CN103512569A - Discrete wavelet multiscale analysis based random error compensation method for MEMS (Micro Electro Mechanical system) gyroscope - Google Patents

Abstract

The invention discloses a discrete wavelet multiscale analysis based random error compensation method for an MEMS (Micro Electro Mechanical system) gyroscope, and the method is used for improving the data measurement accuracy of the MEMS gyroscope. The method comprises the following steps: decomposing a signal of the MEMS gyroscope by using a binary orthogonal discrete wavelet Mallat algorithm step by step, wherein the decomposing scale comprises 3 levels and a decomposed approaching signal and a decomposed detail signal are subjected to time series modeling and kalman filtering after the first level is decomposed; performing the second-level decomposing on the filtered approaching signal and then gradually decomposing and filtering in the same manner. The filtered approaching signal at the final layer and the various detail signals are subjected to signal reconstruction. According to the discrete wavelet multiscale analysis based random error compensation method for the MEMS gyroscope, the random error compensation effect of the MEMS gyroscope is improved, and the method has an important role for a vehicle-mounted or ship-based measurement occasion requiring high accuracy, high efficiency and high stability.

Description

MEMS gyroscope stochastic error compensation method based on discrete wavelet multiscale analysis

Technical field

The invention belongs to signal process field, relate to a kind of MEMS gyro data disposal route, be specifically related to a kind of MEMS gyroscope stochastic error compensation method based on discrete wavelet multiscale analysis.

Background technology

MEMS technology is the emerging technology field growing up over nearly 20 years.Micro-mechanical sensor of angular velocity (gyroscope) is to adopt the produced miniature angular-rate sensor of micromachining technology, is the world's cutting edge technology that integrates the new technologies such as Miniature precision machinery, microelectronics, semiconductor integrated technique.Its appearance makes inertial technology produce new leap.Meanwhile, market is little to volume, price is low, the increase of the novel vibrating angular-rate sensor demand of dependable performance has greatly promoted the R and D of this class sensor.Owing to being subject to the restriction of the technology such as current microfabrication, the MEMS gyroscope manufacturing accuracy of China is also lower, MEMS gyroscope survey precision is not high, does not enter practical stage, and the effect that how to improve MEMS gyroscopes error compensation becomes a key issue in this field.

Conventionally gyroscopic drift can be divided into definite and random partial: determining section has regularity, can eliminate by real Time Compensation.Random partial has uncertainty, is similar to noise, and real Time Compensation is difficult to Removing Random No, thereby finding suitable signal processing method is an indispensable process that improves measuring accuracy.At present, the many time series analysis methods that directly adopt of MEMS gyroscope stochastic error compensation carry out modeling to MEMS gyro data, and apply Kalman wave filter and carry out signal denoising, reduced to a certain extent the impact of MEMS gyroscope random noise, improved MEMS gyroscope survey precision.。

Wavelet transformation is particularly suitable for the processing of non-stationary signal with its good multi-resolution characteristics, and along with its widespread use in signal is processed, Wavelet Denoising Method theory is also gradually improved, thereby can be for the Denoising disposal of gyro signal, and has obtained good denoising effect.But it should be noted that, while adopting Mallat algorithm in the most frequently used now wavelet analysis to decompose signal, signal can be after by Hi-pass filter and low-pass filter, to carry out down-sampling to the signal by two wave filters, two extract processing, just can obtain afterwards detail signal and the approximation signal of signal, known according to Nyquist sampling thheorem, down-sampling can be introduced the distortion of signal, this distortion is called aliasing, if process not in time, reduce the impact of aliasing effect, Wavelet Denoising Method effect can reduce.For reconstructing satisfied signal, just must reduce the impact of aliasing on signal.For each layer of decomposed signal in wavelet decomposition tree, due to MEMS Gyroscope Random Drift, decomposing rear each layer signal is all approximate time series signals stably, can utilize eaily Time Series Method to carry out modeling to each layer of decomposed signal, and be aided with kalman wave filter it is carried out to filtering, after filtering, signal can more accurately reflect original decomposition signal, signal is carried out to denoising, reduce to a certain extent the impact of aliasing, obtain signal more accurately, if decompose therefore adopt step by step, the method of filtering step by step, for improving MEMS gyroscope stochastic error compensation effect, improving MEMS gyroscope survey precision has very great help.

