CN116451020A - Gyro signal denoising method adopting Kalman filtering and Visushrink threshold processing - Google Patents
Gyro signal denoising method adopting Kalman filtering and Visushrink threshold processing Download PDFInfo
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Abstract
The invention relates to a gyro signal denoising method for Kalman filtering and visual threshold processing, which comprises the steps of establishing a time sequence model of a gyro signal; denoising the gyroscope signal by adopting self-adaptive wild value resistant Kalman filtering; performing visual threshold processing on the low-frequency component and the high-frequency component of the gyroscope signal after Kalman filtering by utilizing wavelet analysis; and carrying out wavelet reconstruction on the high-frequency and low-frequency signals of the gyroscope signals after the thresholding. The invention provides a self-adaptive anti-outlier denoising scheme integrating Kalman filtering and wavelet for gyroscope signals, which can more effectively improve the precision of a sensor and reduce errors.
Description
Technical Field
The invention belongs to the field of sensor signal processing, and particularly relates to a gyro signal denoising method for Kalman filtering and Visushrink threshold processing.
Background
The MEMS (Microelectro Mechanical Systems) sensor produced by the microelectronic technology is a novel miniature inertial sensor and is widely applied to a low-cost strapdown inertial navigation system. Before the MEMS gyroscope is used for measuring data, in order to reduce random drift errors and improve sensor precision, denoising processing is needed.
The MEMS gyroscope signal is denoised, kalman filtering or wavelet analysis is generally adopted, kalman filtering calculation is simple and easy to process, but in the actual process, the filter diverges due to the influence of various factors, the divergence of the filter is often restrained by increasing the weight of the current measurement value, and interference data such as wild values in the signal also influence the accuracy of the filter, so that the denoising effect is influenced.
Wavelet analysis is commonly used for signal processing. The high-frequency part of the signal is thresholded through decomposition of the signal, and then the low-frequency and processed high-frequency signal is subjected to wavelet reconstruction to obtain a denoising signal. When a large amount of noise is in the high-frequency component, the wavelet denoising has a good suppression effect on the noise in the signal. But angle random walk and sum in MEMS gyroscope signals zero bias instability is often in the low frequency component.
Disclosure of Invention
The technical problem of the invention is that random drift errors exist in the measured data of the MEMS gyroscope, the random drift errors are required to be subjected to denoising treatment, the precision of the existing Kalman filtering method is influenced by interference data such as wild values in signals, the existing wavelet denoising only carries out threshold treatment on high-frequency components of the signals, and angle random walk and zero-bias instability which are usually positioned in low-frequency components in the signals of the MEMS gyroscope are ignored.
The invention aims to solve the problems, and provides a self-adaptive outlier resisting denoising method of a MEMS gyroscope integrating Kalman and wavelets, which is used for carrying out self-adaptive outlier resisting Kalman filtering on a gyroscope signal, then carrying out wavelet threshold processing on a low-frequency component and a high-frequency component on the premise of determining a wavelet decomposition level, integrating the advantages of Kalman filtering and wavelet denoising, better inhibiting the signal noise of the gyroscope and improving the measurement accuracy of the gyroscope.
The technical scheme of the invention is a gyro signal denoising method for Kalman filtering and Visushrink threshold processing, which comprises the following steps:
step 1: establishing a time sequence ARMA model of the MEMS gyroscope signal;
firstly extracting a trend term and a period term in an original signal of a gyroscope, then establishing a time sequence ARMA model for residual errors, and adopting a final prediction error FPE criterion to order the model to obtain a random drift error of the gyroscope;
step 2: denoising the gyroscope signal by adopting self-adaptive wild value resistant Kalman filtering;
step 2.1: establishing a state equation and a measurement equation of a Kalman filter according to the gyro random drift error model in the step 1;
step 2.2: initializing a self-adaptive wild-value-resistant Kalman filter, and initializing a state vector and a covariance matrix of the filter by using a gyroscope error estimated by a gyroscope random drift error model at the starting moment of filtering;
step 2.3: performing adaptive outlier-resistant Kalman filtering;
step 3: performing threshold processing on a low-frequency component and a high-frequency component of the gyroscope signal after Kalman filtering by utilizing wavelet analysis;
step 3.1: selecting a wavelet function;
step 3.2: determining a wavelet decomposition level, performing wavelet decomposition on the filtered gyroscope signals by adopting a selected wavelet function, and calculating the peak ratio of each layer of high-frequency components;
step 3.3: performing visual threshold processing on the low-frequency signal and the high-frequency signal;
step 4: and carrying out wavelet reconstruction on the high-frequency and low-frequency signals of the gyroscope signals after the thresholding.
