CN108120452A - The filtering method of MEMS gyroscope dynamic data - Google Patents
The filtering method of MEMS gyroscope dynamic data Download PDFInfo
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Abstract
A kind of filtering method of MEMS gyroscope dynamic data, belongs to field of signal processing.The purpose of the present invention is being handled mainly for the dynamical output data of inexpensive MEMS gyroscope system, so as to improve the filtering method of the MEMS gyroscope dynamic data of gyroscope dynamical output data precision.The method of the present invention for improving MEMS gyroscope dynamical output data precision comprises the following steps：It determines MEMS gyroscope constant value drift, establishes MEMS gyroscope output data model, determines Kalman filter process-noise varianceWith measurement noise variance
Description
Technical field
The invention belongs to field of signal processing.
Background technology
MEMS gyroscope is for measuring the sensor of object angular speed, due to small, light-weight, at low cost, reliable
Property it is high the advantages that, be widely used in the various fields such as military, business, civilian.But due to system structure deviation, perturbed force
How the influence of square, ambient noise etc. there are random error in the output data of MEMS gyroscope, therefore improves MEMS gyroscope
Precision be the hot issue studied both at home and abroad at present.For this problem, there are two types of main solutions, and one kind is from hard
Improve gyroscope arrangement in terms of part, gyroscope precision is improved by reducing structural failure；Another kind is set about from software aspects, is led to
It crosses filtering algorithm elimination random error and reaches raising gyroscope precision purpose.Since the construction cycle is short, cost is few, current second
The research work of method is relatively more, and conventional method is first to establish gyroscope output data model based on data with existing, is then based on
This model application filtering algorithm is filtered gyroscope output data.A current research work part is based on MEMS tops
Spiral shell instrument static data is carried out, and filtering algorithm is only applicable to the Static output data of gyroscope；Other filtering algorithm can
Realize dynamic data filtering, but calculation amount is excessive, it is relatively difficult to achieve for inexpensive real-time system.
The content of the invention
The purpose of the present invention is being handled mainly for the dynamical output data of inexpensive MEMS gyroscope system, so as to
Improve the filtering method of the MEMS gyroscope dynamic data of gyroscope dynamical output data precision.
The method of the present invention for improving MEMS gyroscope dynamical output data precision comprises the following steps：
(1) MEMS gyroscope constant value drift is determined：When MEMS gyroscope steady operation, one hour quiet is gathered respectively in four times
State output data calculates constant value drift of the average of four MEMS gyroscope static datas as gyroscope, and what is gathered later is every
A data are required for cutting this constant value drift；
(2) MEMS gyroscope output data model is established：Gyroscope dynamical output data sequence is Xk, dynamic data difference sequence
For Dk, wherein Dk=Xk+1-Xk；
(3) Kalman filter process-noise variance Q and measurement noise variance R are determined：Process noise and measurement noise are and the time
Unrelated white Gaussian noise, their variance Q and R are constant, and the value needs of Q and R are determined by testing；
(4) Kalman filter is carried out to dynamic data：The Kalman filter model of dynamic data is the MEMS established in step 2
Gyroscope output data model.
MEMS gyroscope output data model of the present invention is：
Wherein state vector is MEMS gyroscope Output speed signal XkWith angular velocity difference sub-signal Dk, corresponding state is defeated
Go out respectively xkAnd dk, Wk, VkRespectively systematic procedure noise and measurement noise act on differential signal DkOn.
The present invention to dynamic data carry out Kalman filter the step of be：
(1) state one-step prediction：This when, is predicted by the optimal State Estimation value of last moment
The state at quarter；System mode vectorState-transition matrix
(2) one-step prediction varivance matrix is calculated：It uses
One moment estimation error variance and process-noise variance calculate one-step prediction error variance；Systematic procedure noise inputs matrix
(3) filtering gain matrix are calculated：Pass through one-step prediction variance and survey
It measures noise variance and calculates Kalman filter gain；Systematic survey matrix
(4) state estimation：It is corrected using the reality output data of gyroscope
One-step prediction is as a result, so as to obtain optimal estimation；ZkFor the angular velocity signal and angular speed difference of k moment gyroscope reality outputs
The vector of signal composition；
(5) estimation error variance matrix is calculated：Pk=[I-KkHk]PK, k-1；This estimation error variance is calculated, is next time
Estimation is prepared；Unit diagonal matrix
(6) state output：
The invention discloses a kind of filtering methods of MEMS gyroscope dynamic data, are determined that constant value is floated using static data
It moves, the data using angular velocity signal and angular velocity difference sub-signal as quantity of state is established based on MEMS gyroscope data output characteristic
Output model carries out Kalman filter to dynamic data based on this model, improves the precision of gyroscope dynamical output data.This
The Kalman filter method that invention uses is a kind of iterative estimate method, only needs the estimate of last moment and the measurement at this moment
Value can provide the angular speed optimal estimation value at this moment, and calculation amount is small, is easy to low-cost system Project Realization.
