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CN-115841806-B - Transform domain robust self-adaptive filtering method for system identification

CN115841806BCN 115841806 BCN115841806 BCN 115841806BCN-115841806-B

Abstract

The invention discloses a transform domain robust self-adaptive filtering method for system identification, which comprises the steps of firstly, performing decorrelation on related signals by using an orthogonal transform matrix, and then, improving the robustness of the self-adaptive filtering method in a non-Gaussian noise environment by using a maximum entropy criterion. Meanwhile, aiming at the contradiction that the convergence speed and the steady-state error cannot be optimized simultaneously due to the step length in the self-adaptive filtering method, the two self-adaptive filters are combined by utilizing the combination factor, so that the method has the fast convergence speed and the small steady-state error finally.

Inventors

  • CUI QIN
  • LI KE

Assignees

  • 西南科技大学

Dates

Publication Date
20260512
Application Date
20221110

Claims (3)

  1. 1. The transform domain robust self-adaptive filtering method for system identification is used for effectively improving the robustness of the self-adaptive filtering under non-Gaussian noise, and is characterized by comprising the following steps: step one, modeling an input time series signal by using a first-order autoregressive model, and inputting the signal at n moments Wherein Is an adaptive filter length; step two, setting two lengths as Wherein the step size of one adaptive filter is The corresponding coefficient vector is The step size of the other adaptive filter is The corresponding coefficient vector is And (2) and Then initializing the adaptive filter coefficients; Step three, utilizing Orthogonal transform matrix of (a) For input signals Preprocessing to obtain converted input signal The expression is: , Step four, inputting the signal And respectively carrying out convolution operation with coefficient vectors of the two adaptive filters to obtain corresponding adaptive filter outputs: , , using desired signals Obtaining error signals corresponding to the two filters: , , fifthly, constructing a cost function based on a maximum entropy related entropy criterion according to the error signal obtained in the fourth step, and obtaining an expression for updating the coefficient vector of the adaptive filter by using a gradient descent method: , , In the middle of A diagonal matrix for input signal power estimation: , Wherein the method comprises the steps of A diagonal matrix is represented and, Is the first Input signals Is used for the power estimation of (a), , Wherein The expression is , Wherein the method comprises the steps of Is a constant-value smoothing factor , Step six, setting a combination factor , Performing convex combination on the two adaptive filters, and calculating the adaptive filter coefficient vector after the convex combination according to the two adaptive filter coefficient vectors in the fifth step , , With the same convex combination, the system total output signal and error signal can be expressed as; , 。
  2. 2. a transform-domain robust adaptive filtering method for system identification as claimed in claim 1, characterized by combining factors And (2) and To be about Is used to activate the function of the sigmoid, , , In the formula, Is that Iterative updating step size.
  3. 3. A transform-domain robust adaptive filtering method for system identification according to claim 1, characterized in that the two adaptive filters are independent of each other and parallel.

Description

Transform domain robust self-adaptive filtering method for system identification Technical Field The invention relates to the technical field of digital signal processing, in particular to a transform domain robust self-adaptive filtering method for system identification. Background As one of the important branches in the field of digital signal processing, the adaptive filtering technology has been developed for many years, and has been widely used in the fields of radar, communication, electronic countermeasure, echo cancellation, and the like. The Least Mean Square (LMS) algorithm is simple in structure and easy to implement, and is a widely applied adaptive filtering algorithm. Since the convergence rate of the LMS algorithm depends on the autocorrelation matrix of the input signal, it drops greatly with eigenvalue spread. Narayan et al propose a transform domain minimum mean square error (Transform Domain LMS, TDLMS) algorithm. The algorithm firstly converts input signals into a transformation domain by utilizing orthogonal transformation so as to reduce the correlation between the input signals, then constrains the eigenvalues to be near 1 by power normalization processing, reduces the eigenvalue diffusion, and finally achieves the aim of decorrelation of the input signals, thereby improving the overall convergence speed of the algorithm. The conventional TDLMS algorithm builds a cost function based on a minimum mean square error criterion, which gives the best solution for filtering when the system noise is subject to gaussian distribution. However, the TDLMS algorithm type under this criterion can be severely degraded when the system noise is impulse noise. Inspired by the theory of information learning, the maximum correlation entropy criterion is widely studied and is considered as an effective method for processing non-gaussian system noise. The correlation entropy is a local similarity measure between two random variables X and Y in the kernel space, defined asWhereinIs thatIs a function of the joint probability density of (c),Is a Mercer core. The Mercer core widely used at present is the Gaussian core. Wherein the method comprises the steps ofIs of core width and. A robust adaptive filtering algorithm under the maximum correlation entropy criterion may be implemented by maximizing the following cost function. Disclosure of Invention Aiming at the problems of the existing adaptive filtering technology, a transform domain robust adaptive filtering method for system identification is provided. Based on the maximum entropy criterion, the robustness of the adaptive filtering to non-Gaussian noise can be effectively improved. In order to achieve the above object, the present invention is achieved by the following technical scheme; a transform domain robust adaptive filtering method for system identification, comprising the steps of: step one, modeling an input time series signal by using a first-order autoregressive model, and inputting the signal at n moments WhereinIs an adaptive filter length; step two, setting two lengths as And mutually independent parallel self-adaptive filters, wherein the step length of one self-adaptive filter is as followsThe corresponding coefficient vector isThe step size of the other adaptive filter isThe corresponding coefficient vector isAnd (2) andThen initializing the adaptive filter coefficients; Step three, utilizing Orthogonal transform matrix of (a)For input signalsPreprocessing to obtain converted input signalThe expression is: ; Step four, inputting the signal And respectively carrying out convolution operation with coefficient vectors of the two adaptive filters to obtain corresponding adaptive filter outputs: using desired signals Obtaining error signals corresponding to the two filters: fifthly, constructing a cost function based on a maximum entropy related entropy criterion according to the error signal obtained in the fourth step, and obtaining an expression for updating the coefficient vector of the adaptive filter by using a gradient descent method: In the middle of ,A diagonal matrix for input signal power estimation: Wherein the method comprises the steps of A diagonal matrix is represented and,Is the firstInput signalsIs used for the power estimation of (a),,WhereinThe expression is , Wherein the method comprises the steps ofIs a constant-value smoothing factor; Step six, setting a combination factor,Performing convex combination on the two adaptive filters, and calculating the adaptive filter coefficient vector after the convex combination according to the two adaptive filter coefficient vectors in the fifth step, With the same convex combination, the system total output signal and error signal can be expressed as; combination factor And (2) andTo be aboutSigmoid activation function In the formula,Is thatIterative updating step size. Compared with the prior art, the invention has the following advantages and beneficial effects: the invention provid