Further, in step 1, the calculation model of the gyro random drift error is as follows:
m k+1 ＝am k +ξ k+1
m is in k ,m k+1 Respectively represent t k ,t k+1 The gyroscope error at the moment, a is an autoregressive coefficient, and xi k+1 At t k+1 White noise at the moment.
Preferably, step 2.3 specifically comprises:
at completion t k After one filtering update of time instant, the previous k+1 time instant information sequence epsilon (epsilon) 1 、ε 2 、···ε k+1 ) Variance of (2)Wherein ε is k+1 At t k+1 Information of time, calculate ||ε k+1 |-|E[ε]And I and II are combined withIn comparison, wherein E [. Cndot.]Representing the mean value of the matrix, beta being a constant, beta being E (0, 1);
if it isThen consider this data to be interference data, correct t k+1 Time Kalman filter gain K k+1 Alpha K is calculated k+1 Assignment to K k+1 Alpha is a constant, alpha epsilon (0, 1), and t is recalculated k+1 System status update of time of day->Sum covariance update P k+1|k+1 Filter output +.>Entering the next time filtering cycle;
if it isThen correct t k One-step predictor for time-of-day system state vectorWill->Assign to->And recalculate t k+1 Information epsilon of time of day k+1 Then recalculate t k+1 System status update of time of day->Sum covariance update P k+1|k+1 Filter output +.>Entering the next time filtering cycle;
if it isThe next time the filtering process loops are entered.
Further, the peak ratio of the high frequency component in step 3.2 is calculated as follows
Wherein j is the number of decomposition layers, N j Max (|w) is the number of high-frequency components of the j-th layer j I) is the maximum value of the absolute value of the high frequency component at the j-th layer, |w j，i I is the absolute value of the ith high frequency component at the jth layer, J j The peak ratio of the j-th layer.
When J j ρ is less than or equal to J j+1 >And determining the decomposition layer number L=j when ρ is a threshold value for distinguishing whether noise information is contained in a certain layer of high-frequency component, wherein ρ epsilon (0, 1).
In step 3.3, the low frequency signal of the L layer and the high frequency signal of each layer are subjected to threshold processing, and a visual threshold is adoptedWherein->|c 1 The I is the absolute value of wavelet coefficient of the first layer of wavelet decomposition, M is the length of the signal, and a soft threshold function is adopted
Where r is each wavelet coefficient.
Compared with the prior art, the invention has the beneficial effects that:
1) Compared with the classical Kalman filtering, the adaptive anti-outlier Kalman filtering method has the advantages that an anti-outlier link is added, the influence of outliers in signals on filtering is avoided, and the filtering precision is improved;
2) The invention also carries out threshold processing on the low-frequency signal under the condition of ensuring that the signal is not distorted in the wavelet denoising process. Compared with the traditional wavelet denoising, the method has the advantages that low-frequency noise is better restrained;
3) After the adaptive anti-outlier Kalman filtering, the signal is subjected to wavelet processing, and compared with the traditional Kalman filtering and wavelet fusion method, the algorithm is simpler and more effective;
4) The invention provides a self-adaptive anti-outlier denoising scheme integrating Kalman filtering and wavelet for MEMS gyroscope signals, which can more effectively improve the precision of the sensor and reduce errors.
