CN113078884A - Adaptive algorithm with addition of non-linear fitting - Google Patents

Abstract

The invention discloses a self-adaptive algorithm for adding nonlinear fitting. The algorithm comprises the following steps: step S1, adding a nonlinear filtering module in the linear filtering module of the adaptive filter, collecting the input signal received by the adaptive filter, and intercepting the input signal to obtain the input signal of the nonlinear filtering module; step S2, carrying out nonlinear transformation on the input signal of the nonlinear filtering module to obtain a nonlinear transformation signal; step S3, calculating output signals of the nonlinear filtering module and the linear filtering module; step S4, calculating an error signal; step S5, calculating a filter update value; step S6, calculating the convergence weight coefficients of the linear filtering module and the nonlinear filtering module; and step S7, obtaining output signals of a linear filtering module and a nonlinear filtering module according to filtering operation, and superposing the two output signals to highly fit the expected signal. The algorithm is applied to a scene with a nonlinear effect, and a better system modeling effect is obtained.

Description

Adaptive algorithm for adding nonlinear fitting

technical field

The present invention relates to a method for processing a signal through an adaptive filter, in particular to an adaptive algorithm adding nonlinear fitting.

Background technique

Adaptive filter refers to a filter that uses an adaptive algorithm to change the parameters and structure of the filter according to changes in the environment. In general, the structure of the adaptive filter is not changed, and the weight coefficients of the adaptive filter are time-varying coefficients updated by the adaptive algorithm. The adaptive algorithm is based on the estimation of the statistical characteristics of the input signal and the output signal, and adopts a specific algorithm to automatically adjust the filter weight coefficients to achieve the best filtering characteristics. The least mean square algorithm (LMS algorithm) has been widely used quickly because of its easy implementation and has become the standard algorithm for adaptive filtering. This algorithm uses the steepest descent method to iteratively calculate the weight coefficient vector of the next moment from the filter weight coefficient vector at the current moment by the gradient estimation of the mean square error. The main application fields of this method are acoustic system modeling, active noise control, acoustic echo cancellation, etc.

For a linear system, the frequency components in the output signal are the same as those in the input signal. However, for nonlinear systems, the frequency in the output signal is usually not equal to the frequency in the input signal. If the input signal has more than one frequency component, the output signal will have intermodulation terms and harmonics of the input signal frequency. For example, speaker drivers are prone to nonlinear distortion, especially in the low frequency range. The main cause of nonlinear distortion is the creation of new frequency components through harmonic and intermodulation terms. The commonly used LMS algorithm does not consider the influence of nonlinear distortion in the control strategy, which restricts its application in nonlinear distortion scenarios.

SUMMARY OF THE INVENTION

The purpose of the present invention is to consider nonlinear effects, and to provide an adaptive algorithm that optimizes the addition of nonlinear fitting of the LMS algorithm under the scenario of nonlinear distortion.

In order to achieve the above object, the present invention provides an adaptive algorithm for adding nonlinear fitting, which is special in that it includes:

Step S1, input signal acquisition: adding a nonlinear filter module to the linear filter module of the adaptive filter, collecting the input signal received by the adaptive filter, and intercepting the input signal to obtain the input signal of the nonlinear filter module ;

Step S2, nonlinear transformation: performing nonlinear transformation on the input signal of the nonlinear filtering module to obtain a nonlinear transformation signal;

Step S3, signal filtering: filter to obtain the output signal of the nonlinear filter module according to the nonlinear transformation signal and the weight coefficient of the nonlinear filter module, and simultaneously filter to obtain the output signal of the linear filter module;

Step S4, error signal calculation: according to the output signal of the linear filter module, the output signal of the nonlinear filter module, and the expected signal at the output time, the error signal at the output time is obtained.

