Method for external-field online calibration of micro-array MEMS gyroscope

Abstract

The invention discloses a method for external field on-line calibration of a micro-array MEMS gyroscope. The method comprises the following steps: electrifying and initializing a micro-array inertial sensor; the output of the micro array MEMS gyroscope is converted into three-axis output of a carrier coordinate system; in combination with a maneuvering target tracking theory, establishing a Kalman filter for angular rate tracking, and estimating the angular velocity rate of each axis at each moment; establishing an adaptive Kalman filter for random drift error estimation by using the angular rate of each axis at each moment obtained by estimation, and respectively performing random drift error and deterministic error compensation on the xyz axis; taking the estimated angular rate of the random drift error compensated at each moment as a reference, establishing a deterministic error estimation Kalman filter, and performing compensation; twelve error parameters at the moment are obtained through estimation, and after the random drift error and the deterministic error of the current sampling angular rate are compensated, the final calibration angular rate at the current moment is obtained.

Description

Technical Field

[0001] The invention belongs to the technical field of inertial sensor error calibration in inertial navigation, and in particular relates to a method for calibrating a micro-array MEMS gyroscope online in an external field. Background Art

[0002] The inertial navigation system can independently provide the carrier with information such as attitude, speed, and position. Micromechanical (MEMS) inertial sensors are widely used in inertial navigation due to their miniaturization and low cost. However, due to the limitations of processing technology, a single MEMS inertial sensor has defects such as large measurement error and poor stability, and cannot meet the requirements of high-precision applications. The use of device redundancy configuration technology is a common method to improve system reliability, but complex configuration methods will reduce the measurement accuracy of inertial devices. It is an urgent problem to ensure accuracy while improving the reliability of the inertial navigation system. Under laboratory conditions, a high-precision turntable can be used as a reference to achieve error compensation, but this solution is no longer applicable in field conditions without a turntable. In addition, zero bias, scale factor, and installation error are not fixed, and the error will change over time.

[0003] The existing technology uses the navigation data of auxiliary equipment as a reference for calibration, and additional devices need to be installed on the product, which increases the cost of the product. At the same time, using the constant vector in nature as a reference, all the data collected by the accelerometer and MEMS gyroscope need to be stored for parameter estimation, which cannot achieve online calibration and requires an additional storage unit. Summary of the invention

[0004] In order to overcome the shortcomings of the prior art, a method for online calibration of a micro-array MEMS gyroscope in the field is proposed. The method proposed in the present invention only requires the output of the MEMS gyroscope and can be online calibrated following the output of the MEMS gyroscope in different motion states.

[0005] The technical solution adopted by the present invention is to provide a method for online calibration of a micro-array MEMS gyroscope in an outdoor field, comprising the following steps:

[0006] S1, power on, initialize the microcomputer inertial sensor;

[0007] S2, converting the output of the micro-array MEMS gyroscope into a three-axis output of the carrier coordinate system;

[0008] S3, combining the maneuvering target tracking theory, establishes the Kalman filter for angular velocity tracking, and estimates the angular velocity of each axis at each moment;

[0009] S4, using the estimated angular velocity of each axis at each moment, an adaptive Kalman filter for random drift error estimation is established, and random drift error and deterministic error compensation are performed on the xyz axis respectively;

[0010] S5, using the estimated angular velocity after random drift error compensation at each moment as a reference, establishing a deterministic error estimation Kalman filter and performing compensation;

[0011] S6, estimating and obtaining twelve error parameters at the moment, first obtaining the value of the angular rate estimation after compensating the random drift error estimation at the current sampling moment, and substituting the value into the filter of the deterministic error estimation as a reference to obtain the deterministic error angular rate;

[0012] S7, using the random drift error and deterministic error estimation method to estimate the current sampling angular rate, and obtain the final calibration result.

[0013] Preferably, the step S2 converts the output of the micro-array MEMS gyroscope into a three-axis output of the carrier coordinate system, and the specific process is as follows:

[0014] First, construct the carrier coordinate system (b system) as "xyz" and determine the sensitive axis of the i-th sensor in the array in the carrier coordinate system and O b Z b The angle between the axes is α i , in X b O b Y b Projection on the plane and O b X b The angle between the axis and the i , then the output of the sensitive axis of the n sensors is expressed in the b system as

[0015]

[0016] M=HX+υ

[0017] Where, υ is the measurement noise;

[0018] Using the least squares method to fuse the array MEMS sensor output into three-axis output

[0019]

[0020] Where ω is the sensitive axis output of the redundant MEMS gyroscope, is the three-axis angular velocity of system b relative to the geographic coordinate system (xyz).

[0021] Preferably, the step S3 is combined with the maneuvering target tracking theory to establish the system state space equation as follows:

[0022] X Ik =A I X Ik-1 +W Ik

[0023] Z Ik =H I X IIk +V Ik

[0024]

[0025] in, H I =

[10] , system noise W Ik is zero and has a variance of The white noise sequence, V Ik The mean is zero and the variance is R Ik Gaussian measurement noise.