Drawings
The invention is further described below with reference to the drawings and examples.
FIG. 1 is a schematic flow chart of the method of the present invention.
Fig. 2 is an analysis chart of the denoising effect of the gyroscope x-axis according to the embodiment.
Fig. 3 is a graph of analysis of the denoising effect on the y-axis of the gyroscope according to the embodiment.
Fig. 4 is a graph of analysis of the z-axis denoising effect of the gyroscope according to the embodiment.
Detailed Description
As shown in fig. 1, the gyro signal denoising method for kalman filtering and Visushrink thresholding specifically comprises the following steps,
step 1: establishing a time sequence ARMA model of the MEMS gyroscope signal:
extracting trend items and period items in original signals of the MEMS gyroscope, establishing a time sequence ARMA model for residual errors, and determining the model by adopting a final prediction error FPE criterion to obtain an AR (1) model which is expressed as:
m k+1 ＝am k +ξ k+1
m is in k ，m k+1 Respectively represent t k Time sum t k+1 The gyroscope error at the moment, a is an autoregressive coefficient, and xi k+1 At t k+1 White noise at the moment;
step 2: denoising the gyroscope signal by adopting Kalman filtering;
step 2.1: establishing a state equation and a measurement equation of a Kalman filter according to the AR (1) model obtained in the step 1, wherein the state equation and the measurement equation are specifically as follows:
wherein a=a, b=1, h=1, v k+1 An estimated error of the AR (1) model, the variance of which is R, X k+1 、X k Respectively t k+1 、t k State quantity of time, Z k+1 At t k+1 Measurement of time of day, η k Is the noise of the system process, the variance is Q, and the value is xi in the step 1 k+1 The variance of white noise, Q and R are uncorrelated, and the gyroscope error m is taken as the filter input;
step 2.2: self-adaptive outlier-resistant Kalman filter initialization at the beginning of filteringEngraving t 0 Initializing state vector of filter by using gyroscope signal error m estimated by ARMA modelSum-of-variance matrix P 0 The method specifically comprises the following steps:
wherein E [. Cndot.]Represent the mean value (.) T Is the transpose of the matrix;
step 2.3: performing adaptive outlier-resistant Kalman filtering;
step 3: determining a wavelet base db2;
determining a wavelet decomposition level: wavelet decomposition is carried out on the filtered gyroscope signals by adopting selected db2 wavelets, and the peak value ratio of each layer of high-frequency components is calculated, namely
Wherein j is the decomposition layer number, N j Max (|w) is the number of high-frequency components of the j-th layer j I) is the maximum value of the absolute value of the high frequency component at the j-th layer, |w j,i I is the absolute value of the ith high frequency component at the jth layer, J j Peak ratio for the j-th layer; when J j ρ is less than or equal to J j+1 >When ρ is the threshold value for distinguishing whether noise information is contained in a certain layer of high-frequency component, ρ epsilon (0, 1);
the low-frequency signal of the L layer and the high-frequency signal of each layer are subjected to threshold processing, and a Visushrink threshold value is adopted
Wherein |c 1 The i is the absolute value of the wavelet coefficients of the wavelet decomposition first layer and M is the length of the signal. In embodiments employing a soft threshold function
Where r is each wavelet coefficient.
Step 4: and carrying out wavelet reconstruction on the processed high-frequency and low-frequency signals by adopting a waverec function in matlab software.
In the step 2, the filtering process of the adaptive wild-value-resistant Kalman filtering specifically comprises the following steps:
first, state one-step prediction:
secondly, one-step prediction of a covariance matrix:
P k+1|k ＝AP k|k A T +BQB T
third, calculating a filter gain matrix:
K k+1 ＝P k+1|k H T [HP k+1|k H T +R] -1
fourth, calculating information:
fifthly, updating the state:
sixth, covariance update:
P k+1|k+1 ＝[I n -K k+1|k H]P k+1|k
seventh, the filter output at time k+1:
in the middle ofAt t k One-step prediction of the time-of-day system state vector,/->Respectively t k ，t k+1 Time update of system state vector at time. P (P) k+1|k At t k One-step predictive value, e, of a system covariance matrix of time instant k+1 At t k+1 Information of time, P k|k ，P k+1|k+1 Respectively t k ，t k+1 Time-of-day system covariance update, K k+1 At t k+1 Time Kalman filter gain, I n N is the dimension of the filter state vector, [. Cndot.] -1 Is the inverse of the matrix, ">The filter output at time k+1.