Step S5, filter update value calculation: calculate the gradient value of each filter update, update the filter coefficients of the linear module and the nonlinear module, wherein, the derivation principle of the filter update value is, the error signal function Take the square, find the expected loss function, and obtain the partial derivative operation of the loss function on the weight coefficient of the linear filter module and the weight coefficient of the nonlinear filter module respectively, and obtain the gradient update value of the weight coefficient of the linear filter module and the weight coefficient of the nonlinear filter module. The gradient update value of ;

Step S6, filter update: according to the gradient update value of the weight coefficient of the linear filter module, the gradient descent method is used to obtain the update formula of the weight coefficient of the linear filter module, and the linear filter module is repeatedly calculated according to the update formula of the weight coefficient of the linear filter module. Filtering module convergence weight coefficient; according to the gradient update value of the nonlinear filter module weight coefficient, adopt the gradient descent method to obtain the update formula of the nonlinear filter module weight coefficient, and repeat the calculation according to the update formula of the nonlinear filter module weight coefficient Obtain the nonlinear filter module convergence weight coefficient;

In step S7, the linear filtering module convergence weight coefficient and the nonlinear filtering module convergence weight coefficient are respectively subjected to filtering operation to obtain the output signal of the linear filtering module and the output signal of the non-linear filtering module. The above two output signals can be highly fitted after being superimposed the desired signal.

Preferably, in the step S2, the nonlinear transformation signal is:

u(n)=f(x _cut (n))

in,

x _cut (n)=[x(n), x(n-1),...,x(n-M+1)] ^T , x(n)=[x(n), x(n-1), ..., x(n-N+1)] ^T , M is used to represent the order of the nonlinear filter module, N is used to represent the order of the linear filter module, and M<N, the superscript T is used to represent the transpose operation, x (n) is used to represent the input signal input signal of the linear filtering module, and x _cut (n) is used to represent the input signal of the nonlinear filtering module;

n is used to represent the time;

f is used to represent nonlinear transformation;

u(n) is used to represent the nonlinear transform signal.

Preferably, in the nonlinear transformation, f can adopt the following square nonlinear transformation, which can generate a second harmonic frequency for the single-frequency signal, which is used to model the nonlinear system, as shown below:

in,

ω is used to represent the frequency of the input signal of the nonlinear filtering module;

2ω is used to represent the second harmonic frequency generated after nonlinear transformation;

() ² is used to represent the square operation;

Preferably, in the nonlinear transformation, f can adopt the following RELU nonlinear transformation, which can generate each even-order harmonic component for the single-frequency signal, which is used to model the nonlinear system, as shown below:

in,

ωt is used to represent a frequency of the nonlinear filter module;

2ωt is used to represent another frequency of the nonlinear filter module;

n is used to represent the time;

RELU is used to represent the zero-setting operation of the negative value of the signal;

Preferably, in the step S3, the output signal of the linear filter module and the output signal of the nonlinear filter module obtained by the filtering are calculated according to the following formula:

y _l (n)=x(n) ^T w _l (n)

y _nl (n)=u(n) ^T w _nl (n)

in,

x(n) is used to represent the input signal of the linear filtering module;

w _l (n) is used to represent the linear filter module weight coefficient;

u(n) is used to represent the nonlinear transformation signal of the nonlinear filtering module;

w _nl (n) is used to represent the weight coefficient of the nonlinear filter module;

n is used to represent the time;

The superscript T is used to represent the transpose operation;

y _l (n) is used to represent the output signal of the linear filter block.

y _nl (n) is used to represent the output signal of the nonlinear filter block.

Preferably, in the step S4, the error signal at the output moment is calculated according to the following formula:

e(n)=d(n)+y _l (n)+y _nl (n)

in,

d(n) is used to represent the expected signal at the output moment;

e(n) represents the error signal at the output time.

Preferably, in the step S5, the loss function is calculated according to the following formula:

J=E(e ² (n))

in,

E is used to represent the expected operation;

Preferably, in the step S5, the gradient update value of the weight coefficient of the linear filter module and the gradient update value of the weight coefficient of the nonlinear filter module are respectively:

in,

x(n) is used to represent the input signal of the linear filtering module;

u(n) is used to represent the nonlinear transformation signal of the nonlinear filtering module;

用于表示线性滤波模块权系数的梯度更新值；

The gradient update value used to represent the weight coefficients of the linear filter module;

田于表示非线性滤波模块权系数的梯度更新值；

Tian Yu represents the gradient update value of the weight coefficient of the nonlinear filter module;

The superscript T is used to denote the transpose operation.

