CN111103800A - Noise pollution signal differential obtaining method based on arc tangent amplification differentiator - Google Patents

Abstract

The invention discloses a noise pollution signal differential obtaining method based on an arc tangent augmentation differentiator, which has the main idea that the measured integral of a zero-mean noise pollution signal is expanded into an additional state of a signal dynamic system, so that the augmentation system is designed based on the arc tangent integration augmentation differentiator to obtain signal differential. The method is mainly realized by the following steps: firstly, establishing a zero-mean noise pollution signal dynamic system model; then, the measurement signal integral is expanded to a new system state, and a signal integral expansion dynamic system model is established; further, an integral amplification nonlinear differentiator based on an arc tangent function is constructed; and finally, selecting parameters of an integral amplification differentiator to obtain the differentiation of the zero-mean noise pollution signal. The method can effectively solve the problem that the differential effect of the existing method for obtaining the zero-mean noise pollution signal is poor, and is suitable for the field of obtaining the differential of the zero-mean noise pollution signal.

Description

A Differential Acquisition Method of Noise Polluted Signal Based on Arctangent Augmented Differentiator

technical field

The invention relates to a noise pollution signal differential acquisition method based on an arctangent augmented differentiator, and belongs to the field of signal processing.

Background technique

In the field of signal processing and engineering control, the acquisition of differential signals has always been a technical difficulty. The precise extraction of differential signals is of great significance to control methods such as PID control, inversion control and dynamic sliding mode control, and is also widely used in signal processing and parameter estimation. However, the differentiation of signals is generally considered to be inaccessible by direct measurement. Early methods usually use differential or look-ahead networks for approximate estimation, but have disadvantages such as low accuracy and poor noise suppression capability.

In recent years, higher-order sliding-mode differentiators, nonlinear tracking differentiators, and finite-time differentiators have been used for signal differentiation acquisition. However, when the signal is polluted by noise, there are generally problems such as low precision and unsatisfactory noise suppression effect. Zero-mean noise exists widely in practical systems. In many engineering application scenarios, the signal to be measured is often polluted by zero-mean noise. Therefore, it is necessary to invent a brand-new differential acquisition method of zero-mean-noise-contaminated signals to solve the problem of poor resistance to zero-mean noise of the existing differential acquisition methods.

SUMMARY OF THE INVENTION

The technical problem to be solved by the present invention is to provide a noise-polluted signal differential acquisition method based on an arctangent augmented differentiator, which can effectively solve the problem that the existing method has poor differential effect of zero-average noise-polluted signal.

The present invention adopts the following technical solutions for solving the above-mentioned technical problems:

A method for differential acquisition of noise-polluted signals based on an arctangent augmented differentiator, comprising the following steps:

Step 1, establishing a dynamic system model of the zero-mean-noise-polluted signal according to the actual measured zero-mean-noise-polluted signal;

In step 2, the actual measured zero-mean noise pollution signal is integrated and augmented into a new system state of the dynamic system model established in step 1, thereby establishing a signal integration augmented dynamic system model;

Step 3, build an integral augmented nonlinear differentiator based on the arctangent function; the specific process is:

Step 31: Define z _-1 , z ₀ , and z ₁ to correspond to the estimated values of x _-1 , x ₀ , and x ₁ respectively, and x _-1 , x ₀ , and x ₁ to represent the integral of the measured signal, the true value of the actual signal, Differentiation of the actual signal;

Step 32, build an integral augmented nonlinear differentiator based on the arctangent function, which is:

z_-1(t),z₀(t),z₁(t)分别对应为x_-1(t),x₀(t),x₁(t)的估计值，z_-1(0)为z_-1(t)的初始值，z_-1(0)的取值为z_-10，z₀(0)为z₀(t)的初始值，z₀(0)的取值为z₀₀，z₁(0)为z₁(t)的初始值，z₁(0)的取值为z₁₀，R为微分器加速度因子，b和a_i为待调节的微分器参数，b＞0，a_i＞0,i＝-1,0,1；in,

z _-1 (t), z ₀ (t), z ₁ (t) correspond to the estimated values of x _-1 (t), x ₀ (t), and x ₁ (t), respectively, and z _-1 (0) is The initial value of z _-1 (t), the value of z _-1 (0) is z _-10 , the value of z ₀ (0) is the initial value of z ₀ (t), and the value of z ₀ (0) is z ₀₀ , z ₁ (0) is the initial value of z ₁ (t), z ₁ (0) is z ₁₀ , R is the differentiator acceleration factor, b and a _i are the differentiator parameters to be adjusted, b>0 , a _i > 0, i=-1, 0, 1;

Step 4: Adjust the parameters of the integral-augmented nonlinear differentiator, and obtain the differential of the zero-mean noise pollution signal according to the adjusted integral-augmented nonlinear differentiator.