Description of the drawings
Fig. 1 is the flow chart of gyroscope dynamic data filtering algorithm of the present invention；
Fig. 2 is Kalman filter process, I, II, III in figure, IV, V, and correspond to respectively in technical scheme steps 4 six of VI walk
Suddenly；
Fig. 3 a are first group of static data；
Fig. 3 b are second group of static data；
Fig. 3 c are the 3rd group of static data；
Fig. 3 d are the 4th group of static data；
Fig. 4 a are first group of data mean value；
Fig. 4 b are second group of data mean value；
Fig. 4 c are the 3rd group of data mean value；
Fig. 4 d are the 4th group of data mean value；
Fig. 5 a are first group of data variance；
Fig. 5 b are second group of data variance；
Fig. 5 c are the 3rd group of data variance；
Fig. 5 d are the 4th group of data variance；
Fig. 6 a are first group of data auto-correlation function；
Fig. 6 b are second group of data auto-correlation function；
Fig. 6 c are the 3rd group of data auto-correlation function；
Fig. 6 d are the 4th group of data auto-correlation function；
Fig. 7 is comparison diagram before and after dynamic data filtering.
Specific embodiment
The method of the present invention for improving MEMS gyroscope dynamical output data precision comprises the following steps：
(1) MEMS gyroscope constant value drift is determined：When MEMS gyroscope steady operation, one hour quiet is gathered respectively in four times
State output data calculates constant value drift of the average of four MEMS gyroscope static datas as gyroscope, and what is gathered later is every
A data are required for cutting this constant value drift；
(2) MEMS gyroscope output data model is established：Gyroscope dynamical output data sequence is Xk, dynamic data difference sequence
For Dk, wherein Dk=Xk+1-Xk；
(3) Kalman filter process-noise variance Q and measurement noise variance R are determined：Process noise and measurement noise are and the time
Unrelated white Gaussian noise, their variance Q and R are constant, and the value needs of Q and R are determined by testing；
(4) Kalman filter is carried out to dynamic data：The Kalman filter model of dynamic data is the MEMS established in step 2
Gyroscope output data model.
MEMS gyroscope output data model of the present invention is：
Wherein state vector is MEMS gyroscope Output speed signal XkWith angular velocity difference sub-signal Dk, corresponding state is defeated
Go out respectively xkAnd dk, Wk, VkRespectively systematic procedure noise and measurement noise act on differential signal DkOn.
The present invention to dynamic data carry out Kalman filter the step of be：
(1) state one-step prediction：This when, is predicted by the optimal State Estimation value of last moment
The state at quarter；System mode vectorState-transition matrix
(2) one-step prediction varivance matrix is calculated：It uses
One moment estimation error variance and process-noise variance calculate one-step prediction error variance；Systematic procedure noise inputs matrix
(3) filtering gain matrix are calculated：Pass through one-step prediction variance and survey
It measures noise variance and calculates Kalman filter gain；Systematic survey matrix
(4) state estimation：It is corrected using the reality output data of gyroscope
One-step prediction is as a result, so as to obtain optimal estimation；ZkFor the angular velocity signal and angular speed difference of k moment gyroscope reality outputs
The vector of signal composition；
(5) estimation error variance matrix is calculated：Pk=[I-KkHk]PK, k-1；This estimation error variance is calculated, is next time
Estimation is prepared；Unit diagonal matrix
(6) state output：
Said program is described further with reference to specific embodiments and the drawings, the present invention includes but are not limited to down
State embodiment：
1st, MEMS gyroscope constant value drift is determined：When MEMS gyroscope steady operation, one hour quiet is gathered respectively in four times
State output data, Fig. 3 are the four groups of MEMS gyroscope static datas collected.Calculate the equal of four MEMS gyroscope static datas
It is worth the constant value drift as gyroscope.The average that the present embodiment collects static data is -0.8375 °/s.What is gathered later is every
A data are required for cutting this constant value drift.Judge whether the method for steady operation is to examine static data to MEMS gyroscope
Stationarity, stationarity refer to Random time sequence { xtThe statistical property of (t=1,2,3...) do not change over time, leads here
Examine mean μ=E (xt), the variances sigma of static data2=Var (xt) and covariance function γk=Cov (xt, xt+k) at any time
Situation of change, when meet the time increase when, average tends to definite value and does not change over time, variance tend to definite value not at any time and
Change, when covariance is unrelated with the time, is only related with time interval, judge Random time sequence for stationary sequence.If Fig. 4 is four
Group data mean value changes with time, and Fig. 5 changes with time for four groups of data variances, Fig. 6 for four groups of data covariances at any time
Between variation, as seen from the figure the four of the present embodiment group static data meet stationarity.When the static data of this step acquisition has
During stationarity, the constant value drift calculated could be closer to real constant value drift.