Preferably, the gradient update value of the weight coefficient of the linear filtering module and the gradient update value of the weight coefficient of the nonlinear filtering module are obtained according to the following formula:

in,

用于表示对线性滤波模块权系数进行偏导运算；

It is used to represent the partial derivative operation on the weight coefficients of the linear filter module;

用于表示对非线性滤波模块权系数进行偏导运算；

It is used to indicate that the partial derivative operation is performed on the weight coefficients of the nonlinear filter module;

N is used to represent the linear filter module order;

M is used to represent the order of the nonlinear filter module, and M<N;

The superscript T is used to denote the transpose operation.

Preferably, in the step S6, the update formula of the linear module filter weight coefficient and the update formula of the nonlinear module filter weight coefficient are respectively as follows:

w _l (n+1)=w _l (n)-2μ _l e(n)x(n) ^T

w _nl (n+1)=w _nl (n)-2μ _nl e(n)u(n) ^T

in,

w _l (n) is used to represent the linear filter module weight coefficient;

w _nl (n) is used to represent the weight coefficient of the nonlinear filter module;

μ _l is used to represent the iterative step size that controls the convergence rate in the linear modular gradient descent method;

μ _nl is used to represent the iterative step size that controls the convergence rate in the nonlinear modular gradient descent method;

e(n) represents the error signal at the output moment;

x(n)) is used to represent the input signal of the linear filtering module;

u(n) is used to represent the nonlinear transform signal of the nonlinear filter module.

The advantages of the present invention are:

1. The adaptive algorithm of adding nonlinear fitting proposed by the present invention, adding a nonlinear filtering module to the linear filtering module of the adaptive filter, and performing nonlinear transformation on the input signal of the nonlinear filtering module, in the filtering algorithm. On the basis of , a nonlinear fitting term is added, so that the algorithm can obtain a better system modeling effect in scenarios with nonlinear effects.

2. The nonlinear transformation strategy proposed by the present invention includes squaring and setting of negative values to zero.

3. The present invention has carried out a strict mathematical proof for the proposed self-adaptive algorithm adding nonlinear fitting, and given the derivation process of the algorithm.

Description of drawings

Accompanying drawing 1 is the adaptive algorithm block diagram of linear fitting;

Accompanying drawing 2 is the self-adaptive algorithm block diagram of adding nonlinear fitting proposed by the present invention;

Accompanying drawing 3 is the power spectrum estimation of white noise signal as input signal;

Accompanying drawing 4 is the expected signal power spectrum estimation of the white noise signal output moment in accompanying drawing 3;

Accompanying drawing 5 is the MSE convergence curve comparison diagram in the self-adaptive algorithm, the self-adaptive algorithm of adding nonlinear fitting proposed by the present invention;

In the figure: speaker 1, microphone 2, MSE convergence curve 3 (an adaptive algorithm with N value of 3072), MSE convergence curve 4 (an adaptive algorithm with N value of 2048), MSE convergence curve 5 (nonlinear transformation adopts square operation The adaptive algorithm of adding nonlinear fitting), MSE convergence curve 6 (non-linear transformation adopts the self-adaptive algorithm of adding non-linear fitting with negative value zeroing operation).

Detailed ways

The present invention is described in further detail below in conjunction with the accompanying drawings and specific embodiments:

As shown in Figure 1, an adaptive algorithm is used to model the loudspeaker-enclosed space-microphone system. The input signal x(n) is played through the speaker 1, and the sound is propagated. The desired signal at the microphone 2 is d(n). The system that x(n) passes through mainly includes the speaker 1, the air, and the microphone 2. This process is modeled by an adaptive algorithm, and the update formula of the adaptive filter weight coefficients is as follows:

w(n+1)=w(n)-2μe(n)x(n)

in,

w(n) is used to represent the adaptive filter weight coefficient;

w(n+1) is used to represent the weight coefficient of the adaptive filter at the next moment;

μ is used to represent the iterative step size that controls the convergence rate in the adaptive filter gradient descent method;

e(n) represents the error signal at the output moment, e(n)=d(n)+x(n) ^Tw (n);

x(n) is used to represent the input signal of the adaptive filter, x(n)=[x(n), x(n-1), ..., x(n-N+1)] ^T , the superscript T is used for Yu represents the transpose operation, and N is used to represent the adaptive filter order.