Summary of the invention

The present invention proposes a kind of MEMS gyroscope stochastic error compensation method based on discrete wavelet multiscale analysis, for MEMS gyroscope stochastic error signal, compensate, compensation for MEMS gyroscope stochastic error signal, guaranteeing, under the distortionless prerequisite of signal, to effectively raise the compensation effect of MEMS gyroscope stochastic error.

A kind of MEMS gyroscope stochastic error compensation method based on discrete wavelet multiscale analysis of the present invention, comprises the steps:

Step 1, determine the wavelet basis that wavelet multi-scale analysis is required, this wavelet basis meet following some: 1. linear phase characteristic; 2. tight support characteristic, the computation complexity of the shorter and smaller wave conversion of support is lower; 3. the square characteristic that disappears, determine wavelet transformation after concentration of energy in the degree of low frequency component;

Step 2, for gained MEMS gyroscope stochastic error signal, determine the decomposition number of plies of wavelet multi-scale analysis, according to the character of wavelet decomposition, from signal, extract low frequency component;

Step 3, according to two, enter one deck that orthogonal wavelet MALLAT algorithm completes MEMS gyroscope stochastic error signal and decompose after, extract this layer of approximation signal and each layer of detail signal, carry out time series modeling, and apply basic kalman filtering each signal after to modeling and carry out filtering, use filtered approximation signal to carry out second level decomposition, by that analogy, decompose step by step, filtering step by step, finishes until decompose;

Step 4, the last one deck approximation signal and each layer of detail signal that according to step 3, obtain, directly reconstruct MEMS gyroscope signal.

In step 1, adopt Db5 small echo as wavelet basis.

That in step 2, decomposes the number of plies is chosen to be 3-5 layer.

Accompanying drawing explanation

Fig. 1 is the inventive method detailed step process flow diagram.

Embodiment

Below in conjunction with the accompanying drawing in the embodiment of the present invention, the technical scheme in the embodiment of the present invention is clearly and completely described, obviously, described embodiment is only the present invention's part embodiment, rather than whole embodiment.Embodiment based in the present invention, the every other embodiment that those of ordinary skills obtain, belongs to the scope of protection of the invention.

In embodiments of the present invention, under the normal temperature of laboratory, Stim202MEMS gyroscope is clamped and is placed on the TD – 450 single shaft multi-function turntables of China Shipping Industrial Company, gyroscope output data frequency is 100Hz, after gyroscope preheating, data when collection gyroscope is static.

The invention discloses the compensation method of a kind of MEMS gyroscope stochastic error, concrete steps are as follows:

Step 1, the discretize of wavelet function:

DWT can obtain by the contraction-expansion factor a in discretize continuous wavelet transform and shift factor b.Here get $a=a_0^m,b=n{b}_0{a}_0^m,$ M, n ∈ Z, by wavelet basis function ${\mathrm{\ψ}}_{a,b}\left(t\right)={\left|a\right|}^{-1/2}\mathrm{\ψ}\left(\frac{x-b}{a}\right)$ Obtain

wavelet function now becomes discrete wavelet.Can obtain thus corresponding discrete wavelet transformer is changed to:

$\left(W_{\mathrm{\&psi;}}f\right)(a,b)=<f,{\mathrm{\&psi;}}_{a,b}>={\left|a\right|}^{-m/2}\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}f\left(t\right)\stackrel{\&OverBar;}{(a_0^{-m}t-n{b}_0)}\mathrm{dt}$

In practice, generally get a ₀=2, b ₀=1 a=1 at this moment, 2 ¹, 2 ²..., 2 ^j, now can obtain dyadic wavelet: ψ _m,n(t)=2 ^-m/2ψ (2 ^-mt-n) m, n ∈ Z

In actual applications, more effective for wavelet transformation is calculated, structure has the wavelet function of orthogonality

