CN111339494A - Gyroscope data processing method based on Kalman filtering - Google Patents
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Abstract
The invention discloses a gyroscope data processing method based on Kalman filtering, which is characterized in that real-time mean value processing is carried out on data output by a gyroscope within a time interval of gyroscope data, and the mean value is used as a use value. After the mean value filtering processing, carrying out stabilization pretreatment on gyroscope data to obtain a gyroscope residual sequence; and (3) establishing an AR (1) model according to the residual sequence of the gyroscope, and filtering the random error of the gyroscope for multiple times by adopting a Kalman filtering method. The method can effectively reduce the influence of random noise on the gyroscope, and the method needs less cost.
Description
Technical Field
The invention relates to the field of information processing, in particular to a gyroscope data processing method based on Kalman filtering.
Background
In recent years, as an important research field emerging in the inertial technology, the MEMS gyroscope has been developed greatly due to its advantages of high performance, small size, low energy consumption, light weight, high reliability, and the like, and has been applied more and more widely in low-cost navigation systems. MEMS are miniature sensors of angular velocity manufactured by micromachining techniques, but are limited by the manufacturing process and the level of precision, and output data of the sensors are more random noise than inertial sensors manufactured by conventional manufacturing processes.
In the existing method, a reasonable random drift error model is established to estimate and compensate the random drift error model, so that the gyro precision is improved. However, the models created by these methods tend to have higher orders and are not suitable for real-time online estimation of low-cost systems.
Therefore, a method for effectively reducing random drift errors, improving the gyro precision and effectively controlling the cost is urgently needed.
Disclosure of Invention
The invention aims to solve the technical problems that the random drift error of an MEMS gyroscope is large, the gyroscope precision is influenced, the existing processing method is high in cost and inconvenient to widely use, and the gyroscope data processing method based on Kalman filtering is provided to solve the problem of processing the random drift error of the MEMS gyroscope.
The invention is realized by the following technical scheme:
the gyroscope data processing method based on Kalman filtering comprises the following steps:
(1) carrying out real-time mean value processing on data output by a gyroscope within a time interval of gyroscope data, and taking the mean value as a use value;
(2) after the mean value filtering processing, carrying out stabilization pretreatment on gyroscope data to obtain a gyroscope residual sequence;
(3) and (3) establishing an AR (1) model according to the residual sequence of the gyroscope, and filtering the random error of the gyroscope for multiple times by adopting a Kalman filtering method.
Further, the AR (1) model in the step (3) is as follows: y (t) ═ 0.1130366 y (t-1) + epsilont(1)；
Wherein epsilontIs an error of ytIs a stationary time series.
Meanwhile, the Kalman filtering formula obtained based on the AR (1) model in the step (3) is as follows:
X(k)＝A X(k-1)+B U(k)+W(k) (2)
Z(k)＝H X(k)+V(k) (3)
in the above formulas (2) and (3), x (k) is the system state at time k, and u (k) is the control amount of the system at time k; a and B are system parameters, Z (k) is the measured value at time k, H is the parameter of the measurement system; w (k) and v (k) represent process and measurement noise, respectively.
Secondly, the recursive expression of the Kalman filter algorithm is:
X(k|k-1)＝A X(k-1|k-1)+B U(k) (4)
P(k|k-1)＝A P(k-1|k-1)A’+Q (5)
X(k|k)＝X(k|k-1)+Kg(k)(Z(k)-H X(k|k-1)) (6)
Kg(k)＝P(k|k-1)H’/(H P(k|k-1)H’+R) (7)
P(k|k)＝(I-Kg(k)H)P(k|k-1) (8)；
wherein Kg is Kalman gain, when the system enters a k +1 state, the k +1 state is used as a k state in the formula, and the k state is used as a k-1 state to solve, namely, the autoregressive operation is carried out.
Preferably, a least square fitting method is adopted in the step (2) to fit the non-stationary random sequence as the approximation of the actual trend term; the result after fitting using the polyfit function of MATLAB was:
for the method, in practical application, the data output frequency of the MEMS gyroscope is greater than the frequency of the system using the data of the MEMS gyroscope, and the MEMS gyroscope actually outputs a plurality of data in a time interval of using the data of the gyroscope each time, so that in the method, the data is averaged in real time and then used to improve the high precision of the gyroscope.