It can be seen from the calculation formula of the adaptive algorithm that the algorithm only considers the linear fitting of the signal. As shown in Figure 2, the loudspeaker-enclosed space-microphone system is remodeled, and a nonlinear fitting term is added to the LMS algorithm to obtain a new adaptive algorithm. The steps are as follows:

Step S1, input signal acquisition: adding a nonlinear filter module to the linear filter module of the adaptive filter, collecting the input signal received by the adaptive filter, and intercepting the input signal to obtain the input signal of the nonlinear filter module;

Step S2, nonlinear transformation: perform nonlinear transformation on the input signal of the nonlinear filtering module to obtain a nonlinear transformation signal;

Step S3, signal filtering: filtering to obtain the output signal of the nonlinear filtering module according to the nonlinear transformation signal and the weight coefficient of the nonlinear filtering module; and simultaneously filtering to obtain the output signal of the linear filtering module;

Step S4, error signal calculation: according to the output signal of the linear filter module, the output signal of the nonlinear filter module and the expected signal at the output time, the error signal at the output time is obtained.

Step S5, filter update value calculation: calculate the gradient value of each filter update, and update the filter coefficients of the linear module and the nonlinear module, wherein the derivation principle of the filter update value is to square the error signal function. , Find the expected loss function, and calculate the partial derivative operation of the loss function on the weight coefficient of the linear filter module and the weight coefficient of the nonlinear filter module respectively, and obtain the gradient update value of the weight coefficient of the linear filter module and the gradient update value of the weight coefficient of the nonlinear filter module. ;

Step S6, filter update: According to the gradient update value of the weight coefficient of the linear filter module, the gradient descent method is used to obtain the update formula of the weight coefficient of the linear filter module, and the convergence weight of the linear filter module is obtained by repeated operation according to the update formula of the weight coefficient of the linear filter module. coefficient; according to the gradient update value of the weight coefficient of the nonlinear filter module, the gradient descent method is used to obtain the update formula of the weight coefficient of the nonlinear filter module, and the convergence weight coefficient of the nonlinear filter module is obtained by repeated operation according to the update formula of the weight coefficient of the nonlinear filter module ;

In step S7, the linear filtering module convergence weight coefficient and the nonlinear filtering module convergence weight coefficient are respectively subjected to filtering operation to obtain the output signal of the linear filtering module and the output signal of the non-linear filtering module. After the above two output signals are superimposed, the desired signal can be highly fitted .

In a preferred embodiment of the present invention, in step S2, the nonlinear transformation signal is:

u(n)=f(x _cut (n))

in,

x _cut (n)=[x(n), x(n-1),...,x(n-M+1)] ^T , x(n)=[x(n), x(n-1), ..., x(n-N+1)] ^T , M is used to represent the order of the nonlinear filter module, N is used to represent the order of the linear filter module, and M<N, the superscript T is used to represent the transpose operation, x (n) is used to represent the input signal input signal of the linear filtering module, and x _cut (n) is used to represent the input signal of the nonlinear filtering module;

n is used to represent time;

f is used to represent nonlinear transformation;

u(n) is used to represent the nonlinear transform signal.

In a preferred embodiment of the present invention, in the nonlinear transformation, f can take the following square nonlinear transformation, which can generate a second harmonic frequency for the single-frequency signal, which is used to model the nonlinear system, as follows Show:

in,

ω is used to represent the frequency of the input signal of the nonlinear filtering module;

2ω is used to represent the second harmonic frequency generated after nonlinear transformation;

() ² is used to represent the square operation;

In a preferred embodiment of the present invention, in the nonlinear transformation, f can adopt the following RELU nonlinear transformation, which can generate each even-order harmonic component for the single-frequency signal, which is used to model the nonlinear system, as shown below :

in,

ωt is used to represent a frequency of the nonlinear filter module;

2ωt is used to represent another frequency of the nonlinear filter module;

n is used to represent time;

RELU is used to represent the zero-setting operation of the negative value of the signal;

In a preferred embodiment of the present invention, in step S3, the output signal of the linear filter module and the output signal of the nonlinear filter module obtained by filtering are calculated according to the following formula:

y _l (n)=x(n) ^T w _l (n)

y _nl (n)=u(n) ^T w _nl (n)

in,

x(n) is used to represent the input signal of the linear filtering module;

w _l (n) is used to represent the linear filter module weight coefficient;

u(n) is used to represent the nonlinear transformation signal of the nonlinear filtering module;

w _nl (n) is used to represent the weight coefficient of the nonlinear filter module;

n is used to represent the time;

The superscript T is used to represent the transpose operation;

y _l (n) is used to represent the output signal of the linear filtering module;

y _nl (n) is used to represent the output signal of the nonlinear filter block.