$<{\mathrm{\&psi;}}_{m,n},{\mathrm{\&psi;}}_{j,k}>=\underset{-\&infin;}{\overset{\&infin;}{\&Integral;}}{\mathrm{\&psi;}}_{m,n}\left(t\right)\stackrel{\&OverBar;}{{\mathrm{\&psi;}}_{j,k}\left(t\right)}\mathrm{dt}={\mathrm{\&delta;}}_{m,j}{\mathrm{\&delta;}}_{n,k}$

Step 2, according to definite above wavelet basis and the wavelet decomposition number of plies, integrating step one, adopt the db5 small echo after discrete to carry out three Scale Decompositions to gained MEMS gyroscope signal, decompose step by step filtering step by step, the 3rd layer of approximation signal and each layer of detail signal after the filtering needing when obtaining signal reconstruction, adopt two to enter orthogonal wavelet MALLAT algorithm decomposition MEMS gyroscope signal, concrete decomposition step is as follows:

1, according to the db5 small echo after discrete, obtain the high-pass and low-pass filter of wavelet decomposition.

2, establish x' for the signal of device after filtering,

for initialize signal, h (k) is wave filter.

3, after two extractions, by

obtain approximation signal and detail signal after wavelet decomposition, wherein

represent detail signal,

represent approximation signal.

Before launching next stage decomposition, according to the 4-7 in this step, signal is processed.

4, remove

in exceptional value and use runs test method check

stationarity;

5, according to AIC criterion, determine

the order of corresponding time series arma modeling, after arma modeling is determined, is used least square fitting to go out model parameter, writes out ARMA mathematical model;

6, write out the state-space model of the kalman filtering equations corresponding with definite arma modeling:

State equation: X _k=AX _k+ BV _k

Output equation: Y _k=CX _k+ W _k

Wherein, V _k, W _kstatistical property be

E(W _k)=0;E(V _k)=0; $E\left(W_k{W}_j^T\right)=Q_k{\mathrm{\&delta;}}_{\mathrm{kj}};E\left(V_k{V}_j^T\right)=R_k{\mathrm{\&delta;}}_{\mathrm{kj}};E\left(W_k{V}_j^T\right)=0$ 。The state of system is

process noise is V _k=[a _k, 0] ^t.

7, adopt following KALMAN wave filter to carry out filtering processing to MEMS gyroscope ground floor approximation signal and detail signal:

$\left\{\begin{array}{c}{\hat{X}}_{k,k-1}=A{\hat{X}}_{k-1,k-1}\\ {\hat{X}}_{k,k}={\hat{X}}_{k,k-1}+K_k[Y_k-C_k{\hat{X}}_{k,k-1}]\\ K_k=P_{k,k-1}{C}^T{[C{P}_{k,k-1}{C}^T+R_k]}^{-1}\\ P_{k,k-1}=A{P}_{k,k-1}{A}^T+B{Q}_{k-1}{B}^T\\ P_{k,k}=[I-K_{k}C]P_{k,k-1}\\ {\hat{Y}}_k=C{\hat{X}}_{k,k}\end{array}\right.$

In formula,

for the further estimation of filter status,

for the state of k moment wave filter, K _kfor its gain matrix of constantly filtering of k, R is system measurements noise error, and Q is systematic procedure noise variance, P _k,kfor filtering error covariance matrix,

for the k output of wave filter constantly.

8, order

be represented as after KALMAN filtering the approximation signal of two layers and bottom, be represented as after filtering the detail signal of two layers and bottom, according to method pair described in this step 1-7

carry out resolution process, can obtain

and make filtered

for

Step 4, making S is required reconstruction signal, by

reconstruct S, calculate the variance of S and original signal.

