture norm filters, and maximum correlation entropy (MCC) filters based on information theory criteria. These filters suppress the effects of large errors by introducing nonlinear functions and exhibit good robustness under impulse noise, but often at the cost of sacrificing convergence speed. Researchers have attempted to combine robustness with fast convergence, such as AP q-Rényi (APQR), AP tanh (APTA), and augmented AP (AAP) filters; however, these filters still have high computational complexity and are difficult to deploy on resource-constrained platforms. Therefore, designing a robust adaptive filter that combines low computational complexity and efficient decorrelation capability is of high engineering necessity. Summary of the Invention

[0005] Therefore, the technical problem to be solved by the present invention is to overcome the problems of slow convergence speed or high computational complexity of existing adaptive filters when processing highly correlated input signals, and poor robustness in impulse noise environment.

[0006] To address the aforementioned technical problems, this invention provides a robust gradient-adaptive lattice filter, comprising:

[0007] Get The input signal sample values ​​at current and historical times are used to construct... Input signal vector at any time;

[0008] by The input signal sampling values ​​at each time step are the 0th-order forward prediction error and the 0th-order backward prediction error. A lattice filter structure is used to obtain... Forward prediction errors and backward prediction errors at each time step;

[0009] Based on the forward prediction errors and backward prediction errors of each order, the normalized gradient descent method is used to update and obtain... The reflection coefficients of each order of the time-lattice filter structure are constructed. The transformation matrix at time step;

[0010] use The transformation matrix at time step performs a linear orthogonal transformation on the input signal vector to obtain... The backward prediction error vector at time step 1 is used as a transverse filter. The input vector at time step;

[0011] Calculate the transverse filter in The dot product of the adaptive weight vector and the backward prediction error vector at each time step is used to obtain the transverse filter. Output signal at time;

[0012] Calculate the transverse filter in The difference between the output signal and the desired response signal at time t is used to obtain... The estimation error signal at time;

[0013] based on Given the estimation error signal at time step 1, construct a nonlinear cost function in rational fractional form; calculate the nonlinear cost function with respect to... The gradient of the adaptive weight vector at time step;

[0014] based on The gradient and backward prediction error vector at time step, for the transverse filter at... The adaptive weight vector at time step is updated to obtain the transverse filter at time step step. The adaptive weight vector at time step.

[0015] Preferably, with The input signal sampling values ​​at each time step are the 0th-order forward prediction error and the 0th-order backward prediction error. A lattice filter structure is used to obtain... The forward prediction errors and backward prediction errors at each time step include:

[0016] by Input signal sampling value at any time Forward prediction error of order 0 With 0th order backward prediction error ;

[0017] calculate time The reflection coefficient of the lattice filter structure and time The product of the backward prediction errors of order X and then multiplied by X. time The forward prediction errors of each order are summed to obtain the result. time Forward prediction error of order;

[0018] calculate time The reflection coefficient of the lattice filter structure and time The product of the forward prediction errors of order 1 and then multiplied by 2. time The backward prediction errors of each order are summed to obtain the result. time The backward prediction error of the order; , This indicates the total order of the lattice filter structure.

[0019] Preferably, time Forward prediction error of order , is represented as:

[0020] ;

[0021] time backward prediction error of order , is represented as:

[0022] ;

[0023] in, express time Reflection coefficient of lattice-type filter structure.

[0024] Preferably, based on the forward prediction errors and backward prediction errors of each order, a normalized gradient descent method is used to update and obtain... The reflection coefficients of each order of the time-lattice filter structure include:

[0025] Timing Grid Filter Structure First-order reflection coefficient , is represented as:

[0026] ;

[0027] in, This indicates the update step size of the reflection coefficient. express time Forward prediction error of order 1 express time The backward prediction error of the order, Represents the regularization constant; , This indicates the total order of the lattice filter structure.

[0028] Preferably, based on The reflection coefficients of each order of the time-lattice filter structure are constructed. The transformation matrix at time; The transformation matrix at time t is the first line, number Column elements , is represented as:

[0029] .