In a preferred embodiment of the present invention, in step S4, the error signal at the output moment is calculated according to the following formula:

e(n)=d(n)+y _l (n)+y _nl (n)

in,

d(n) is used to represent the expected signal at the output moment;

e(n) represents the error signal at the output time.

In a preferred embodiment of the present invention, in step S5, the loss function is calculated according to the following formula:

J=E(e ² (n))

in,

E is used to represent the expected operation;

In a preferred embodiment of the present invention, in step S5, the gradient update value of the weight coefficient of the linear filter module and the gradient update value of the weight coefficient of the nonlinear filter module are respectively:

in,

x(n) is used to represent the input signal of the linear filtering module;

u(n) is used to represent the nonlinear transformation signal of the nonlinear filtering module;

田于表示线性滤波模块权系数的梯度更新值；

Tian Yu represents the gradient update value of the weight coefficient of the linear filter module;

田于表示非线性滤波模块权系数的梯度更新值；

Tian Yu represents the gradient update value of the weight coefficient of the nonlinear filter module;

The superscript T is used to denote the transpose operation.

In a preferred embodiment of the present invention, the gradient update value of the weight coefficient of the linear filter module and the gradient update value of the weight coefficient of the nonlinear filter module are obtained according to the following formula:

in,

用于表示对线性滤波模块权系数进行偏导运算；

It is used to represent the partial derivative operation on the weight coefficients of the linear filter module;

用于表示对非线性滤波模块权系数进行偏导运算；

It is used to indicate that the partial derivative operation is performed on the weight coefficients of the nonlinear filter module;

N is used to represent the linear filter module order;

M is used to represent the order of the nonlinear filter module, and M<N;

The superscript T is used to denote the transpose operation.

In a preferred embodiment of the present invention, in step S6, the update formula of the linear block filter weight coefficient and the update formula of the nonlinear block filter weight coefficient are respectively as follows:

w _l (n+1)=w _l (n)-2μ _l e(n)x(n) ^T

w _nl (n+1)=w _nl (n)-2μ _nl e(n)u(n) ^T

in,

w _l (n) is used to represent the linear filter module weight coefficient;

w _nl (n) is used to represent the weight coefficient of the nonlinear filter module;

μ _l is used to represent the iterative step size that controls the convergence rate in the linear modular gradient descent method;

μ _nl is used to represent the iterative step size that controls the convergence rate in the nonlinear modular gradient descent method;

e(n) represents the error signal at the output moment;

x(n) is used to represent the input signal of the linear filtering module;

u(n) is used to represent the nonlinear transform signal of the nonlinear filter module.

Below with a specific embodiment, the above-mentioned technical scheme is described in detail:

As shown in Figures 3 to 4, in the above speaker-enclosed space-microphone system, a white noise signal is used as the input signal x(n) through the speaker 1, and its power spectrum is shown in Figure 3. The desired signal of the played white noise propagating to the microphone is d(n), and its power spectrum is shown in Figure 4. In order to increase the nonlinear components in the system, poor performance speakers and microphones are used. Comparing Figures 3 and 4, it can be seen that the desired signal d(n) is severely lost at high frequencies relative to the input signal x(n).

得到如图5所示的MSE收敛曲线对比图。Substitute x(n) and d(n) into the self-adaptive algorithm and the self-adaptive algorithm of the present invention adding nonlinear fitting respectively, and obtain the average values of the obtained y(n), y _l (n), and y _nl (n). The squared error (MSE), which is

The MSE convergence curve comparison chart shown in Figure 5 is obtained.

in,

Curve 3 represents: in the adaptive algorithm, the MSE convergence curve with N value of 3072 and μ value of 0.001, the converged noise reduction amount is 7.59dB;

Curve 4 represents: in the adaptive algorithm, the MSE convergence curve with N value of 2048 and μ value of 0.001, the converged noise reduction amount is 9.28dB;

Curve 5 represents: in the adaptive algorithm with nonlinear fitting added, N is 2048, M is 1024, μl is 0.001, _μnl is 0.001, the _nonlinear transformation adopts the MSE convergence curve of square operation, the convergent The amount of noise reduction is 11.48dB.