The random error of the MEMS gyroscope is considered to be the output of the linear time invariant system with white noise as input, which is zero-mean, and thus the output of the linear time invariant system with white noise as input is also zero-mean. Therefore, the data output by the gyroscope in the time interval of using the gyroscope data each time is subjected to real-time mean value processing, and the mean value is taken as a using value, so that the random error of the MEMS gyroscope can be obviously inhibited.
And (4) carrying out stability test on the random sequence, and if the random sequence is found to be a non-stable random sequence, carrying out stabilization treatment on the random sequence. In consideration of various possible long-term variation trends of MEMS gyroscope data, a least square fitting method is adopted in the method to fit a non-stationary random sequence as an approximation of an actual trend term, and the processing method is more favorable for accuracy of post-filtering processing and further improves precision.
Furthermore, after the signals are collected, the original measurement data are obtained, and according to the modeling requirement of the time series, the data are subjected to statistical test, median filtering and stabilization preprocessing to obtain a stable, normal and zero-mean time series, which is the basis of the modeling work.
The parameter models constructed by the time series method comprise an autoregressive moving average (ARMA) model, an Autoregressive (AR) model and a Moving Average (MA) model, and the Wold decomposition theorem explains the relationship among the three models: the stationary random process of any finite variance ARMA or MA model can be represented by an infinite AR model, and the stationary random process of any finite variance ARMA or MA model can be represented by an infinite AR model. However, only the parameter estimation of the AR model is a set of linear equations, and the actual physical system is often an all-pole system, so that the AR is most widely applied and more beneficial to use.
Meanwhile, in other existing data processing methods, reasonable random drift error models are built to estimate and compensate the random drift error models, and the models built by the methods often have higher orders and are not suitable for low-cost systems. The invention adopts the Kalman filtering method to process data, thus solving the problem.
Compared with the prior art, the invention has the following advantages and beneficial effects:
the invention relates to a gyroscope data processing method based on Kalman filtering, which comprises the steps of firstly carrying out mean filtering processing and stabilizing preprocessing, then establishing a first-order AR model of MEMS gyroscope residual signals, and finally carrying out Kalman filtering processing according to the model, thereby not only effectively reducing the influence of random noise on a gyroscope, but also having lower cost and more convenient wide use, better inhibiting the noise component in random data when in use and improving the gyroscope precision.
Drawings
The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the principles of the invention. In the drawings:
FIG. 1 is raw measurement data of a gyroscope;
FIG. 2 is mean filtered gyroscope data;
FIG. 3 is a trend term for extraction;
FIG. 4 is a residual sequence with trend terms removed;
FIG. 5 is a graph comparing an original signal and a Kalman filtered signal;
fig. 6 comparison before and after filtering of residual signals.
Detailed Description
In order to make the objects, technical solutions and advantages of the present invention more apparent, the present invention is further described in detail below with reference to examples and accompanying drawings, and the exemplary embodiments and descriptions thereof are only used for explaining the present invention and are not used as limitations of the present invention.
Example 1
As shown in fig. 1, the gyroscope data processing method based on kalman filtering of the present invention includes the following steps:
(1) carrying out real-time mean value processing on data output by a gyroscope within a time interval of gyroscope data, and taking the mean value as a use value;
(2) after the mean value filtering processing, carrying out stabilization pretreatment on gyroscope data to obtain a gyroscope residual sequence;
fitting a non-stationary random sequence by adopting a least square fitting method to be used as an approximation of an actual trend term; the result after fitting using the polyfit function of MATLAB was:
(3) and (3) establishing an AR (1) model according to the residual sequence of the gyroscope, and filtering the random error of the gyroscope for multiple times by adopting a Kalman filtering method.
The mathematical formula of the autoregressive model of the AR model is as follows:
yt＝φ1yt-1+φ2yt-2+…+φpyt-p+εt(2)
wherein p is the order of the autoregressive modeli(i ═ 1, 2, … …, p) is the coefficient to be determined for the model, εtIs an error of ytIs a stationary time series.