[0030] Preferably, using The transformation matrix at time step 1 performs a linear orthogonal transformation on the input signal vector to obtain the backward prediction error vector, which is expressed as:

[0031] Using the transformation matrix For the input signal vector Perform a linear transformation to obtain the backward prediction error vector. , represented as ;

[0032] Among them, the th in the backward prediction error vector backward prediction error It can be represented as a linear combination of the sampled values ​​of the input signal, and its expression is: , , This indicates the total order of the lattice filter structure. express The transformation matrix at time t is the first line, number The elements of the column.

[0033] Preferably, the transverse filter is calculated in Adaptive weight vector at time step With backward prediction error vector The inner product is obtained. Output signal at time , represented as .

[0034] Preferably, based on the estimation error signal, a nonlinear cost function in rational fraction form is constructed, expressed as:

[0035] ;

[0036] in, The estimation error signal is expressed as follows: ; express The expected response signal at time. express Output signal at time; This indicates the preset scale adjustment parameters. .

[0037] Preferably, the gradient of the nonlinear cost function with respect to the adaptive weight vector is calculated as follows:

[0038] ;

[0039] in, Represents the gradient operator. express The backward prediction error vector at time t.

[0040] Preferably, based on The gradient and backward prediction error vector at time step [time], for The adaptive weight vector at time step is updated to obtain... The adaptive weight vector at time step is expressed as:

[0041] ;

[0042] in, express The adaptive weight vector at time step, This indicates the step size of the transverse filter. The norm of a vector Represents the regularization constant. This represents the gradient of the nonlinear cost function with respect to the adaptive weight vector.

[0043] Compared with the prior art, the above-described technical solution of the present invention has the following advantages:

[0044] The robust gradient adaptive lattice filter described in this invention integrates the orthogonalization characteristics of the lattice filter structure into the front-end processing of the transverse filter. It fully utilizes the inherent decorrelation advantage of the lattice filter structure on the input signal, converting the original correlated input signal into an approximately orthogonal backward prediction error vector as the input to the transverse filter. This accelerates the convergence speed of the transverse filter weights and improves filtering efficiency. Furthermore, it updates the adaptive weight vector using the gradient of a nonlinear cost function in rational fraction form constructed based on the estimation error signal. This gradient approximates the MSE criterion to ensure steady-state accuracy when the estimation error is small, and suppresses impulse interference when the error is large. This effectively avoids drastic fluctuations in weights caused by impulse noise, significantly improving the filter's robustness in environments with impulse interference.

[0045] This invention combines a rational fractional nonlinear cost function with a lattice-lateral cascade structure. It drives the weight update of the lateral filter through the backward prediction error vector and adopts a normalized gradient mechanism to achieve adaptive adjustment. It can cope with the colored characteristics at the input and the impulse interference at the output. Furthermore, it achieves joint optimization in complex scenarios where the two coexist. While ensuring low computational complexity, it significantly improves the overall filtering performance and robustness. Attached Figure Description

[0046] 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:

[0047] Figure 1 This is a flowchart of the robust gradient adaptive lattice filter provided by the present invention.

[0048] Figure 2 This is a block diagram of a gradient adaptive lattice filter;

[0049] Figure 3 This is a comparison chart of the excess mean square error of the adaptive filtering system in the system identification scenario;

[0050] Figure 4 This is a convergence comparison graph under different input signal correlation scenarios. Detailed Implementation

[0051] 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.