Curve 6 represents: in the adaptive algorithm with nonlinear fitting added, N is 2048, M is 1024, μl is 0.001, _μnl is 0.001, and the _nonlinear transformation adopts the MSE convergence curve of negative value zeroing operation. , the convergent noise reduction is 11.87dB.

It can be seen that the noise reduction of the MSE convergence curve obtained by adding the adaptive algorithm of nonlinear fitting is significantly improved, which can effectively improve the modeling ability of the adaptive filter for nonlinear systems.

The above descriptions are only preferred embodiments of the present invention, and are not intended to limit the embodiments and protection scope of the present invention. Those skilled in the art should be aware of the equivalents made by using the description and illustrations of the present invention. The solutions obtained by substitution and obvious changes shall all be included in the protection scope of the present invention.

Claims (10)

1. an adaptive algorithm for adding nonlinear fitting, is characterized in that, comprises: Step S1, input signal acquisition: adding a nonlinear filter module to the linear filter module of the adaptive filter, collecting the input signal received by the adaptive filter, and intercepting the input signal to obtain the input signal of the nonlinear filter module ; Step S2, nonlinear transformation: performing nonlinear transformation on the input signal of the nonlinear filtering module to obtain a nonlinear transformation signal; Step S3, signal filtering: filter to obtain the output signal of the nonlinear filter module according to the nonlinear transformation signal and the weight coefficient of the nonlinear filter module, and simultaneously filter to obtain the output signal of the linear filter module; Step S4, error signal calculation: according to the output signal of the linear filter module, the output signal of the nonlinear filter module, and the expected signal at the output time, the error signal at the output time is obtained. Step S5, filter update value calculation: calculate the gradient value of each filter update, update the filter coefficients of the linear module and the nonlinear module, wherein, the derivation principle of the filter update value is, the error signal function Take the square, find the expected loss function, and obtain the partial derivative operation of the loss function on the weight coefficient of the linear filter module and the weight coefficient of the nonlinear filter module respectively, and obtain the gradient update value of the weight coefficient of the linear filter module and the weight coefficient of the nonlinear filter module. The gradient update value of ; Step S6, filter update: according to the gradient update value of the weight coefficient of the linear filter module, the gradient descent method is used to obtain the update formula of the weight coefficient of the linear filter module, and the linear filter module is repeatedly calculated according to the update formula of the weight coefficient of the linear filter module. Filtering module convergence weight coefficient; according to the gradient update value of the nonlinear filter module weight coefficient, adopt the gradient descent method to obtain the update formula of the nonlinear filter module weight coefficient, and repeat the calculation according to the update formula of the nonlinear filter module weight coefficient Obtain the nonlinear filter module convergence weight coefficient; In step S7, the linear filtering module convergence weight coefficient and the nonlinear filtering module convergence weight coefficient are respectively subjected to filtering operation to obtain the output signal of the linear filtering module and the output signal of the non-linear filtering module. The above two output signals can be highly fitted after being superimposed the desired signal. 2. The adaptive algorithm adding nonlinear fitting according to claim 1, wherein: in the step S2, the nonlinear transformation signal is: u(n)=f(x _cut (n)) in, x _cut (n)=[x(n), x(n-1),...,x(n-M+1)] ^T , x(n)=[x(n), x(n-1), ..., x(n-N+1)] ^T , M is used to represent the order of the nonlinear filter module, N is used to represent the order of the linear filter module, and M<N, the superscript T is used to represent the transpose operation, x (n) is used to represent the input signal input signal of the linear filtering module, and x _cut (n) is used to represent the input signal of the nonlinear filtering module; n is used to represent the time; f is used to represent nonlinear transformation; u(n) is used to represent the nonlinear transform signal. 3. The adaptive algorithm of adding nonlinear fitting according to claim 2, characterized in that: in the nonlinear transformation, f can take the following square nonlinear transformation, which can generate a quadratic to the single-frequency signal Harmonic frequencies, used to model nonlinear systems as follows:

