CN109344678B - MEMS gyro denoising method based on wavelet threshold - Google Patents

MEMS gyro denoising method based on wavelet threshold Download PDF

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CN109344678B
CN109344678B CN201810790260.1A CN201810790260A CN109344678B CN 109344678 B CN109344678 B CN 109344678B CN 201810790260 A CN201810790260 A CN 201810790260A CN 109344678 B CN109344678 B CN 109344678B
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杨菊花
陈光武
张琳婧
王迪
李文元
程鉴皓
刘射德
刘昊
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Lanzhou Jiaotong University
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Abstract

The invention discloses a MEMS gyroscope denoising method based on a wavelet threshold, which comprises the steps of sampling MEMS gyroscope signals; performing trend analysis on the MEMS gyroscope signals; determining wavelet basis and the number of decomposition layers based on the result of the trend analysis; selecting a wavelet coefficient transformation function based on the determined wavelet basis and the decomposition layer number, and distinguishing noise and detail parts of the signals based on the selected wavelet coefficient transformation function; and selecting a threshold function and a threshold value, and removing noise components of detailed parts of the signals. The output signal of the MEMS gyroscope is analyzed to obtain a linear trend term of the drift of the MEMS gyroscope, the linear trend term is a slowly changing process, and the stable signal of which the gyro output signal is mainly low frequency is obtained through analysis. The influence of MEMS gyro random error is reduced on the basis of analysis, the real-time output precision of the MEMS gyro sensor is improved, and the MEMS gyro sensor is simple and convenient to calculate and easy to realize because only wavelet coefficient transformation is used, and has the advantage of high precision.

Description

MEMS gyro denoising method based on wavelet threshold
Technical Field
The invention relates to the field of random error compensation of MEMS (micro-electromechanical systems) micro-mechanical gyroscope in integrated navigation, in particular to an MEMS gyroscope denoising method based on a wavelet threshold.
Background
At present, the output signal of the MEMS gyroscope is a typical non-stationary sequence, and in practical use, due to a complex and variable environment, the error is accumulated continuously, and the gyro random error is a main cause affecting the precision of the MEMS gyroscope.
Common MEMS gyro noise reduction methods include modeling compensation, artificial intelligence algorithm, wavelet transformation algorithm and the like. The general modeling compensation method depends too much on the established model and the prior statistical information, and the method fails due to poor fault tolerance and inaccurate statistics. Although the artificial intelligent neural network algorithm has certain fault tolerance, the structure is huge, and the artificial intelligent neural network algorithm is not suitable for calculation processing of a part of gyro noise reduction in attitude estimation.
Disclosure of Invention
The invention aims to provide a wavelet threshold-based MEMS gyroscope denoising method for solving at least part of the problems in the prior art.
In order to achieve the purpose, the invention adopts the technical scheme that:
a MEMS gyro denoising method based on wavelet threshold comprises the following steps:
sampling MEMS gyro signals;
performing trend analysis on the MEMS gyroscope signals;
determining wavelet basis and the number of decomposition layers based on the result of the trend analysis;
selecting a wavelet coefficient transformation function based on the determined wavelet basis and the decomposition layer number, and distinguishing noise and detail parts of the signals based on the selected wavelet coefficient transformation function;
and selecting a threshold function and a threshold value, and removing noise components of detailed parts of the signals.
Preferably, the MEMS gyroscope signal is sampled, specifically, the MEMS gyroscope signal is continuously sampled.
Preferably, in said continuously sampling the MEMS gyroscope signal,
the sampling frequency was 20Hz and the sampling time was 750S.
Preferably, the trend analysis for the MEMS gyroscope signal includes:
setting characteristic parameters of the MEMS gyroscope in a Matlab simulation environment, wherein the setting of the characteristic parameters of the MEMS gyroscope comprises injecting an MEMS gyroscope error in the Matlab simulation environment;
and carrying out Matlab simulation test analysis, thereby completing trend analysis.
Preferably, the error of the MEMS gyroscope includes:
the zero offset error is 0.01 degree/h, and the angle random walk error is
Figure BDA0001734717280000023
h represents hour.