[0052] Reference Figure 1 The flowchart of the robust gradient adaptive lattice filter of the present invention is shown, and the specific steps include:

[0053] S101: Obtain The input signal sample values ​​at current and historical times are used to construct... Input signal vector at time 1 , is represented as: ;

[0054] S102: with The input signal sampling values ​​at each time step are the 0th-order forward prediction error and the 0th-order backward prediction error. A lattice filter structure is used to obtain... The forward prediction errors and backward prediction errors at each time step include:

[0055] S102-1: with Input signal sampling value at any time Forward prediction error of order 0 With 0th order backward prediction error ;

[0056] S102-2: Calculation time lattice filter structure reflection coefficient and time The product of the backward prediction errors of order X and then multiplied by X. time The forward prediction errors of each order are summed to obtain the result. time Forward prediction error of order , is represented as:

[0057] ;

[0058] S102-3: Calculation time lattice filter structure reflection coefficient and time The product of the forward prediction errors of order 1 and then multiplied by 2. time The backward prediction errors of each order are summed to obtain the result. time The backward prediction error of order 1 is expressed as:

[0059] ;

[0060] , Indicates the total order of the lattice filter structure;

[0061] S103: Based on the forward prediction errors and backward prediction errors of each order, the normalized gradient descent method is used to update and obtain... The reflection coefficients of each order of the time-lattice filter structure are constructed. The transformation matrix at time step;

[0062] S104: Utilization Transformation matrix at time step For the input signal vector Perform a linear orthogonal transformation to obtain backward prediction error vector at time 1 As a transverse filter The input vector at time step;

[0063] in, The backward prediction error vector contains the first... backward prediction error It can be represented as a linear combination of the sampled values ​​of the input signal, and its expression is: , ;

[0064] S105: Calculate the transverse filter in Adaptive weight vector at time step The inner product with the backward prediction error vector Obtain the transverse filter Output signal at time ;

[0065] S106: Calculate the transverse filter in Output signal at time With expected response signal The difference, obtain Time estimation error signal ;

[0066] S107: Based on Given the estimation error signal at time step 1, construct a nonlinear cost function in rational fractional form; calculate the nonlinear cost function with respect to... The gradient of the adaptive weight vector at time step;

[0067] S107-1: The nonlinear cost function in rational fraction form is expressed as: ;

[0068] S107-2: Nonlinear cost function with respect to The gradient of the adaptive weight vector at time step 1 is expressed as:

[0069] ;

[0070] in, This indicates the preset scale adjustment parameters. , Represents the gradient operator;

[0071] S108: Based on The gradient and backward prediction error vector at time step, for the transverse filter at... The adaptive weight vector at time step is updated to obtain the transverse filter at time step step. The adaptive weight vector at time step is expressed as:

[0072] ; This indicates the step size of the transverse filter.

[0073] The robust gradient adaptive lattice filter described in this invention utilizes... A linear transformation matrix composed of reflection coefficients of various orders is used to perform a linear orthogonal transformation on the input signal vector at each time step, generating the corresponding backward prediction error vector, which is then used as the input vector of the transverse filter; using... The inner product of the adaptive weight vector and the backward prediction error vector at time step 1 generates the filter output, which is then combined with the output of the system to be estimated. The expected response signal at time t is used to calculate the estimation error; based on A nonlinear cost function is constructed from the estimation error signal at time step 1, and its gradient with respect to the adaptive weight vector is calculated. Then, using this gradient, the backward prediction error vector, and its normalization factor, the current adaptive weight vector is robustly iteratively updated to obtain... The adaptive weight vector at time step.

[0074] Specifically, in step S103, the construction of the transformation matrix includes:

[0075] S103-1: Based on the forward prediction errors and backward prediction errors of each order, the normalized gradient descent method is used to update and obtain... Timing Grid Filter Structure First-order reflection coefficient , is represented as:

[0076] ;

[0077] S103-2: Based on The reflection coefficients of each order of the time-lattice filter structure are constructed. The transformation matrix at time step;

[0078] The The transformation matrix at time t is the first line, number Column elements , is represented as:

[0079] ;

[0080] in, This indicates the update step size of the reflection coefficient. express time Forward prediction error of order 1 express time The backward prediction error of the order, This represents the regularization constant.