The self-adaptive wild value resisting link comprises the following steps: at completion t k After one filtering update of time instant, the previous k+1 time instant information sequence epsilon (epsilon) 1 、ε 2 、…ε k+1 ) Variance S of (2) k+1 ：
And comparing:
where |·| is expressed as absolute value, if equation (1) is satisfied, the data is considered as interference data, and aK is taken as k+1 Assignment to K k+1 A epsilon (0, 1) embodiment takes a=0.5, returns to the fifth step to update the state again;
if the formula (1) is not satisfied, continuing to compare whether the formula (1) is satisfied:
in the examples, β=0.7 is taken, and if the formula (2) is satisfied, the reaction mixture isAssign to->g e (0, 1), in the embodiment, g=0.5 is taken, and the fourth step of recalculating information is returned; if neither equation (1) nor equation (2) is satisfied, the next filtering process cycle is entered.
The experiment is verified by the experiment, and the experiment content is as follows:
1. the test data are derived from the actual measurement data of a static base of a certain MEMS gyroscope, the standing time is 1 hour, and the sampling frequency is 200HZ.
2. The autoregressive coefficients a of the gyroscopes x, y and z axes are respectively 0.0092, 0.0299 and 0.0080, and the variances of the corresponding white noise are 3.8595 multiplied by 10 -7 (rad 2 /s 2 )、4.6831×10 -7 (rad 2 /s 2 )、3.6487×10 -7 (rad 2 /s 2 )。
3. The initial conditions of the Kalman filters of the X, y and z axes of the gyroscope are respectively set as follows:
wherein the method comprises the steps ofInitial state vectors of the x, y and z axis filters, P 0x 、P 0y 、P 0z The initial covariance of the x, y, z axis filters, respectively.
4. According to step 3, when the peak ratio of the gyroscope error signal, J j ≤ρ,J j+1 >When ρ=0.05, determining the decomposition layers of the x, y and z triaxial data as L x ＝L y ＝L z ＝13。
5. And respectively carrying out classical Kalman filtering, visual denoising and denoising of the X, Y and Z triaxial data of the gyroscope, and carrying out method comparison by estimating the noise coefficient of the gyroscope through an alan variance.
Through computer simulation, the denoising effect contrast diagrams of the x, y and z axes of the gyroscopes are shown in fig. 2, 3 and 4, and the noise coefficient contrast of the x, y and z axes of the gyroscopes is shown in table 1, table 2 and table 3 respectively.
Table 1 gyroscope x-axis noise figure comparison analysis table
Table 2 comparison analysis table for y-axis noise figure of gyroscope
Table 3 gyroscope z-axis noise figure comparison analysis table
It can be seen from tables 1-3 that the quantization noise factor, the angle random walk and the zero offset instability of the method using the scheme are smaller than that of Kalman filtering and wavelet denoising, and especially, the zero offset instability of gyroscopes x, y and z axes is respectively improved by 31.0%, 29.3%, 30.5% and 2.4%, 12.1% and 12.4% compared with that of the Kalman filtering.
The variance pairs after denoising of the gyroscope x, y and z axes are shown in table 4. As can be seen from table 4, the variance after denoising in this scheme is smaller than that of kalman filtering and wavelet denoising.