in, ω is used to represent the frequency of the input signal of the nonlinear filtering module; 2ω is used to represent the second harmonic frequency generated after nonlinear transformation; () ² is used to represent the square operation. 4. the self-adaptive algorithm of adding nonlinear fitting according to claim 2, is characterized in that, in described nonlinear transformation, f can adopt following RELU nonlinear transformation, it can produce each even harmonic to single frequency signal Wave components, used to model nonlinear systems, as follows:

in, ωt is used to represent a frequency of the nonlinear filter module; 2ωt is used to represent another frequency of the nonlinear filter module; n is used to represent the time; RELU is used to represent the zero-setting operation of the negative value of the signal. 5. The adaptive algorithm of adding nonlinear fitting according to claim 3 or 4, wherein in the step S3, the linear filter module output signal obtained by the filtering and the output signal of the nonlinear filter module are based on It is calculated by the following formula: y _l (n)=x(n) ^T w _l (n) y _nl (n)=u(n) ^T w _nl (n) in, x(n) is used to represent the input signal of the linear filtering module; w _l (n) is used to represent the linear filter module weight coefficient; u(n) is used to represent the nonlinear transformation signal of the nonlinear filtering module; w _nl (n) is used to represent the weight coefficient of the nonlinear filter module; n is used to represent the time; The superscript T is used to represent the transpose operation; y _l (n) is used to represent the output signal of the linear filter block. y _nl (n) is used to represent the output signal of the nonlinear filter block. 6. The adaptive algorithm of adding nonlinear fitting according to claim 5, wherein: in the step S4, the error signal at the output moment is calculated according to the following formula: e(n)=d(n)+y _l (n)+y _nl (n) in, d(n) is used to represent the expected signal at the output moment; e(n) represents the error signal at the output time. 7. The adaptive algorithm of adding nonlinear fitting according to claim 6, wherein, in the step S5, the loss function is calculated according to the following formula: J=E(e ² (n)) in, E is used to denote an expectation operation. 8 . The adaptive algorithm for adding nonlinear fitting according to claim 7 , wherein, in the step S5 , the gradient update value of the weight coefficients of the linear filtering module and the gradient update value of the weight coefficients of the nonlinear filtering module are updated 8 . The values are:

in, x(n) is used to represent the input signal of the linear filtering module; u(n) is used to represent the nonlinear transformation signal of the nonlinear filtering module;

The gradient update value used to represent the weight coefficients of the linear filter module;

The gradient update value used to represent the weight coefficients of the nonlinear filter module; The superscript T is used to denote the transpose operation. 9. The adaptive algorithm of adding nonlinear fitting according to claim 8, wherein the gradient update value of the weight coefficient of the linear filter module and the gradient update value of the weight coefficient of the nonlinear filter module are obtained according to the following formula :

in,

It is used to represent the partial derivative operation on the weight coefficients of the linear filter module;

It is used to indicate that the partial derivative operation is performed on the weight coefficients of the nonlinear filter module; N is used to represent the linear filter module order; M is used to represent the order of the nonlinear filter module, and M<N; The superscript T is used to denote the transpose operation. 10. The adaptive algorithm for adding nonlinear fitting according to claim 9, characterized in that, in the step S6, the update formula of the linear module filter weight coefficient and the update of the nonlinear module filter weight coefficient The formulas are as follows: w _l (n+1)=w _l (n)-2μ _l e(n)x(n) ^T w _nl (n+1)=w _nl (n)-2μ _nl e(n)u(n) ^T in, w _l (n) is used to represent the linear filter module weight coefficient; w _nl (n) is used to represent the weight coefficient of the nonlinear filter module; μ _l is used to represent the iterative step size that controls the convergence rate in the linear modular gradient descent method; μ _nl is used to represent the iterative step size that controls the convergence rate in the nonlinear modular gradient descent method; e(n) represents the error signal at the output moment; x(n) is used to represent the input signal of the linear filtering module; u(n) is used to represent the nonlinear transform signal of the nonlinear filter module.

Images