As a preferred solution of the present invention, the zero-average noise-polluted signal dynamic system model in step 1 is:

Among them, y(t)=υ(t) is the actual measured zero-average noise pollution signal, n(t) is the zero-average noise signal, and x ₀ (t) and x ₁ (t) are the true value of the actual signal and its value, respectively. Differential, t represents time, x ₀ (0) is the initial value of x ₀ (t), x ₀ (0) is x ₀₀ , x ₁ (0) is the initial value of x ₁ (t), x ₁ ( 0) takes the value x ₁₀ .

As a preferred solution of the present invention, the specific process of the step 2 is:

后增广为步骤1建立的动态系统模型新的系统状态；Step 21: Integrate the actual measured zero mean noise pollution signal

After augmentation, it is the new system state of the dynamic system model established in step 1;

Step 22, establishing a signal integral augmented dynamic system model, which is:

Among them, x _-1 (t) is the integral of the measurement signal υ(τ), x _-1 (0) is the initial value of x _-1 (t), x _-1 (0) is the value of x _-10 , n (t) zero-mean noise signal, x ₀ (t) and x ₁ (t) are the true value of the actual signal and its differential, t represents time, x ₀ (0) is the initial value of x ₀ (t), x ₀ (0) is x ₀₀ , x ₁ (0) is the initial value of x ₁ (t), and x ₁ (0) is x ₁₀ .

As a preferred solution of the present invention, the specific process of the step 4 is:

Step 41: Gradually increase the differentiator acceleration factor R until the desired signal estimation accuracy and anti-noise performance are obtained, and the adjustment of the parameter R is completed;

Step 42: Gradually increase the differentiator parameters a ₀ and b until the expected signal estimation response speed is obtained, and the adjustment of the parameters a ₀ and b is completed;

Step 43: On the basis of steps 41 and 42, gradually increase the differentiator parameter a _-1 and gradually decrease the differentiator parameter a ₁ , until the desired signal differential estimation accuracy is obtained, and the adjustment of the parameters a _-1 and a ₁ is completed. , so as to complete the adjustment of the differentiator parameters, and obtain the differential of the zero-average noise pollution signal according to the adjusted integral augmented nonlinear differentiator.

Compared with the prior art, the present invention adopts the above technical scheme, and has the following technical effects:

1. The method of the present invention can realize the accurate extraction of the differential signal of the signal polluted by zero mean noise.

2. The method of the present invention has a wide range of applications, and can be widely used in the fields of signal processing and engineering control for differential extraction of signals polluted by zero mean noise.

3. The method of the present invention has the advantages of simple method, standardized parameter adjustment and easy engineering realization.

Description of drawings

Figure 1 is a flow chart of the present invention.

FIG. 2 is a filtering estimation result of a noise-contaminated signal in an embodiment of the present invention.

FIG. 3 is a differential estimation result of a noise-contaminated signal in an embodiment of the present invention.

FIG. 4 is the result of the differential estimation error of the noise-contaminated signal in the embodiment of the present invention.

Detailed ways

Embodiments of the present invention are described in detail below, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are exemplary and are only used to explain the present invention, but not to be construed as a limitation of the present invention.

The present invention is a method for differential acquisition of zero-average noise-contaminated signals based on arctangent integral augmented differentiators. First, a dynamic system model of zero-average noise-contaminated signals is established; then, the integral of the measurement signal is augmented into a new system state, and a signal is established. The integral-augmented dynamic system model; then, an integral-augmented nonlinear differentiator based on the arctangent function is constructed; finally, the parameters of the integral-augmented differentiator are selected to obtain the differential of the zero-mean noise pollution signal.

As shown in FIG. 1 , the method for obtaining the differential signal of zero-mean noise pollution signal based on the arctangent integral augmented differentiator specifically includes the following steps:

In this embodiment, the signal to be measured is selected as the sinusoidal signal 2sin(t), and the variance of the zero mean noise signal n(t) is 0.01.