[0081] This embodiment utilizes The input vector is constructed from the input signals at the given time and historical time points. Forward and backward prediction errors of each order are calculated using a lattice filter structure. Based on these prediction errors, the reflection coefficients are updated using a normalized gradient descent method, enabling online calculation of the lattice filter reflection coefficients. A transformation matrix is ​​constructed from the reflection coefficients of the lattice filter using recursive rules. The orthogonality of the lattice filter structure is integrated into the front-end processing of the transverse filter. By using the backward prediction error vector generated by the lattice filter structure as the input to the transverse filter, intrinsic decorrelation processing of the input signal is effectively achieved, accelerating the convergence speed of the transverse filter.

[0082] Based on the above embodiments, in this embodiment of the invention, the step of system identification using the robust gradient adaptive lattice filter provided by the present invention in a scenario where the desired signal contains impulse noise specifically includes:

[0083] S201: Obtain An input signal vector is constructed from the sampled values ​​of the input signal at time 1 and historical time 2. A lattice filter structure is then used to apply this vector. Input signal calculation at any time Forward prediction error and backward prediction error at each time step;

[0084] Input signal vector , is represented as: ;

[0085] Let the 0th order forward prediction error and backward prediction error Equal to the input signal at the current moment, denoted as ;

[0086] Update # Forward prediction error and backward prediction error for:

[0087] ;

[0088] ;

[0089] in, Indicates the first Lattice filter structure in Reflection coefficient at time; superscript This represents the vector transpose operation;

[0090] S202: Based on the aforementioned forward prediction error and backward prediction error, update using a normalized gradient descent method. The reflection coefficient of the time-space lattice structure;

[0091] exist At any time, update the number First-order reflection coefficient for:

[0092] ;

[0093] in, Update the step size for the reflection coefficient; To prevent regularization constants with denominators of zero.

[0094] S203: Exploit The transformation matrix, composed of reflection coefficients of each order, performs a linear orthogonal transformation on the input signal vector at each time step, generating the corresponding backward prediction error vector, which is then used as the input vector of the transverse filter.

[0095] Using the transformation matrix For the input signal vector Between linear transformations, the backward prediction error vector is obtained, represented as follows: ;

[0096] No. backward prediction error Represented as a linear combination of the sampled values ​​of the input signal:

[0097] , ;

[0098] in, for Transformation matrix at time step The Middle line, number The elements of the column are determined by the reflection coefficient. The calculation is expressed as:

[0099] ;

[0100] Initial conditions are =1, The order of the lattice filter structure;

[0101] This invention fully utilizes the inherent decorrelation capability of the lattice filter structure for the input signal, converts the input signal into an approximately orthogonal backward prediction error vector, and uses it as the input of the transverse filter to accelerate the convergence speed.

[0102] S204: Obtain the transverse filter in Time-adaptive weight vector To obtain the system to be estimated in Expected response signal at time ;

[0103] S205: Calculate the inner product of the adaptive weight vector and the backward prediction error vector, and use it as the transverse filter. The output signal at time is represented as ;calculate The desired signal at time and the transverse filter The difference between the output signals at each moment is obtained. The estimation error signal at time is represented as ;

[0104] S206: Based on the estimated error signal, construct a nonlinear cost function in the form of a rational fraction. , is represented as:

[0105] ;

[0106] Calculate the cost function Regarding adaptive weight vectors The gradient is:

[0107] ;

[0108] in, This is a scaling parameter used to control the sensitivity of the cost function to the magnitude of the error; For gradient operators;

[0109] This embodiment introduces a robust gradient update mechanism by introducing a nonlinear cost function based on rational fractions, which suppresses the interference of abnormal errors caused by impulse noise on weight adjustment and effectively reduces the adverse effects of input noise.

[0110] S207: Update the adaptive weight vector using the gradient of the nonlinear cost function, the backward prediction error vector, and the normalization factor of the backward prediction error vector to obtain... The adaptive weight vector at time step is expressed as:

[0111] ;

[0112] in, This represents the step size of the transverse filter; Let be the norm of the vector.