Preferably, the determining wavelet basis and decomposition level number based on the result of trend analysis includes:
the Matlab simulation signal is separately subjected to multi-layered wavelet decomposition and reconstruction using DbN wavelet families,
performing comparative analysis on wavelet decomposition and reconstruction by using standard deviation data;
the wavelet basis and the number of decomposition layers are determined based on the results of the comparative analysis.
Preferably, the wavelet basis is Db5, and the number of decomposition layers is 9.
Preferably, the selecting a wavelet coefficient transform function includes:
selecting a wavelet transformation function;
amplifying the difference between the wavelet coefficients to be transformed by using a wavelet transform function;
and substituting the wavelet coefficient after the difference amplification into the inverse function of the wavelet transform function to obtain a wavelet estimation coefficient, thereby obtaining the wavelet coefficient transform function.
Preferably, the selecting a threshold function and a threshold, and removing the noise component of the detail part of the signal, where the threshold function is:
Figure BDA0001734717280000021
in the formula:
Figure BDA0001734717280000022
defining it as an adaptation factor, a, b, c as a regulatory factor, gamma1Is a threshold constant, n is the number of sampling points, and j is the wavelet decomposition scale.
Preferably, a is 1.18, b is-1.24, and c is 0.33.
The technical scheme of the invention has the following beneficial effects:
according to the technical scheme, the output signal of the MEMS gyroscope is analyzed to obtain the linear trend term of the drift of the MEMS gyroscope, the linear trend term is a slowly changing process, and the stable signal of which the gyro output signal is mainly low frequency is obtained through analysis. The influence of MEMS gyro random error is reduced on the basis of analysis, the real-time output precision of the MEMS gyro sensor is improved, and the MEMS gyro sensor is simple and convenient to calculate and easy to realize because only wavelet coefficient transformation is used, and has the advantage of high precision.
The technical solution of the present invention is further described in detail by the accompanying drawings and embodiments.
Drawings
FIG. 1 is a flowchart of a denoising method of an MEMS gyroscope based on a wavelet threshold according to an embodiment of the present invention;
FIG. 2 is a schematic block diagram of a wavelet-threshold-based MEMS gyro denoising system according to an embodiment of the present invention;
fig. 3 is a flowchart of the work flow of the MEMS gyroscope denoising system based on wavelet threshold according to the embodiment of the present invention.
Detailed Description
The preferred embodiments of the present invention will be described in conjunction with the accompanying drawings, and it should be understood that the preferred embodiments described herein are merely for purposes of illustration and explanation, and are not intended to limit the present invention.
The wavelet transform algorithm is particularly suitable for characterizing non-stationary signals by virtue of excellent multi-resolution characteristics, is convenient for feature extraction and protection of original signals, and has simple wavelet transform calculation and good filtering effect.
As shown in fig. 1, a MEMS gyro denoising method based on wavelet threshold includes:
s101: sampling MEMS gyro signals;
s102: performing a trend analysis on the MEMS gyroscope signal,
namely, the MEMS gyro signal is subjected to trend analysis according to the output characteristics of the MEMS gyro signal.
S103: determining wavelet basis and the number of decomposition layers based on the result of the trend analysis;
s104: selecting a wavelet coefficient transformation function based on the determined wavelet basis and the decomposition layer number, and distinguishing noise and detail parts of the signals based on the selected wavelet coefficient transformation function;
s105: and selecting a threshold function and a threshold value, and removing noise components of detailed parts of the signals.
Preferably, the MEMS gyroscope signal is sampled, specifically, the MEMS gyroscope signal is continuously sampled.
Preferably, in said continuously sampling the MEMS gyroscope signal,
the sampling frequency was 20Hz and the sampling time was 750S.
Namely, a simulation test processor is used for obtaining test data with the signal sampling frequency of 20Hz, namely 20 data are output in 1 second and the sampling time of 750S.
Preferably, the trend analysis for the MEMS gyroscope signal includes:
setting characteristic parameters of the MEMS gyroscope in a Matlab simulation environment, and setting the characteristic parameters of the MEMS gyroscope, wherein the setting comprises injecting MEMS gyroscope errors in the Matlab simulation environment;
and carrying out Matlab simulation test analysis, thereby completing trend analysis.