2nd, MEMS gyroscope output data model is established：Gyroscope dynamical output data sequence is Xk, dynamic data difference
Sequence is Dk, wherein Dk=Xk+1-Xk.Since gyroscope actual angular speed is a signal become slowly, from k-1 moment to k
The angular speed increment at moment and the angular speed increment approximately equal from the k moment to the k+1 moment, i.e. Dk=Dk-1.So MEMS gyro
Instrument output data model is：
Wherein state vector is MEMS gyroscope Output speed signal XkWith angular velocity difference sub-signal Dk, corresponding state is defeated
Go out respectively xkAnd dk, Wk, VkRespectively system noise and measurement noise act on differential signal DkOn.What this step was established
Output data model is the model that Kalman filter is used in the 4th step.
3rd, Kalman filter process-noise variance Q and measurement noise variance R are determined：Process noise and measurement noise be and when
Between unrelated white Gaussian noise, their variance Q and R is constant, and the value needs of Q and R are determined by testing.It sets respectively
The value of multigroup Q and R takes the value of the preferable one group of Q and R of static data filter effect as process-noise variance and measurement noise side
Difference.Here judge the value of Q and R with static data filter effect and be without the reason for dynamic data, since top can not be obtained
The actual value of spiral shell instrument dynamic data, therefore the quality of dynamic filter effect can not be analyzed, and static data actual value is 0, filtering
Effect can represent that variance is smaller, and filter effect is better with the variance of filtered data and static data actual value.This implementation
When taking in exampleWhen, Static Filtering effect is preferable, if Fig. 7 is four groups of static numbers
According to filter effect figure.The variance of static data such as table 1 before and after filtering.
Table 1
| Data | First group | Second group | 3rd group | 4th group |
| Poor in front of filtering (°/s)2 | 1.9745 | 1.9604 | 1.9450 | 1.9612 |
| Variance after filtering (°/s)2 | 0.1643 | 0.1708 | 0.1689 | 0.1719 |
4th, Kalman filter is carried out to dynamic data：
The Kalman filter model of dynamic data is the MEMS gyroscope output data model established in step 2：
It is to the step of dynamic data progress Kalman filter：
(1) state one-step prediction：It is predicted by the optimal State Estimation value of last moment
The state at this moment.System mode vectorState-transition matrix
(2) one-step prediction varivance matrix is calculated：With
Last moment estimation error variance and process-noise variance calculate one-step prediction error variance.System noise input matrixSystematic procedure noise variance
(3) filtering gain matrix are calculated：Pass through one-step prediction variance
Kalman filter gain is calculated with measurement noise variance.Systematic survey matrixMeasurement noise variance
(4) state estimation：Come using the reality output data of gyroscope
One-step prediction is corrected as a result, so as to obtain optimal estimation.ZkFor the angular velocity signal and angular speed of k moment gyroscope reality outputs
The vector of differential signal composition.
(5) estimation error variance matrix is calculated：Pk=[I-KkHk]PK, k-1.This estimation error variance is calculated, for next time
Estimation prepare.Unit diagonal matrix
(6) state output：
It is above Kalman filter step, since Kalman filter is an iterative process, gives ability after filtering initial value
Start filtering, it is therefore desirable to determine state initial valueWith estimation error variance initial value P0.Selection state initial valueWhen should not
It is excessive to deviate true initial state, estimation error variance initial value P0It is chosen in the range of (0,1).The present embodiment chooses state initial valueChoose estimation error variance initial valueFig. 7 is that one group of dynamic data of the present embodiment filters
Front and rear comparison diagram, as seen from the figure filtering method proposed by the present invention effectively inhibit in gyroscope dynamical output data with
Chance error is poor, improves the precision of gyroscope dynamical output data.
Fig. 3 (a), (b), (c), four groups of static datas that (d) is the MEMS gyroscope in the present embodiment, every group of static data
Length be one hour.The average of four groups of data is calculated to obtain the constant value drift of the present embodiment MEMS gyroscope.When acquisition
When data volume is bigger, obtained constant value drift is closer to actual constant value drift.The present embodiment thinks that gathering four groups of data obtains
The close enough truthful data of constant value drift constant value drift.