Step 1. Establish a dynamic system model of zero mean noise pollution signal; specifically:

In the formula, y(t)=υ(t) is the actual measured zero-average noise pollution signal, n(t) is zero-average noise; x ₀ (t) and x ₁ (t) are the true value of the actual signal and its differential , x ₀₀ and x ₁₀ are their initial values, respectively.

In this step, the initial values x ₀₀ =0 and x ₁₀ =0 are selected.

增广为新的系统状态，建立信号积分增广动态系统模型。Step 2. Integrate the measurement signal

The augmentation is a new system state, and a signal integral augmented dynamic system model is established.

Specific steps are as follows:

增广为原信号动态系统新的系统状态；Step 201. Integrate the measurement signal

Augment the new system state of the original signal dynamic system;

Step 202, establishing a signal integral augmentation dynamic system model; the details are as follows:

In the formula, x _-1 (t) is the integral of the measurement signal υ(τ).

Step 3: Build an integral augmented nonlinear differentiator based on the arctangent function.

Specific steps are as follows:

Step 301, define z _-1 , z ₀ , and z ₁ as the estimated values of formula (2) x _-1 , x ₀ , and x ₁ in step 202, respectively;

Step 302: Build an integral augmented nonlinear differentiator based on the arctangent function; the details are as follows:

In the formula, atan(x ₁ , x ₂ , x ₃ )=x ₂ atan(x ₃ (x ₁ )), z _-10 , z ₀₀ and z ₁₀ are the initial values respectively, R is the differentiator acceleration factor, b >0 and a _i >0, i=-1, 0, 1 are differentiator parameters to be adjusted.

Step 4: Adjust the parameters of the integral augmented differentiator to obtain the differential of the zero-average noise-polluted signal.

Specific steps are as follows:

Step 401, gradually increase R until the desired signal estimation accuracy and anti-noise performance are obtained, and the adjustment of the parameter R is completed;

Step 402, gradually increase a ₀ and b until the desired signal estimation response speed is obtained;

Step 403 , on the basis of step 401 and step 402 , gradually increase a _-1 while gradually decreasing a ₁ , so as to further improve the estimation accuracy of signal differentiation, thereby completing the adjustment of the differentiator parameters.

In this step, the differentiator parameters are selected as: R=15, a _-1 =5, a ₀ =5, a ₁ =10, b=2.

Using a method for differential acquisition of signals polluted by zero-mean noise pollution based on arctangent integral augmented differentiator of the present invention, for the signal to be measured 2sin(t) and zero-mean noise n(t) set as above, the estimation of the signal to be measured is obtained by simulation Result plots of value, noise-contaminated signal differential estimation, and noise-contaminated signal differential estimation error.

As shown in FIG. 2 , it is the filtering estimation result of the noise-contaminated signal in this embodiment. It can be seen that although the measurement signal is polluted by noise, the signal to be measured can be accurately estimated by using the integral-augmented differentiator based on the present invention after accumulating integral augmentation. There is no obvious noise pollution in the estimated value of the signal, and the overall situation is relatively smooth.

As shown in FIG. 3 , it is the result of differential estimation of the noise-contaminated signal in this embodiment. It can be seen that although the differential of the signal to be measured has a noise limit, the differential of the signal to be measured can be accurately estimated by using the integral augmented differentiator based on the present invention. The estimated value of the signal differential has a good fit with the ideal differential signal 2cos(t). At t=0s, the differential estimate deviates significantly from the true value, which is because the initial value of the differentiator is set to x ₀₀ =0. Subsequently, the signal differential estimate quickly approaches the true value 2cos(t).

As shown in FIG. 4 , it is the result of the differential estimation error of the noise-contaminated signal in this embodiment. It can be seen that at t=0s, the differential estimation error is relatively large (2), which is because the initial value of the differentiator is set to x ₀₀ =0. Subsequently, the differential estimation error of the zero-mean-noise-contaminated signal quickly falls within a small range and remains in the range [-0.3, 0.3] all the time.

Based on the above analysis and simulation verification, the effectiveness of the noise-contaminated signal differential acquisition method based on the arctangent integral augmented differentiator of the present invention in obtaining the zero-average noise-contaminated signal differential is fully verified.