Preferably, the error of the MEMS gyroscope includes:
the zero offset error is 0.01 degree/h, and the angle random walk error is
Figure BDA0001734717280000041
h represents hour.
The method is characterized in that a linear trend item of the MEMS gyro drift is obtained according to simulation test analysis and is a slowly changing process, high-frequency information contained in a low-frequency part in the size decomposition is reduced along with the increase of layers, the information with higher frequency is removed every time the decomposition layer is added, and the rest is the development trend of signals, which shows that the output signals of the MEMS gyro are stable signals with low frequency as the main.
Preferably, the determining wavelet basis and decomposition level number based on the result of trend analysis includes:
the Matlab simulation signal is separately subjected to multi-layered wavelet decomposition and reconstruction using DbN wavelet families,
performing comparative analysis on wavelet decomposition and reconstruction by using standard deviation data;
the wavelet basis and the number of decomposition layers are determined based on the results of the comparative analysis.
The Matlab simulation signal is subjected to wavelet decomposition and reconstruction of 2-10 layers by using DbN wavelet family, comparative analysis of standard deviation data is performed, the wavelet base is Db5, the number of decomposition layers N is 9, and if the number of decomposition layers is increased, the standard deviation can be reduced, but the calculation speed is slowed down.
Preferably, the selecting a wavelet coefficient transform function includes:
selecting a wavelet transformation function;
amplifying the difference between the wavelet coefficients to be transformed by using a wavelet transform function;
and substituting the wavelet coefficient after the difference amplification into the inverse function of the wavelet transform function to obtain a wavelet estimation coefficient, thereby obtaining the wavelet coefficient transform function.
The wavelet coefficient transformation function is selected as follows:
Figure RE-GDA0001929577190000051
in the formula: d is cmax-cmin, where cmin and cmax are the minimum and maximum coefficients in the wavelet coefficients, respectively; α is a constant and α ∈ [0.6, 1], where α is taken to be 1.
Figure RE-GDA0001929577190000052
Using g1(x) Amplifying the difference between wavelet coefficients to be transformed to prevent the detail features of original signal from being filtered out by threshold noise reduction, and then substituting the wavelet coefficients into g1(x) Inverse g of1' (x) the wavelet estimation coefficients are obtained.
The threshold function is:
Figure BDA0001734717280000053
in the formula: wEstimating vectors for the wavelet coefficients after threshold processing, wherein W is the wavelet coefficient without threshold processing; is composed ofSetting a threshold value, also called threshold;
Figure BDA0001734717280000054
it is a positive real number and greater than 1 for the adjustment factor.
In the process of denoising a signal by using a threshold, firstly, performing N layers of wavelet decomposition on the signal, forming a vector W by a decomposed scale coefficient and the wavelet coefficient, then amplifying a region in the signal, in which the signal and the noise are difficult to distinguish, so as to be convenient for selecting a subsequent threshold. And finally, selecting a threshold and reconstructing the signal with detailed characteristics.
The existing wavelet threshold denoising method has a soft threshold and a hard threshold, namely a soft threshold and hard threshold method, namely, a new wavelet vector W is obtained by carrying out thresholding transformation on a coefficient vector WThen apply the vector WThe wavelet reconstruction method is used for obtaining a signal after noise reduction, and the difference lies in the selection of a threshold function:
soft threshold function:
Figure BDA0001734717280000061
hard threshold function:
Figure BDA0001734717280000062
although the whole continuity of the soft threshold function is good, when W is greater than or equal to W, WDeviations from W may result in blurring of the edges of the reconstructed signal. The estimated wavelet coefficient | W | after thresholding in the hard threshold function is discontinuous within ±, and affects the smoothness of the reconstructed signal very much.
