CN116127285A

CN116127285A - Improved wavelet threshold denoising method

Info

Publication number: CN116127285A
Application number: CN202310129191.0A
Authority: CN
Inventors: 刘宇; 姜晗; 李汪润; 陈越川; 赵博隆
Original assignee: Chongqing University of Post and Telecommunications
Current assignee: Chongqing University of Post and Telecommunications
Priority date: 2023-02-17
Filing date: 2023-02-17
Publication date: 2023-05-16

Abstract

The invention discloses an improved wavelet threshold denoising method, which is characterized in that a signal containing noise is decomposed by a plurality of layers of wavelets, so that the corresponding coefficient of the high-frequency wavelets of each layer can be obtained. The corresponding analysis wavelet coefficients are of lower amplitude, the useful signal is of higher noise, the improved threshold function is applied to process the wavelet coefficients for each layer, coefficients smaller than the threshold are left, the coefficients are removed above the value, then the wavelet coefficients are reconstructed by wavelet inverse transformation, and the processed denoised signals are output. The invention constructs a new threshold function and solves the defect of the traditional wavelet denoising algorithm in the aspect of noise reduction. The processing results of the experimental data show that: compared with the traditional noise reduction scheme, the scheme provided by the invention has the advantages that the signal has better smoothness and good noise reduction effect.

Description

Improved wavelet threshold denoising method

Technical Field

The invention belongs to the technical field of inertial measurement units, and relates to an improved denoising method based on a wavelet threshold.

Background

Compared with the traditional gyro, the micro-electromechanical (MEMS) inertial device of the inertial measurement unit has the characteristics of low production cost, small size, low overall power consumption and the like, and has wide application range, such as the fields of positioning, aerospace, vehicle-mounted and the like. However, because of incomplete structure, imperfect compensation method, etc., the random drift error is larger, so that the navigation positioning accuracy is reduced, and long-time navigation is not possible. Therefore, if the navigation precision of the gyroscope is obviously improved, the use value is improved, and the key point is how to reduce the error of the MEMS gyroscope.

At the hardware platform level, factors causing noise in the output of the inertial measurement unit include drift errors of the device, and interference among components, such as electromagnetic effects, errors occurring when the device is used for receiving signal output, and the like. Among these errors, the most critical issue is the noise generated by itself.

Because of the uncertainty of the application environment, the MEMS gyroscope signal has a non-stationarity characteristic, and an accurate error model is difficult to obtain. There are two main methods for improving the output performance of MEMS gyroscopes: firstly, the output performance is improved through industrial and process technologies, such as vacuum packaging technology, temperature compensation technology, integration level, micro-machining process technology and the like for improving sensitive structures. However, the MEMS precision is limited by the prior art, and the cost is increased by tens of times or even hundreds of times every order of magnitude, so that the MEMS gyroscope has far less competitiveness than the fiber optic gyroscope or mechanical gyroscope in the high-precision field. Secondly, by means of mathematical means, the output is corrected by modeling the system model. Considering that the MEMS gyroscope is not generally used alone, but is fused with other sensors to jointly complete the navigation task, a Kalman filtering algorithm is often adopted. However, the performance of the MEMS gyroscope is easily affected by external environment, and random drift of the gyroscope has the characteristics of nonlinearity, non-stability and slow time variation, so that the accuracy of the statistical characteristics is affected, and the system model is inaccurately built, so that the system filtering precision is reduced, and even the filtering divergence is caused.

And the output of the inertial measurement unit is subjected to classical finite length unit impulse response filtering, wiener filtering and self-adaptive filtering by adopting a noise reduction method. These filtering methods have certain drawbacks, namely, the problem of spectrum overlap between useful signals and noise, and at the same time, the wavelet transformation method is excellent in terms of time-frequency local characterization characteristics, and can reduce high-frequency noise in output due to the difference between the wavelet coefficients of the required output signals in the wavelet domain and the noise. Which transforms by adding a window function to the raw data to process the data, it does not require an accurate error model when processing non-stationary signals.

In a signal noise reduction algorithm based on an improved wavelet threshold function proposed by the prior art Yao Zhijuan and Gu Jiajia, the threshold processing formula w (x, m) is divided into three sections according to different thresholds, and the scheme solves part of the problems of a soft threshold and a hard threshold, but the algorithm has a complex flow and is difficult to realize in the application process; in the wavelet denoising method based on the improved threshold function, which is proposed by the prior art, the improved threshold function has two adjusting parameters, and the result of the method is not obvious and direct when the parameters are adjusted.

Therefore, in the wavelet threshold denoising method, the invention provides an improved wavelet threshold function based on a compromise method, and the function is applied at the same time, and the wavelet denoising method is used for processing the MEMS gyroscope output, so that the signal-to-noise ratio is obviously reduced, and the accuracy of the output signal is improved.