The above embodiments are only to illustrate the technical idea of the present invention, and cannot limit the protection scope of the present invention. Any modification made on the basis of the technical solution according to the technical idea proposed by the present invention falls within the protection scope of the present invention. Inside.

Claims (4)

1. a noise pollution signal differential acquisition method based on arctangent augmented differentiator, is characterized in that, comprises the steps: Step 1, establishing a dynamic system model of the zero-mean-noise-polluted signal according to the actual measured zero-mean-noise-polluted signal; In step 2, the actual measured zero-mean noise pollution signal is integrated and augmented into a new system state of the dynamic system model established in step 1, thereby establishing a signal integration augmented dynamic system model; Step 3, build an integral augmented nonlinear differentiator based on the arctangent function; the specific process is: Step 31: Define z _-1 , z ₀ , and z ₁ to correspond to the estimated values of x _-1 , x ₀ , and x ₁ respectively, and x _-1 , x ₀ , and x ₁ to represent the integral of the measured signal, the true value of the actual signal, Differentiation of the actual signal; Step 32, build an integral augmented nonlinear differentiator based on the arctangent function, which is:

in,

z _-1 (t), z ₀ (t), z ₁ (t) correspond to the estimated values of x _-1 (t), x ₀ (t), and x ₁ (t), respectively, and z _-1 (0) is The initial value of z _-1 (t), the value of z _-1 (0) is z _-10 , the value of z ₀ (0) is the initial value of z ₀ (t), and the value of z ₀ (0) is z ₀₀ , z ₁ (0) is the initial value of z ₁ (t), z ₁ (0) is z ₁₀ , R is the differentiator acceleration factor, b and a _i are the differentiator parameters to be adjusted, b>0 , a _i > 0, i=-1, 0, 1; Step 4: Adjust the parameters of the integral-augmented nonlinear differentiator, and obtain the differential of the zero-mean noise pollution signal according to the adjusted integral-augmented nonlinear differentiator. 2. The noise pollution signal differential acquisition method based on arctangent augmented differentiator according to claim 1, is characterized in that, the zero mean noise pollution signal dynamic system model described in step 1 is:

Among them, y(t)=υ(t) is the actual measured zero-average noise pollution signal, n(t) is the zero-average noise signal, and x ₀ (t) and x ₁ (t) are the true value of the actual signal and its value, respectively. Differential, t represents time, x ₀ (0) is the initial value of x ₀ (t), x ₀ (0) is x ₀₀ , x ₁ (0) is the initial value of x ₁ (t), x ₁ ( 0) takes the value x ₁₀ . 3. the noise pollution signal differential acquisition method based on arctangent augmented differentiator according to claim 1, is characterized in that, the concrete process of described step 2 is: Step 21: Integrate the actual measured zero mean noise pollution signal

After augmentation, it is the new system state of the dynamic system model established in step 1; Step 22, establishing a signal integral augmented dynamic system model, which is:

Among them, x _-1 (t) is the integral of the measurement signal υ(τ), x _-1 (0) is the initial value of x _-1 (t), x _-1 (0) is the value of x _-10 , n (t) zero-mean noise signal, x ₀ (t) and x ₁ (t) are the true value of the actual signal and its differential, t represents time, x ₀ (0) is the initial value of x ₀ (t), x ₀ (0) is x ₀₀ , x ₁ (0) is the initial value of x ₁ (t), and x ₁ (0) is x ₁₀ . 4. the noise pollution signal differential acquisition method based on arctangent augmented differentiator according to claim 1, is characterized in that, the concrete process of described step 4 is: Step 41: Gradually increase the differentiator acceleration factor R until the desired signal estimation accuracy and anti-noise performance are obtained, and the adjustment of the parameter R is completed; Step 42: Gradually increase the differentiator parameters a ₀ and b until the expected signal estimation response speed is obtained, and the adjustment of the parameters a ₀ and b is completed; Step 43: On the basis of steps 41 and 42, gradually increase the differentiator parameter a _-1 and gradually decrease the differentiator parameter a ₁ , until the desired signal differential estimation accuracy is obtained, and the adjustment of the parameters a _-1 and a ₁ is completed. , so as to complete the adjustment of the differentiator parameters, and obtain the differential of the zero-average noise pollution signal according to the adjusted integral augmented nonlinear differentiator.

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