Preferably, the technical scheme of the invention selects a threshold function and a threshold value to remove signalsIn the noise component of the detail part of (1), the threshold function is:
Figure BDA0001734717280000063
in the formula:
Figure BDA0001734717280000064
defining it as an adaptation factor, a, b, c as a regulatory factor, gamma1Is a threshold constant, n is the number of sampling points, and j is the wavelet decomposition scale. The threshold function has clear structure, neutralizes the advantages and disadvantages of the hard threshold function and the soft threshold function, can repeatedly test and adjust the value of the adaptive factor to meet the requirement, and is a flexible processing mode. The advantage of improving the threshold function is 3 points, the first ensures the continuity of the wavelet coefficient estimation values at the threshold, the second avoids the oscillation phenomenon of the signal reconstruction, and the third is that the deviation of the reconstructed signal is not constant in the soft thresholding in the given case, but decreases with increasing parameter | W |. Based on the three points, the reconstructed signal can better keep edge information, and the method has the obvious advantage of noise reduction compared with the traditional wavelet threshold. After a plurality of experiments, the final determination result is that a is 1.18, b is-1.24, and c is 0.33, and the noise reduction effect of the used MEMS gyroscope is good. And substituting the values of the regulating factors a, b and c into a threshold function to obtain the threshold.
The technical scheme correspondingly discloses a MEMS gyroscope denoising system based on a wavelet threshold, which comprises a power supply module, a measurement module, a data transmission module and a processing module as shown in FIG. 2. The power supply module comprises a power supply, an electric wire and a power supply indicating warning lamp, and the measuring module comprises an inertia measuring unit and a three-axis rotary table. The power supply is electrically connected with the three-axis turntable through an electric wire, the inertia measurement unit is fixed on the three-axis turntable and is set along with the rotation of the three-axis turntable, and the inertia measurement unit rolls or pitches.
The data transmission module comprises an RS232 serial port line and is connected with the three-axis turntable and the processing module, when the set posture of the three-axis turntable changes, the inertia measurement unit can recognize and output three-dimensional posture information, and the output three-dimensional posture information is transmitted to the processing module through the data transmission module.
The hardware environment of the processing module is Intel (R) core (TM) T9600 CPU 2.80GHz, 4G RAM, Windows7 operating system. And (3) according to the acquired gyro attitude data, the processing module performs oversampling and operates the MEMS gyro denoising method based on the wavelet threshold.
Specifically, the detailed process of the work of the MEMS gyro denoising system based on the wavelet threshold is as follows: as shown in fig. 3.
1. And starting the power supply module.
2. And starting the three-axis turntable, and starting initialization and leveling after the three-axis turntable is preheated for 5 minutes.
3. And fixing the inertia measurement unit in an inner frame of the three-axis turntable, and setting a rotation mode. Because the three frames of the three-axis turntable respectively form the universal support for the outer frame, the middle frame and the inner frame, or the three frames of the three-axis turntable can be called as an outer ring, a middle ring and an inner ring, the three frames of the three-axis turntable can carry out angular velocity motion on the measured object in any space direction.
4. The inertial measurement unit rotates according to a set rotation mode, the sensor of the inertial measurement unit outputs real-time attitude information in the rotation process, and the attitude data change can be visually displayed in a display matched with the three-axis rotary table.
5. And setting time and a rotation mode, finishing the test, storing data, stopping the work of the three-axis turntable and setting the three-axis turntable to be horizontal. And transmitting the data to a processing module, and setting a simulation environment to perform noise reduction processing on the data.
6. After the noise reduction is completed, the signal after the noise reduction is evaluated by using the standard deviation, the signal-to-noise ratio and the mean square error, namely the method disclosed by the technical scheme of the invention is also evaluated. The invention relates to a quality evaluation method, which adopts the technical scheme that the quality of signal denoising is measured by selecting the error of a reconstructed signal deviating from an original signal, and the common indexes comprise standard deviation (S), mean square error (RMSE) and signal-to-noise ratio (SNR). The definition is as follows:
Figure BDA0001734717280000081
in the formula: x is the number ofiThe ith sample of the sample, x is the sample mean value, and n is the number of sampling points.
Figure BDA0001734717280000082
X (n) is the original signal and x' (n) is the filtered signal.