Claims (4)

1. the MEMS gyroscope stochastic error compensation method based on discrete wavelet multiscale analysis, is characterized in that, comprises the steps:

Step 1, determine the wavelet basis that wavelet multi-scale analysis is required, this wavelet basis meet following some: 1. linear phase characteristic; 2. tight support characteristic, the computation complexity of the shorter and smaller wave conversion of support is lower; 3. the square characteristic that disappears, determine wavelet transformation after concentration of energy in the degree of low frequency component;

Step 2, for gained MEMS gyroscope stochastic error signal, determine the decomposition number of plies of wavelet multi-scale analysis, according to the character of wavelet decomposition, from signal, extract low frequency component;

Step 3, according to two, enter one deck that orthogonal wavelet MALLAT algorithm completes MEMS gyroscope stochastic error signal and decompose after, extract this layer of approximation signal and each layer of detail signal, carry out time series modeling, and apply basic kalman filtering each signal after to modeling and carry out filtering, use filtered approximation signal to carry out second level decomposition, by that analogy, decompose step by step, filtering step by step, finishes until decompose;

Step 4, the last one deck approximation signal and each layer of detail signal that according to step 3, obtain, directly reconstruct MEMS gyroscope signal.

2. a kind of MEMS gyroscope stochastic error compensation method based on discrete wavelet multiscale analysis as claimed in claim 1, is characterized in that, adopts Db5 small echo as wavelet basis in step 1.

3. a kind of MEMS gyroscope stochastic error compensation method based on discrete wavelet multiscale analysis as claimed in claim 1, is characterized in that, that in step 2, decomposes the number of plies is chosen to be 3-5 layer.

4. a kind of MEMS gyroscope stochastic error compensation method based on discrete wavelet multiscale analysis as described in claim 1 or 2 or 3, is characterized in that, adopts two to enter orthogonal wavelet MALLAT algorithm decomposition MEMS gyroscope signal, specifically comprises the following steps:

Step 1, according to the db5 small echo after discrete, obtain the high-pass and low-pass filter of wavelet decomposition; If x' is the signal of device after filtering,

for initialize signal, h (k) is wave filter;

Step 2, after two extractions, by obtain approximation signal and detail signal after wavelet decomposition, wherein

represent detail signal,

represent approximation signal;

Step 3, removal

in exceptional value and use runs test method check

stationarity;

Step 4, according to AIC criterion, determine

the order of corresponding time series arma modeling, after arma modeling is determined, is used least square fitting to go out model parameter, writes out ARMA mathematical model;

Step 5, write out the state-space model of the kalman filtering equations corresponding with definite arma modeling:

State equation: X _k=AX _k+ BV _k

Output equation: Y _k=CX _k+ W _kwherein, V _k, W _kstatistical property be:

，

E(W _k)=0;E(V _k)=0; $E\left(W_k{W}_j^T\right)=Q_k{\mathrm{\&delta;}}_{\mathrm{kj}};E\left(V_k{V}_j^T\right)=R_k{\mathrm{\&delta;}}_{\mathrm{kj}};E\left(W_k{V}_j^T\right)=0;$ The state of system is

process noise is V _k=[a _k, 0] ^t;

Step 6, the following KALMAN wave filter of employing carry out filtering processing to MEMS gyroscope ground floor approximation signal and detail signal:

$\left\{\begin{array}{c}{\hat{X}}_{k,k-1}=A{\hat{X}}_{k-1,k-1}\\ {\hat{X}}_{k,k}={\hat{X}}_{k,k-1}+K_k[Y_k-C_k{\hat{X}}_{k,k-1}]\\ K_k=P_{k,k-1}{C}^T{[C{P}_{k,k-1}{C}^T+R_k]}^{-1}\\ P_{k,k-1}=A{P}_{k,k-1}{A}^T+B{Q}_{k-1}{B}^T\\ P_{k,k}=[I-K_{k}C]P_{k,k-1}\\ {\hat{Y}}_k=C{\hat{X}}_{k,k}\end{array}\right.$

In formula,

for the further estimation of filter status, for the state of k moment wave filter, K _kfor its gain matrix of constantly filtering of k, R is system measurements noise error, and Q is systematic procedure noise variance, P _k,kfor filtering error covariance matrix, for the k output of wave filter constantly;

Step 7, order be represented as after KALMAN filtering the approximation signal of two layers and bottom,

be represented as after filtering the detail signal of two layers and bottom, right

carrying out resolution process can obtain and make filtered

for

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