The AR model parameters are estimated by using a covariance method, a programming tool is VC + +6.0, and a first-order AR model is established as follows:
y(t)＝－0.1130366*y(t-1)+εt(3)；
after the random error signal is modeled, a more accurate system model and an observation model can be established, and optimal estimation is carried out through a Kalman filter, so that the estimation precision of the drift signal is improved.
First a system for discrete control of the process was introduced. The system can be described by a linear random differential equation:
X(k)＝A X(k-1)+B U(k)+W(k) (4)
plus the system measurements:
Z(k)＝H X(k)+V(k) (5)
in the formula (4) and (5), x (k) is a system state at time k, and u (k) is a control amount of the system at time k. A and B are system parameters, Z (k) is the measured value at time k, and H is a parameter of the measurement system. W (k) and v (k) represent process and measurement noise, respectively. They are assumed to be white gaussian noise and their covariance difference is Q, R (here we assume that they do not change with system state changes). The AR (1) model established above can be treated as a state space model.
Secondly, the recursive expression of the Kalman filter algorithm is:
X(k|k-1)＝A X(k-1|k-1)+B U(k) (6)
P(k|k-1)＝A P(k-1|k-1)A’+Q (7)
X(k|k)＝X(k|k-1)+Kg(k)(Z(k)-H X(k|k-1)) (8)
Kg(k)＝P(k|k-1)H’/(H P(k|k-1)H’+R) (9)
P(k|k)＝(I-Kg(k)H)P(k|k-1) (10)；
wherein Kg is Kalman gain, when the system enters a k +1 state, the k +1 state is used as a k state in the formula, and the k state is used as a k-1 state to be solved, so that the autoregressive operation can be carried out.
Example 2
On the basis of embodiment 1, in this embodiment, a fixed position gyro output signal is selected, the sampling period is 1s, and raw measurement data of the gyro is shown in fig. 1. From the analysis of the raw data, the drift of the MEMS gyroscope contains random components, and the sample sequence is a random time sequence.
The output data of the gyroscope after the mean filtering is shown in fig. 2, and it can be seen from fig. 2 that the trend of the output data of the gyroscope after the mean filtering is basically unchanged, that is, the output information of the gyroscope is not affected by the mean filtering. The standard deviations of the original data of the gyroscope and the data after mean value filtering are respectively as follows: 0.001703383, and 0.00144727. The standard deviation is obviously reduced, and the random error of the gyroscope data after average value filtering is restrained to a certain extent.
The trend term extracted from the data after the mean filtering process is shown in fig. 3, the residual sequence after the trend term is removed is shown in fig. 4, and if the mean filtering and the smoothing preprocessing are not performed in advance, the standard deviations of the original signal and the Kalman filtered signal are respectively: 0.001703383, and 0.001126152. A comparison of the signals before and after Kalman filtering is shown in FIG. 5.
And adding mean filtering and stabilizing pretreatment, wherein standard deviations of gyro residual signals before and after Kalman filtering are respectively as follows: 0.001117479 and 0.000396025, compare fig. 6.
As can be seen from FIGS. 5 and 6, after filtering, gyro random drift is obviously suppressed, so that the algorithm of the invention can effectively improve the accuracy of the gyro.
The method firstly carries out mean filtering processing and stabilizing preprocessing on the output signal of the gyroscope, then establishes an AR (1) statistical model of the residual signal, and Kalman filtering based on the model can reduce the standard deviation of the residual signal, thereby better inhibiting the noise component in random data, effectively reducing the random drift error of the MEMS gyroscope, improving the use efficiency and further reducing the cost.
The above-mentioned embodiments, objects, technical solutions and advantages of the present invention are further described in detail, it should be understood that the above-mentioned embodiments are only exemplary embodiments of the present invention, and are not intended to limit the scope of the present invention, and any modifications, equivalent substitutions, improvements and the like made within the spirit and principle of the present invention should be included in the scope of the present invention.