Fig. 4, Fig. 5, Fig. 6 are respectively the mean function, variance function and auto-correlation function of four groups of static datas, by can in figure
To obtain, when increasing the time, the average of four groups of numbers tends to definite value, and variance tends to definite value, and auto-correlation function is unrelated with time point,
It is only related with time interval, it is taken as that the four groups of static datas collected in the present embodiment meet stationarity.
Fig. 7 is comparison diagram before and after the filtering of MEMS gyroscope dynamic data in the present embodiment, and fine line is initial data in figure,
Heavy line is filtered data, and filtered dynamic data is more smooth as can be seen from Figure, preferably eliminates and makes an uproar at random
Sound, hence it is demonstrated that the validity of the method for the present invention.
Claims (3)
1. a kind of filtering method of MEMS gyroscope dynamic data, it is characterised in that：Its step is：
(1) MEMS gyroscope constant value drift is determined：When MEMS gyroscope steady operation, one hour quiet is gathered respectively in four times
State output data calculates constant value drift of the average of four MEMS gyroscope static datas as gyroscope, and what is gathered later is every
A data are required for cutting this constant value drift；
(2) MEMS gyroscope output data model is established：Gyroscope dynamical output data sequence is Xk, dynamic data difference sequence
For Dk, wherein Dk=Xk+1-Xk；
(3) Kalman filter process-noise variance Q and measurement noise variance R are determined：Process noise and measurement noise are and the time
Unrelated white Gaussian noise, their variance Q and R are constant, and the value needs of Q and R are determined by testing；
(4) Kalman filter is carried out to dynamic data：The Kalman filter model of dynamic data is the MEMS established in step 2
Gyroscope output data model.
2. the filtering method of MEMS gyroscope dynamic data according to claim 1, it is characterised in that：MEMS gyroscope is defeated
Going out data model is：
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Wherein state vector is MEMS gyroscope Output speed signal XkWith angular velocity difference sub-signal Dk, corresponding state is defeated
Go out respectively xkAnd dk, Wk, VkRespectively systematic procedure noise and measurement noise act on differential signal DkOn.
3. the filtering method of MEMS gyroscope dynamic data according to claim 1, it is characterised in that：To dynamic data into
The step of row Kalman filter is：
(1) state one-step prediction：This when, is predicted by the optimal State Estimation value of last moment
The state at quarter；System mode vectorState-transition matrix
(2) one-step prediction varivance matrix is calculated：Use one
Moment estimation error variance and process-noise variance calculate one-step prediction error variance；Systematic procedure noise inputs matrix
(3) filtering gain matrix are calculated：Pass through one-step prediction variance and measurement
Noise variance calculates Kalman filter gain；Systematic survey matrix
(4) state estimation：One is corrected using the reality output data of gyroscope
Prediction result is walked, so as to obtain optimal estimation；ZkBelieve for the angular velocity signal and angular speed difference of k moment gyroscope reality outputs
Number composition vector；
(5) estimation error variance matrix is calculated：Pk=[I-KkHk]PK, k-1；This estimation error variance is calculated, for estimating next time
Meter is prepared；Unit diagonal matrix
(6) state output：
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| CN111339494A (en) * | 2020-01-16 | 2020-06-26 | 四川建筑职业技术学院 | Gyroscope data processing method based on Kalman filtering |
| CN112632454A (en) * | 2020-12-17 | 2021-04-09 | 长光卫星技术有限公司 | MEMS gyro filtering method based on adaptive Kalman filtering algorithm |
| US11680798B2 (en) | 2020-08-24 | 2023-06-20 | Invensense, Inc. | Digital demodulator and complex compensator for MEMS gyroscope |
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Cited By (5)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN110485222A (en) * | 2019-07-29 | 2019-11-22 | 中国铁路总公司 | A kind of dynamic data inversion method and device |
| CN110485222B (en) * | 2019-07-29 | 2020-11-27 | 中国铁路总公司 | Dynamic data inversion method and device |
| CN111339494A (en) * | 2020-01-16 | 2020-06-26 | 四川建筑职业技术学院 | Gyroscope data processing method based on Kalman filtering |
| US11680798B2 (en) | 2020-08-24 | 2023-06-20 | Invensense, Inc. | Digital demodulator and complex compensator for MEMS gyroscope |
| CN112632454A (en) * | 2020-12-17 | 2021-04-09 | 长光卫星技术有限公司 | MEMS gyro filtering method based on adaptive Kalman filtering algorithm |
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