CN111103800A - Noise pollution signal differential obtaining method based on arc tangent amplification differentiator - Google Patents
Noise pollution signal differential obtaining method based on arc tangent amplification differentiator Download PDFInfo
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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
Technical Field
The invention relates to a noise pollution signal differential obtaining method based on an arc tangent amplification differentiator, belonging to the field of signal processing.
Background
In the signal processing field and the engineering control field, the acquisition of differential signals is always a technical difficulty. The accurate extraction of the differential signal has very important significance to control methods such as PID control, inversion control, dynamic sliding mode control and the like, and is widely applied to signal processing and parameter estimation. However, the differentiation of the signal is generally considered to be not directly measurable and obtainable, and early methods generally adopt a differential or lead network to approximate the estimation, but have the disadvantages of low precision, poor noise suppression capability and the like.
In recent years, high-order sliding mode differentiators, nonlinear tracking differentiators and finite time differentiators are used for signal differential acquisition. However, when the signal is contaminated by noise, the problems of low precision, poor noise suppression effect and the like generally exist. Zero-mean noise widely exists in an actual system, and in many engineering application scenes, a signal to be measured is often polluted by the zero-mean noise. Therefore, it is necessary to invent a brand new differential acquisition method for zero-mean noise pollution signals to solve the problem of poor zero-mean noise resistance of the existing differential acquisition method.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the noise pollution signal differential obtaining method based on the arc tangent amplification differentiator can effectively solve the problem that the effect of obtaining the zero-mean noise pollution signal differential by the existing method is poor.
The invention adopts the following technical scheme for solving the technical problems:
a noise pollution signal differential obtaining method based on an arc tangent amplification differentiator comprises the following steps:
step 31, define z-1,z0,z1Respectively correspond to x-1,x0,x1Estimate of (a), x-1,x0,x1Respectively representing measurement signalsIntegral of (1), true value of the actual signal, differential of the actual signal;
step 32, constructing an integral amplification nonlinear differentiator based on the arctangent function, and comprising the following steps:
wherein,
z-1(t),z0(t),z1(t) each correspond to x-1(t),x0(t),x1(t) estimated value, z-1(0) Is z-1(t) initial value, z-1(0) Is taken as z-10，z0(0) Is z0(t) initial value, z0(0) Is taken as z00，z1(0) Is z1(t) initial value, z1(0) Is taken as z10R is the differentiator acceleration factor, b and aiFor the differentiator parameter to be adjusted, b > 0, ai＞0,i＝-1,0,1；
And 4, adjusting parameters of the integral amplification nonlinear differentiator, and acquiring the differential of the zero-mean noise pollution signal according to the adjusted integral amplification nonlinear differentiator.
As a preferred scheme of the present invention, the zero-mean noise pollution signal dynamic system model in step 1 is:
where, y (t) is actually measured zero-mean noise pollution signal, n (t) is zero-mean noise signal, and x0(t) and x1(t) is the true value and the differential of the actual signal, t represents time, x0(0) Is x0(t) initial value, x0(0) Value of x00，x1(0) Is x1(t) initiation ofValue, x1(0) Value of x10。
As a preferred scheme of the present invention, the specific process of step 2 is:
step 21, integrating the actually measured zero-mean noise pollution signal
The later augmentation is the new system state of the dynamic system model established in the step 1;
step 22, establishing a signal integral amplification dynamic system model, which is as follows:
wherein x is-1(t) is the integral of the measurement signal v (τ), x-1(0) Is x-1(t) initial value, x-1(0) Is taken as x-10N (t) is a zero mean noise signal, x0(t) and x1(t) is the true value and the differential of the actual signal, t represents time, x0(0) Is x0(t) initial value, x0(0) Value of x00，x1(0) Is x1(t) initial value, x1(0) Value of x10。
As a preferred embodiment of the present invention, the specific process of step 4 is:
step 41, gradually increasing the acceleration factor R of the differentiator until the expected signal estimation precision and anti-noise performance are obtained, and completing the adjustment of the parameter R;
step 42, gradually increasing the differentiator parameter a0And b, completing the parameter a until a desired signal estimation response speed is obtained0And b;
step 43, on the basis of steps 41 and 42, gradually increasing the differentiator parameter a-1While gradually decreasing the differentiator parameter a1Until the desired signal differential estimation accuracy is obtained, parameter a is completed-1And a1To complete the adjustment of the parameters of the differentiator, and acquiring zero according to the adjusted integral-augmented nonlinear differentiatorThe mean noise contaminates the differential of the signal.
Compared with the prior art, the invention adopting the technical scheme has the following technical effects:
1. the method can realize the accurate extraction of the differential signal of the signal polluted by the zero-mean noise.
2. The method has wide application range, and can be widely applied to the fields of signal processing, engineering control and the like of differential extraction of pollution signals with zero mean noise.
3. The method is simple, standard in parameter adjustment and easy to realize in engineering.
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FIG. 1 is a flow chart of the present invention.