Claims (5)
1. The gyroscope data processing method based on Kalman filtering is characterized by comprising the following steps:
(1) carrying out real-time mean value processing on data output by a gyroscope within a time interval of gyroscope data, and taking the mean value as a use value;
(2) after the mean value filtering processing, carrying out stabilization pretreatment on gyroscope data to obtain a gyroscope residual sequence;
(3) and (3) establishing an AR (1) model according to the residual sequence of the gyroscope, and filtering the random error of the gyroscope for multiple times by adopting a Kalman filtering method.
2. The kalman filter-based gyroscope data processing method according to claim 1, wherein the AR (1) model in step (3) is: y (t) ═ 0.1130366 y (t-1) + epsilont(1)；
Wherein epsilontIs an error of ytIs a stationary time series.
3. The Kalman filtering based gyroscope data processing method according to claim 2, wherein the Kalman filtering formula obtained based on the AR (1) model in step (3) is:
X(k)＝AX(k-1)+BU(k)+W(k) (2)
Z(k)＝HX(k)+V(k) (3)
in the above formulas (2) and (3), x (k) is the system state at time k, and u (k) is the control amount of the system at time k; a and B are system parameters, Z (k) is the measured value at time k, H is the parameter of the measurement system; w (k) and v (k) represent process and measurement noise, respectively.
4. The Kalman filtering based gyroscope data processing method according to claim 3, characterized in that the recursive expression of Kalman filtering algorithm is:
X(k|k-1)＝AX(k-1|k-1)+BU(k) (4)
P(k|k-1)＝AP(k-1|k-1)A’+Q (5)
X(k|k)＝X(k|k-1)+Kg(k)(Z(k)-HX(k|k-1)) (6)
Kg(k)＝P(k|k-1)H’/(HP(k|k-1)H’+R) (7)
P(k|k)＝(I-Kg(k)H)P(k|k-1) (8)；
wherein Kg is Kalman gain, when the system enters a k +1 state, the k +1 state is used as a k state in the formula, and the k state is used as a k-1 state to solve, namely, the autoregressive operation is carried out.
5. The Kalman filtering based gyroscope data processing method according to claim 1, characterized in that in step (2) a least square fitting method is adopted to fit a non-stationary random sequence as an approximation of an actual trend term; the result after fitting using the polyfit function of MATLAB was:
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| CN115859007A (en) * | 2023-02-17 | 2023-03-28 | 广东石油化工学院 | Sliding window constraint fault-tolerant filtering and noise reduction method and device for sampling data of petrochemical instrument |
| CN116007661A (en) * | 2023-02-21 | 2023-04-25 | 河海大学 | Gyro error suppression method based on improved AR model and smooth filtering |
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| CN102679984A (en) * | 2012-05-29 | 2012-09-19 | 北京理工大学 | Finite model filtering method based on vector distance minimizing criterion |
| CN105021210A (en) * | 2014-04-16 | 2015-11-04 | 苏州圣赛诺尔传感器技术有限公司 | MEMS gyro random drift error processing method |
| CN108120452A (en) * | 2017-12-21 | 2018-06-05 | 吉林大学 | The filtering method of MEMS gyroscope dynamic data |
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| Publication number | Priority date | Publication date | Assignee | Title |
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| CN102679984A (en) * | 2012-05-29 | 2012-09-19 | 北京理工大学 | Finite model filtering method based on vector distance minimizing criterion |
| CN105021210A (en) * | 2014-04-16 | 2015-11-04 | 苏州圣赛诺尔传感器技术有限公司 | MEMS gyro random drift error processing method |
| CN108120452A (en) * | 2017-12-21 | 2018-06-05 | 吉林大学 | The filtering method of MEMS gyroscope dynamic data |
Cited By (3)
| Publication number | Priority date | Publication date | Assignee | Title |
|---|---|---|---|---|
| CN115859007A (en) * | 2023-02-17 | 2023-03-28 | 广东石油化工学院 | Sliding window constraint fault-tolerant filtering and noise reduction method and device for sampling data of petrochemical instrument |
| CN115859007B (en) * | 2023-02-17 | 2023-05-12 | 广东石油化工学院 | Petrochemical instrument sampling data sliding window constraint fault-tolerant filtering noise reduction method and device |
| CN116007661A (en) * | 2023-02-21 | 2023-04-25 | 河海大学 | Gyro error suppression method based on improved AR model and smooth filtering |
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