Disclosure of Invention

The present invention is directed to solving the above problems of the prior art. The improved method based on wavelet threshold denoising is provided, so that the signal-to-noise ratio of the obtained MEMS gyroscope output signal is obviously reduced, and the accuracy of the output signal is improved.

In order to achieve the above purpose, the technical scheme adopted by the invention is as follows: an improved wavelet threshold denoising method comprising the steps of:

1) Decomposing a noise-containing signal from the MEMS gyroscope through a plurality of layers of wavelets to obtain the corresponding coefficient of the high-frequency wavelets of each layer;

2) Processing the wavelet coefficients of each layer using an improved threshold function, leaving coefficients less than the threshold, culling above the value;

3) And (3) carrying out wavelet reconstruction on the wavelet coefficient obtained in the step (2) by using wavelet inverse transformation, and outputting a filtered MEMS gyroscope signal.

The present invention also provides a computer readable storage medium having stored thereon a computer program which when executed by a processor performs the steps of the improved wavelet threshold denoising method described above.

The invention finally provides an electronic device comprising a MEMS gyroscope, a memory, a processor and a computer program stored on the memory and running on the processor, which processor implements the steps of the improved wavelet threshold denoising method described above when executing the computer program.

The innovation point of the invention is mainly that the threshold function is improved in the traditional wavelet threshold noise reduction algorithm, and the invention has the advantages of being convenient for calculating the noise reduction signal and avoiding inaccurate signal distortion.

The invention solves the problems that in the common wavelet threshold noise reduction method, the hard threshold function has discontinuity, the noise-reduced signal is easy to oscillate, a certain deviation exists between the wavelet coefficient estimated by the soft threshold function and the wavelet coefficient of the original signal, and the distortion is easy to occur after the signal is reconstructed.

The invention can change the parameter alpha in the threshold function, so that the function can be switched from the soft threshold function to the hard threshold function, and the application range of the function is widened.

Drawings

FIG. 1 is an overall flow chart of the present invention;

FIG. 2 is a graph of static signal acquisition at a sampling frequency of 50Hz with the MEMS gyroscope resting on a horizontal plane at a constant temperature of 25 ℃. A soft threshold function is applied to process a result obtained by the gyro signal in a wavelet denoising algorithm;

FIG. 3 is a graph of the results of processing gyro signals in a wavelet denoising algorithm using a hard threshold function under the above conditions;

fig. 4 is a result of processing a gyro signal in a wavelet denoising algorithm using a compromise threshold function under the above conditions.

Fig. 5 is the result of processing gyro signals in a wavelet denoising algorithm using the improved threshold function of the present invention under the above conditions.

Detailed Description

The technical solutions in the embodiments of the present invention will be clearly and specifically described below with reference to the drawings in the embodiments of the present invention. The described embodiments are only a few embodiments of the present invention.

An improved method for denoising based on wavelet thresholds. And decomposing the MEMS gyroscope signal containing noise through a plurality of layers of wavelets to obtain the corresponding coefficient of the high-frequency wavelets of each layer. The corresponding magnitude of the analysis wavelet coefficient utilizes an improved threshold function to process the wavelet coefficient of each layer, the coefficient smaller than the threshold value is left, the coefficient higher than the value is removed, then the wavelet coefficients are reconstructed by using wavelet inversion, the output is the processed denoising signal, the burr value is rarely existed in the whole, the wavelet coefficient is more approximate to the ideal signal, the information is kept more completely, and the denoising effect is obviously improved. The overall structure is shown in fig. 1.

The improved wavelet threshold denoising method comprises the following steps:

1) The original input noisy MEMS gyroscope signal is processed by wavelet transformation, so that the wavelet basis function and the decomposition layer number used by decomposition are determined. The signal is subjected to wavelet decomposition of a plurality of layers, and the corresponding coefficient of the high-frequency wavelet of each layer can be obtained. The corresponding analysis wavelet coefficient amplitude, useful signal is lower, and noise is higher.

On the selection of wavelet basis functions, the selection is more suitable for denoising processing of MEMS signals. The primary aspects to be solved are: degree of support and vanishing moment. The degree of support is too long, so that the resolution in the time domain becomes large, the calculated amount becomes large, and the vanishing moment order mainly shows the singularity of the signals. When in use, the selection needs to be made according to specific conditions, such as the characteristics of specific signals. Because of its better symmetry, sym wavelets are chosen as wavelet basis functions in the present invention.