Fig. 2 shows the result of the noise pollution signal filtering estimation in the embodiment of the present invention.
Fig. 3 is a differential estimation of a noise pollution signal according to an embodiment of the present invention.
Fig. 4 shows the result of the differential estimation error of the noise pollution signal in the embodiment of the invention.
Detailed Description
Reference will now be made in detail to embodiments of the present invention, examples of which are illustrated in the accompanying drawings. The embodiments described below with reference to the accompanying drawings are illustrative only for the purpose of explaining the present invention, and are not to be construed as limiting the present invention.
The invention relates to a zero-mean noise pollution signal differential obtaining method based on an arc tangent integral amplification differentiator, which comprises the following steps of 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.
As shown in fig. 1, the method for obtaining the zero-mean noise pollution signal differential based on the arctan integral-augmented differentiator specifically includes the following steps:
in this embodiment, the signal to be measured is selected to be a sine signal 2sin (t), and the variance of the zero mean noise signal n (t) is 0.01.
Step one, establishing a zero-mean noise pollution signal dynamic system model; specifically, the method comprises the following steps:
where, y (t) is a zero-mean noise pollution signal actually measured, and n (t) is zero-mean noise; x is the number of0(t) and x1(t) is the true value of the actual signal and its differential, x00And x10The initial values are respectively.
In this step, an initial value x is selected000 and x10＝0。
Step two, integrating the measuring signal
And (4) expanding new system states and establishing a signal integral expansion dynamic system model.
The method comprises the following specific steps:
step 201, integrating the measurement signal
The system state is expanded to be a new system state of the original signal dynamic system;
step 202, establishing a signal integral amplification dynamic system model; the method comprises the following specific steps:
in the formula, x-1(t) is the integral of the measurement signal v (τ).
And step three, constructing an integral amplification nonlinear differentiator based on the arctan function.
The method comprises the following specific steps:
step 301, define z-1,z0,z1Are respectively the formula (2) x in step 202-1,x0,x1An estimated value of (d);
step 302, constructing an integral amplification nonlinear differentiator based on an arc tangent function; the method comprises the following specific steps:
in the formula, atan (x)1,x2,x3)＝x2atan(x3(x1))，z-10、z00And z10Are respectively an initial value, R is a differentiator acceleration factor, b > 0 and ai> 0, i-1, 0,1 are differentiator parameters to be adjusted.
And step four, adjusting parameters of the integral amplification differentiator to obtain the differentiation of the zero-mean noise pollution signal.
The method comprises the following specific steps:
step 401, gradually increasing R until the desired signal estimation accuracy and anti-noise performance are obtained, and completing the adjustment of the parameter R;
step 402, gradually increasing a0And b, until a desired signal estimation response speed is obtained;
step 403, on the basis of step 401 and step 402, gradually increasing a-1While gradually decreasing a1So as to further improve the estimation accuracy of the signal differentiation, thereby completing the parameter adjustment of the differentiator.
In this step, the differentiator parameter is selected as: r15, a-1＝5，a0＝5，a1＝10，b＝2。
The zero-mean noise pollution signal differential obtaining method based on the arc tangent integral amplification differentiator is adopted to simulate and obtain a result graph of a signal to be measured estimation value, noise pollution signal differential estimation and noise pollution signal differential estimation error aiming at the set signal to be measured 2sin (t) and zero-mean noise n (t).
As shown in fig. 2, it is the result of the noise pollution signal filtering estimation in the present 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 integration-amplification differentiator based on the invention after accumulation integration-amplification. The signal estimation value has no obvious noise pollution condition, and the overall condition is smoother.
As shown in fig. 3, it is the differential estimation result of the noise pollution signal in the present embodiment. It can be seen that although the differential of the signal to be measured has a noise limit term, the differential of the signal to be measured can be accurately estimated by adopting the integral amplification differentiator based on the invention. The signal differential estimate fits better to the ideal differential signal 2cos (t) as a whole. At t-0 s, the differential estimate deviates significantly from the true value, since the initial value of the differentiator is set to x00The reason for 0. The signal differential estimate then quickly approaches the true value of 2cos (t).
As shown in fig. 4, it is the result of the differential estimation error of the noise pollution signal in the present embodiment. It can be seen that the differential estimation error is large (2) at t-0 s, since the initial value of the differentiator is set to x00The reason for 0. Then, the differential estimation error of the zero mean noise pollution signal is fast within a small range and is always kept in the range of [ -0.3,0.3 [ -0.3 []Within the range.
By combining the analysis and the simulation verification, the effectiveness of the noise pollution signal differential obtaining method based on the arc tangent integral amplification differentiator in solving the zero-mean noise pollution signal differential is fully verified.
The above embodiments are only for illustrating the technical idea of the present invention, and the protection scope of the present invention is not limited thereby, and any modifications made on the basis of the technical scheme according to the technical idea of the present invention fall within the protection scope of the present invention.