[0113] The robust gradient adaptive lattice filter described in this invention uses the backward prediction error vector generated by the lattice filter structure as the input of the transverse filter to achieve decorrelation processing of the input signal, and combines the normalized gradient based on the rational fractional nonlinear cost function to update the adaptive weight vector, so as to achieve stronger robustness in scenarios where the desired signal contains impulse noise.

[0114] To demonstrate the effectiveness of this invention, this embodiment employs computer experiments to verify the performance of the robust gradient adaptive lattice (RGAL) filter provided by this invention. The experiment estimates an unknown system under conditions of impulse noise interference and signal input, and compares the results with those of the normalized least mean square (NLMS) filter, the log-hyperbolic cosine (Lncosh) filter, and the simplified Champernowne adaptive filter (SCMAF).

[0115] Reference Figure 2 The diagram shown is a block diagram of a gradient adaptive lattice filter. In this embodiment, the noise signal is Gaussian noise plus impulse noise; the excess mean square error (EMSE) is used as the performance metric in the system's scene identification experiment. The unit is dB, where Indicates taking the logarithm. Indicates time Additive noise.

[0116] The noise signal used in the experiment It consists of two parts: one part is zero-mean Gaussian white noise. The other part is zero-mean sparse impulse noise. ,Right now Among them, the expected signal and The signal-to-noise ratio is 30 dB, and the desired signal and impulse noise are... The signal-to-noise ratio between them is -10 dB. Let be a Bernoulli random variable, with a probability of 0.9 for the variable and a probability of 0.1 for the variable. (Refer to...) Figure 3 The figure shows a comparison of the excess mean square error (NLMS) of the adaptive filtering system in the system identification scenario. The parameters of each filter are: NLMS( ); Lncosh( , ); SCMAF( , ); RGAL( , ). Reference Figure 4As shown, this is a convergence comparison diagram under different input signal correlation scenarios. The parameters of the two contrast filters are SCMAF( , ), RGAL , The correlation values ​​for different input signals were 0.3, 0.7, and 0.9. Among the parameters mentioned above, Indicates step size, Indicates the kernel width. These are design parameters. (From...) Figure 3 and Figure 4 As can be seen, the RGAL adaptive filtering system of this application has good anti-pulse performance and faster convergence speed in scenarios where the input signal is colored.

[0117] The robust gradient adaptive lattice filter described in this invention fully utilizes the inherent decorrelation advantage of the lattice filter structure for the input signal, converting the original correlated input signal into an approximately orthogonal backward prediction error vector as the input to the transverse filter. This accelerates the convergence speed of the transverse filter weights and improves filtering efficiency. Furthermore, it updates the adaptive weight vector by incorporating the gradient of a rational fractional nonlinear cost function constructed based on the estimation error signal. This gradient approximates the MSE criterion to ensure steady-state accuracy when the estimation error is small, and suppresses impulse interference when the error is large, effectively avoiding drastic weight fluctuations caused by impulse noise and significantly improving the filter's robustness in environments with impulse interference. This invention combines a rational fractional nonlinear cost function with a lattice-transverse cascade structure, drives the weight update of the transverse filter through the backward prediction error vector, and uses a normalized gradient mechanism to achieve adaptive adjustment. It can cope with colored characteristics at the input and impulse interference at the output, and achieves joint optimization in complex scenarios where both coexist. While maintaining low computational complexity, it significantly improves the overall filtering performance and robustness.

[0118] 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.

[0119] 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.

[0120] 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.

[0121] 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.