Figure BDA0001734717280000083
The technical scheme of the invention aims to overcome the problems of fuzzy reconstructed signal edges, signal discontinuity and the like in the noise reduction process of the existing wavelet soft and hard threshold method, and particularly pays attention to the detail characteristic protection of the reconstructed signal so as to ensure that the acquired processed signal has more detail characteristics of the original signal under the condition of minimum random error.
According to the technical scheme, the output signal of the MEMS gyroscope is analyzed, the gyroscope drift has a linear trend term and is a slowly changing process, and the stable signal of which the gyro output signal is mainly low frequency is obtained through analysis.
Finally, it should be noted that: although the present invention has been described in detail with reference to the foregoing embodiments, it will be apparent to those skilled in the art that modifications may be made to the embodiments described above, or equivalents may be substituted for elements thereof. Any modification, equivalent replacement, or improvement made without departing from the spirit and principle of the present invention shall fall within the protection scope of the present invention.

Claims (9)

1. A MEMS gyro denoising method based on wavelet threshold is characterized by comprising the following steps:
sampling MEMS gyro signals;
performing trend analysis on the MEMS gyroscope signals;
determining wavelet basis and the number of decomposition layers based on the result of the trend analysis;
selecting a wavelet coefficient transformation function based on the determined wavelet basis and the decomposition layer number, and distinguishing noise and detail parts of the signals based on the selected wavelet coefficient transformation function; selecting a threshold function and a threshold value, and removing noise components of detail parts of the signals, wherein the threshold function is as follows:
Figure 836891DEST_PATH_IMAGE001
(ii) a In the formula:
Figure 85470DEST_PATH_IMAGE002
>1，
Figure 339733DEST_PATH_IMAGE002
defining it as an adaptation factor, a, b, c as a regulation factor,
Figure 888526DEST_PATH_IMAGE003
is a threshold constant, n is the number of sampling points, and j is the wavelet decomposition scale.
2. The wavelet threshold based MEMS gyroscope denoising method of claim 1, wherein the MEMS gyroscope signal is sampled, in particular, continuously sampled.
3. The wavelet threshold based MEMS gyroscope denoising method of claim 2, wherein in the continuous sampling of the MEMS gyroscope signals,
the sampling frequency was 20Hz and the sampling time was 750S.
4. The wavelet threshold based MEMS gyroscope denoising method of claim 1, wherein the trend analysis for the MEMS gyroscope signal comprises:
setting characteristic parameters of the MEMS gyroscope in a Matlab simulation environment, wherein the setting of the characteristic parameters of the MEMS gyroscope comprises injecting an MEMS gyroscope error in the Matlab simulation environment;
and carrying out Matlab simulation test analysis, thereby completing trend analysis.
5. The wavelet threshold based MEMS gyroscope denoising method of claim 4, wherein the error of the MEMS gyroscope comprises:
the zero offset error is 0.01 degree/h, and the angle random walk error is h, which represents hours.
6. The wavelet threshold based MEMS gyro denoising method of claim 4, wherein the determining wavelet basis and decomposition level number based on the trend analysis result comprises:
the Matlab simulation signal is separately subjected to multi-layered wavelet decomposition and reconstruction using DbN wavelet families,
performing comparative analysis on wavelet decomposition and reconstruction by using standard deviation data;
the wavelet basis and the number of decomposition layers are determined based on the results of the comparative analysis.
7. The wavelet threshold based MEMS gyroscope denoising method of claim 6, wherein the wavelet basis is Db5, and the decomposition level is 9.
8. The wavelet threshold based MEMS gyroscope denoising method of claim 6, wherein the selecting wavelet coefficient transformation function comprises:
selecting a wavelet transformation function;
amplifying the difference between the wavelet coefficients to be transformed by using a wavelet transform function;
and substituting the wavelet coefficient after the difference amplification into the inverse function of the wavelet transform function to obtain a wavelet estimation coefficient, thereby obtaining the wavelet coefficient transform function.
9. The wavelet threshold based MEMS gyroscope denoising method of claim 1, wherein a is 1.18, b is-1.24, and c is 0.33.
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