Claims (4)
1. A noise pollution signal differential obtaining method based on an arc tangent amplification differentiator is characterized by comprising the following steps:
step 1, establishing a zero-mean noise pollution signal dynamic system model according to an actually measured zero-mean noise pollution signal;
step 2, integrating and amplifying the actually measured zero-mean noise pollution signal into a new system state of the dynamic system model established in the step 1, thereby establishing a signal integration and amplification dynamic system model;
step 3, constructing an integral amplification nonlinear differentiator based on an arc tangent function; the specific process is as follows:
step 31, define z-1,z0,z1Respectively correspond to x-1,x0,x1Estimate of (a), x-1,x0,x1Respectively representing the integral of the measurement signal, the true value of the actual signal and the differential of the actual signal;
step 32, constructing an integral amplification nonlinear differentiator based on the arctangent function, and comprising the following steps:
wherein,
z-1(t),z0(t),z1(t) each correspond to x-1(t),x0(t),x1(t) estimated value, z-1(0) Is z-1(t) initial value, z-1(0) Is taken as z-10，z0(0) Is z0(t) initial value, z0(0) Is taken as z00，z1(0) Is z1(t) initial value, z1(0) Is taken as z10R is the differentiator acceleration factor, b and aiFor the differentiator parameter to be adjusted, b > 0, ai＞0,i＝-1,0,1；
And 4, adjusting parameters of the integral amplification nonlinear differentiator, and acquiring the differential of the zero-mean noise pollution signal according to the adjusted integral amplification nonlinear differentiator.
2. The differential obtaining method of noise pollution signals based on the arctan-tangent amplifying differentiator according to claim 1, wherein the zero-mean noise pollution signal dynamic system model in step 1 is:
where, y (t) is actually measured zero-mean noise pollution signal, n (t) is zero-mean noise signal, and x0(t) and x1(t) is the true value and the differential of the actual signal, t represents time, x0(0) Is x0(t) initial value, x0(0) Value of x00，x1(0) Is x1(t) initial value, x1(0) Value of x10。
3. The method for obtaining the noise pollution signal differential based on the arctan-tangent-augmented differentiator according to claim 1, wherein the specific process of the step 2 is as follows:
step 21, integrating the actually measured zero-mean noise pollution signal
The later augmentation is the new system state of the dynamic system model established in the step 1;
step 22, establishing a signal integral amplification dynamic system model, which is as follows:
wherein x is-1(t) is the integral of the measurement signal v (τ), x-1(0) Is x-1(t) initial value, x-1(0) Is taken as x-10N (t) is a zero mean noise signal, x0(t) and x1(t) is the true value and the differential of the actual signal, t represents time, x0(0) Is x0(t) initial value, x0(0) Value of x00，x1(0) Is x1(t) initial value, x1(0) Value of x10。
4. The method for obtaining the noise pollution signal differential based on the arctan-tangent-augmented differentiator according to claim 1, wherein the specific process of the step 4 is as follows:
step 41, gradually increasing the acceleration factor R of the differentiator until the expected signal estimation precision and anti-noise performance are obtained, and completing the adjustment of the parameter R;
step 42, gradually increasing the differentiator parameter a0And b, completing the parameter a until a desired signal estimation response speed is obtained0And b;
step 43, on the basis of steps 41 and 42, gradually increasing the differentiator parameter a-1While gradually decreasing the differentiator parameter a1Until the desired signal differential estimation accuracy is obtained, parameter a is completed-1And a1And adjusting parameters of the differentiator, and acquiring the differential of the zero-mean noise pollution signal according to the adjusted integral amplification nonlinear differentiator.
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Citations (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20080049144A1 (en) * | 2006-08-23 | 2008-02-28 | Nextchip Co., Ltd. | Frequency demodulator for recovering SECAM chrominance signal and method thereof |
| CN102638281A (en) * | 2011-02-10 | 2012-08-15 | Nxp股份有限公司 | Method and apparatus for reducing or removing click noise |
| CN110347170A (en) * | 2019-06-19 | 2019-10-18 | 南京航空航天大学 | Re-entry of reusable launch vehicle robust Fault-Tolerant guidance system and working method |
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| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| US20080049144A1 (en) * | 2006-08-23 | 2008-02-28 | Nextchip Co., Ltd. | Frequency demodulator for recovering SECAM chrominance signal and method thereof |
| CN102638281A (en) * | 2011-02-10 | 2012-08-15 | Nxp股份有限公司 | Method and apparatus for reducing or removing click noise |
| CN110347170A (en) * | 2019-06-19 | 2019-10-18 | 南京航空航天大学 | Re-entry of reusable launch vehicle robust Fault-Tolerant guidance system and working method |
Non-Patent Citations (2)
| Title |
|---|
| ZIKANG SU，ETC.: ""Integral augmented nonlinear differentiator for noisy signals"", 《2017 11TH ASIAN CONTROL CONFERENCE (ASCC)》 * |
| 卜祥伟，等: ""改进的反正切跟踪微分器设计"", 《上海交通大学学报》 * |
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