The number of decomposition layers is an important factor affecting the noise effect of the final output signal, the number of decomposition layers is increased, the wavelet coefficients of useful signals and the wavelet coefficients of noise are obviously different, and the useful signals and the noise can be easily separated; however, when the number of layers is set to be relatively large, this has the following consequences: the resulting signal after the inverse wavelet transform has an increased offset from the original signal, resulting in severe signal distortion, which is detrimental to processing the MEMS signal. In wavelet denoising, the number of wavelet decomposition layers is usually 3-6, and the number of the wavelet decomposition layers is 4.

2) For the input signal, a corresponding threshold function is used to solve the high frequency wavelet coefficients. Specifically, the wavelet coefficients for each layer are processed using an improved threshold function, leaving coefficients below the threshold, culling above that value.

If the set threshold is relatively large, some useful data is removed, and if the set threshold is too small, the denoising effect is poor. In addition, the selection of the threshold function has an effect on the smoothness of the reconstructed signal. The wavelet denoising algorithm with improved threshold function is applied, the waveform of the signal output result is displayed smoothly, the reconstruction accuracy is high, and the average value of the signal is close to a true value.

The proposed new improved threshold function is shown in the following formula:

wherein the method comprises the steps of

Alpha is a regulating factor, 0.ltoreq.alpha.ltoreq.1,>

w _j,k ,/>

the wavelet transform coefficients before and after denoising are respectively referred to; λ is a threshold; sign (·) is expressed as a sign function.

Analytical formula (1) can be obtained:

1)

in the time-course of which the first and second contact surfaces,

when w is _j,k At the time of → lambda,

/>

w _j,k at the time of-lambda, the reaction product,

formula (1) is w _j,k Continuing at = ±λ, to give the formula (1) at (- ≡, ++ infinity continuous.

2)w _j,k →∞ ⁺ In the time-course of which the first and second contact surfaces,

w _j,k →∞ ^- in the time-course of which the first and second contact surfaces,

when w is _j,k When →infinity:

to sum up, formula (1)

Is asymptotic.

The construction method of formula (1) is similar to the general threshold function, and the main direction is to want to get |w _j,k Partial zeroing of < lambda, processing only |w _j,k And the I is more than or equal to lambda. The function is continuous, obtained by equations (2), (3), and thus does not resemble a hard threshold function, so that the output is problematic, i.e., does not oscillate severely. As can be seen from (4), (5) and (6), the function is as follows

Is an asymptote. When wavelet coefficient |w _j,k When I.fwdarw.infinity, let +.>

And w _j,k In this way, the constant deviation problem present in the soft threshold function can not occur. By changing the parameter α, when α=0, the function is a soft threshold function, and α→infinity is a hard threshold function. It can be further found that the function can change the parameter to become a soft threshold or a hard threshold function, and the range of operation is widened.

3) And then, the wavelet coefficients reserved in the step 2) are subjected to wavelet reconstruction by using wavelet inverse transformation, and the wanted MEMS gyroscope signals after filtering processing are output.

And selecting sym wavelet, setting the decomposition layer number as 4 layers, processing by applying the threshold function in the invention, and then reconstructing the wavelet to obtain an output signal.

Fig. 2-5 are comparisons of the effects of other threshold functions.

Compared with other 3 threshold functions, the wavelet denoising algorithm for improving the threshold functions is applied, the waveform display of the signal output result is smoother, the reconstruction accuracy is higher, and the average value of the signal is close to a true value.

Claims

1. An improved wavelet threshold denoising method, comprising the steps of:

1) Decomposing a noise-containing signal output by the MEMS gyroscope through a plurality of layers of wavelets to obtain the corresponding coefficient of the high-frequency wavelets of each layer;

2. An improved wavelet threshold denoising method according to claim 1, wherein: and 1) selecting sym wavelets as wavelet basis functions in the step 1).

3. An improved wavelet threshold denoising method according to claim 1, wherein: the number of layers of the wavelet decomposition in the step 1) is 3-6.

4. An improved wavelet threshold denoising method according to claim 3, wherein: the number of layers of the wavelet decomposition in the step 1) is 4.

5. An improved wavelet threshold denoising method according to claim 1, wherein: the improved threshold function is represented by the following formula:

wherein the method comprises the steps of

Alpha is a regulating factor, 0.ltoreq.alpha.ltoreq.1,>

w _j,k ，/>

respectively refers to wavelet transformation coefficients before and after denoising, lambda is a threshold value, sign () As a sign function.

6. A computer readable storage medium having stored thereon a computer program, characterized in that the computer program when executed by a processor implements the steps of the improved wavelet threshold denoising method of any of claims 1 to 5.

7. An electronic device comprising a MEMS gyroscope, a memory, a processor, and a computer program stored on the memory and running on the processor, wherein the processor implements the steps of the improved wavelet threshold denoising method of any of claims 1 to 5 when the computer program is executed by the processor.