[0122] 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 gradient-adaptive lattice filter, characterized in that, include: Get The input signal sample values ​​at current and historical times are used to construct... Input signal vector at any time; by The input signal sampling values ​​at each time step are the 0th-order forward prediction error and the 0th-order backward prediction error. A lattice filter structure is used to obtain... Forward prediction errors and backward prediction errors at each time step; Based on the forward prediction errors and backward prediction errors of each order, the normalized gradient descent method is used to update and obtain... The reflection coefficients of each order of the time-lattice filter structure are constructed. The transformation matrix at time step; use The transformation matrix at time step performs a linear orthogonal transformation on the input signal vector to obtain... The backward prediction error vector at time step 1 is used as a transverse filter. The input vector at time step; Calculate the transverse filter in The dot product of the adaptive weight vector and the backward prediction error vector at each time step is used to obtain the transverse filter. Output signal at time; Calculate the transverse filter in The difference between the output signal and the desired response signal at time t is used to obtain... The estimation error signal at time; based on The estimation error signal at time t is used to construct a nonlinear cost function in rational fraction form, which is expressed as: ;in, The estimation error signal is expressed as follows: ; express The expected response signal at time. express Output signal at time; This indicates the preset scale adjustment parameters. ; Calculate the nonlinear cost function with respect to The gradient of the adaptive weight vector at time step 1 is expressed as: ;in, Represents the gradient operator. express The backward prediction error vector at time step; based on The gradient and backward prediction error vector at time step, for the transverse filter at... The adaptive weight vector at time step is updated to obtain the transverse filter at time step step. The adaptive weight vector at time step.

2. The robust gradient adaptive lattice filter according to claim 1, characterized in that, by The input signal sampling values ​​at each time step are the 0th-order forward prediction error and the 0th-order backward prediction error. A lattice filter structure is used to obtain... The forward prediction errors and backward prediction errors at each time step include: by Input signal sampling value at any time Forward prediction error of order 0 With 0th order backward prediction error ; calculate time The reflection coefficient of the lattice filter structure and time The product of the backward prediction errors of order X and then multiplied by X. time The forward prediction errors of each order are summed to obtain the result. time Forward prediction error of order; calculate time The reflection coefficient of the lattice filter structure and time The product of the forward prediction errors of order 1 and then multiplied by 2. time The backward prediction errors of each order are summed to obtain the result. time The backward prediction error of the order; , This indicates the total order of the lattice filter structure.

3. The robust gradient adaptive lattice filter according to claim 2, characterized in that, time Forward prediction error of order , is represented as: ； time backward prediction error of order , is represented as: ； in, express time Reflection coefficient of lattice-type filter structure.

4. The robust gradient adaptive lattice filter according to claim 3, characterized in that, Based on the forward prediction errors and backward prediction errors of each order, the normalized gradient descent method is used to update and obtain... The reflection coefficients of each order of the time-lattice filter structure include: Timing Grid Filter Structure First-order reflection coefficient , is represented as: ； in, This indicates the update step size of the reflection coefficient. express time Forward prediction error of order 1 express time The backward prediction error of the order, Represents the regularization constant; , This indicates the total order of the lattice filter structure.

5. The robust gradient adaptive lattice filter according to claim 4, characterized in that, based on The reflection coefficients of each order of the time-lattice filter structure are constructed. The transformation matrix at time; The transformation matrix at time t is the first line, number Column elements , is represented as: 。 6. The robust gradient adaptive lattice filter according to claim 1, characterized in that, use The transformation matrix at time step 1 performs a linear orthogonal transformation on the input signal vector to obtain the backward prediction error vector, which is expressed as: Using the transformation matrix For the input signal vector Perform a linear transformation to obtain the backward prediction error vector. , represented as ; Among them, the th in the backward prediction error vector backward prediction error It can be represented as a linear combination of the sampled values ​​of the input signal, and its expression is: , , This indicates the total order of the lattice filter structure. express The transformation matrix at time t is the first line, number The elements of the column.

7. The robust gradient adaptive lattice filter according to claim 1, characterized in that, Calculate the transverse filter in Adaptive weight vector at time step With backward prediction error vector The inner product is obtained. Output signal at time , represented as .

8. The robust gradient adaptive lattice filter according to claim 1, characterized in that, based on The gradient and backward prediction error vector at time step [time], for The adaptive weight vector at time step is updated to obtain... The adaptive weight vector at time step is expressed as: ； in, express The adaptive weight vector at time step, This indicates the step size of the transverse filter. The norm of a vector Represents the regularization constant. This represents the gradient of the nonlinear cost function with respect to the adaptive weight vector.

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