TABLE 4 comparison analysis of x, y, z-axis variance of gyroscopes
Claims (5)
1. The gyro signal denoising method for Kalman filtering and Visushrink threshold processing is characterized by comprising the following steps of:
step 1: establishing a time sequence ARMA model of the gyroscope signal;
firstly extracting a trend term and a period term in an original signal of a gyroscope, then establishing a time sequence ARMA model for residual errors, and adopting a final prediction error FPE criterion to order the model to obtain a random drift error of the gyroscope;
step 2: denoising the gyroscope signal by adopting self-adaptive wild value resistant Kalman filtering;
step 2.1: establishing a state equation and a measurement equation of a Kalman filter according to the gyro random drift error model in the step 1;
step 2.2: initializing a self-adaptive wild-value-resistant Kalman filter, and initializing a state vector and a covariance matrix of the filter by using a gyroscope error estimated by a gyroscope random drift error model at the starting moment of filtering;
step 2.3: performing adaptive outlier-resistant Kalman filtering;
step 3: performing threshold processing on a low-frequency component and a high-frequency component of the gyroscope signal after Kalman filtering by utilizing wavelet analysis;
step 3.1: selecting a wavelet function;
step 3.2: determining a wavelet decomposition level, performing wavelet decomposition on the filtered gyroscope signals by adopting a selected wavelet function, and calculating the peak ratio of each layer of high-frequency components;
step 3.3: performing visual threshold processing on the low-frequency signal and the high-frequency signal;
step 4: and carrying out wavelet reconstruction on the high-frequency and low-frequency signals of the gyroscope signals after the thresholding.
2. The gyro signal denoising method according to claim 1, wherein in step 1, the calculation model of gyro random drift error is as follows:
m k+1 ＝am k +ξ k+1
m is in k ,m k+1 Respectively represent t k ,t k+1 The gyroscope error at the moment, a is an autoregressive coefficient, and xi k+1 At t k+1 White noise at the moment.
3. The gyro signal denoising method according to claim 2, wherein step 2.3 specifically comprises:
at completion t k After one filtering update of the time instant, the previous k+1 time instant information sequence e (e 1 、e 2 、…ε k+1 ) Variance of (2)Wherein ε is k+1 At t k+1 Information of time, calculate ||ε k+1 |-|E[ε]And I and II are combined withIn comparison, wherein E [. Cndot.]Representing the mean value of the matrix, beta being a constant, beta being E (0, 1);
if it isThen consider this data to be interference data, correct t k+1 Time Kalman filter gain K k+1 Alpha K is calculated k+1 Assignment to K k+1 Alpha is a constant, alpha epsilon (0, 1), and t is recalculated k+1 System status update of time of day->Sum covariance update P k+1|k+1 Filter output +.>Entering the next time filtering cycle;
if it isThen correct t k One-step predictor of time-of-day system state vector +.>Will beAssign to->And recalculate t k+1 Information epsilon of time of day k+1 Then recalculate t k+1 System status update of time of day->Sum covariance update P k+1|k+1 Filter output +.>Entering the next time filtering cycle;
if it isThe next time the filtering process loops are entered.
4. The gyro signal denoising method according to claim 3, wherein the peak ratio of the high frequency component in step 3.2 is calculated as follows
Wherein j is the number of decomposition layers, N j Max (|w) is the number of high-frequency components of the j-th layer j I) is the maximum value of the absolute value of the high frequency component at the j-th layer, |w j,i I is the absolute value of the ith high frequency component at the jth layer, J j Peak ratio for the j-th layer;
when J j ρ is less than or equal to J j+1 >And determining the decomposition layer number L=j when ρ is a threshold value for distinguishing whether noise information is contained in a certain layer of high-frequency component, wherein ρ epsilon (0, 1).
5. The gyro signal denoising method according to claim 4, wherein the low frequency signal of the L layer and the high frequency signal of each layer are thresholded in step 3.3 using a Visushrink threshold valueWherein the method comprises the steps of|c 1 The I is the absolute value of wavelet coefficient of the first layer of wavelet decomposition, M is the length of the signal, and a soft threshold function is adopted
Where r is each wavelet coefficient.
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