[0026] Preferably, the random error drift compensation method in step S4 is: 400 data points are selected from each axis data in a static state for preprocessing, and after removing the linear trend term, the nonlinear trend term is removed by using the GM (1, 1) model, and the data is normalized. The preprocessed data is a zero-mean stationary random sequence with normality. According to the AIC criterion, the optimal ARMA (2, 1) model is established; the equation is

[0027]

[0028] Using ARMA model coefficients and θ j The constructed adaptive Kalman filter is as follows:

[0029] X IIk =A II X IIk-1 +W IIk

[0030] Z IIk =H II X IIk +V IIk

[0031] Among them, the system state variable X IIk =[x k x k-1 ] T , x k is the random drift error estimate. System noise variable W IIk =a k , H II =[1 0], G0=1,

[0032] The adaptive parameter update process in the adaptive Kalman filter is:

[0033]

[0034] q IIk =q IIk-1 +γQ IIk-1 D k e IIk

[0035]

[0036] Among them, P IIk，k-1 is the covariance matrix, e IIk is the estimation error, q Ik and Q Ik are the mean and variance of the time-varying system noise, R IIk-1 is the measurement noise variance, γ=(1-b) / (1-b k+1 ), b is the forgetting factor.

[0037] 5. The method for calibrating a micro-array MEMS gyroscope in an outdoor field online according to claim 4, characterized in that: the step S5 takes into account the zero bias, scale factor and installation error of the MEMS gyroscope, and constructs an error model as follows:

[0038] ω m =S g ω t +b g

[0039] Among them, ω m =[ω mx ω my ω mz ] T is the orthogonal three-axis output of the uncalibrated array MEMS gyroscope in frame b, ω t =[ω x ω y ω z ] T is the actual angular velocity of the carrier, b g is the bias of the MEMS gyroscope, S g is the coefficient matrix. g and g It can be expressed as

[0040]

[0041] The state equation and observation equation of the Kalman filter for deterministic error compensation are:

[0042]

[0043] Preferably, the method uses 17 MEMS chips to construct an array-type MEMS inertial navigation system.

[0044] Preferably, each of the 17 MEMS chips is an inertial measurement unit (IMU) including a three-axis accelerometer and a three-axis MEMS gyroscope; there are nine chips on the front, eight of which are evenly arranged in a circle, and the angle between adjacent chips is 45°; the eight chips on the back and the eight chips arranged in a circle on the front are in corresponding positions.

[0045] The beneficial effects of the present invention are:

[0046] The present invention proposes a calibration method with low cost, small calculation amount and capable of following online error compensation of different motion states of MEMS gyroscopes; the three-axis output of a micro-array MEMS gyroscope is integrated to reduce the calculation amount of array system calibration; a small section of static data is first stored for autoregressive moving average (ARMA) modeling, and then an adaptive Kalman filter is used to follow and estimate the random drift error of the MEMS gyroscope, and the random drift error of the angular rate followed by the Kalman filter is compensated, and the deterministic error is estimated and compensated by the Kalman filter based on the reference, thereby realizing the online calibration of the random drift error and the deterministic error of the MEMS gyroscope, and being suitable for low-cost assembled array-type MEMS inertial navigation systems. BRIEF DESCRIPTION OF THE DRAWINGS

[0047] Figure 1 A flow chart of a method for online calibration of a micro-array MEMS gyroscope in an out-of-field according to the present invention;

[0048] Figure 2 for Figure 1 Schematic diagram of the error calibration of the MEMS gyroscope M in the actual experiment. DETAILED DESCRIPTION

[0049] The present invention will be further described below in conjunction with specific drawings.

[0050] Specifically, Figure 1 As shown, a method for calibrating a micro-array MEMS gyroscope in an external field online is provided, comprising the following steps:

[0051] S1, power on, initialize the microcomputer inertial sensor;

[0052] S2, converting the output of the micro-array MEMS gyroscope into the three-axis output of the carrier coordinate system. The specific process is as follows:

[0053] First, construct the carrier coordinate system (b system) as "xyz" and determine the sensitive axis of the i-th sensor in the array in the carrier coordinate system and O b Z b The angle between the axes is α i , in X b O b Y bProjection on the plane and O b X b The angle between the axis and the i , then the output of the sensitive axis of the n sensors is expressed in the b system as

[0054]

[0055] M=HX+υ

[0056] Where, υ is the measurement noise;

[0057] Using the least squares method to fuse the array MEMS sensor output into three-axis output

[0058]

[0059] Where ω is the sensitive axis output of the redundant MEMS gyroscope, is the three-axis angular velocity of system b relative to the geographic coordinate system (xyz);

[0060] S3, combined with the maneuvering target tracking theory, establish the Kalman filter for angular velocity tracking, and estimate the angular velocity of each axis at each moment. Specifically, establish the system state space equation as follows:

[0061] X Ik =A I X Ik-1 +W Ik

[0062] Z Ik =H I X IIk +V Ik

[0063]

[0064] in, H I = [1 0], system noise W Ik is zero and has a variance of The white noise sequence, V Ik The mean is zero and the variance is R Ik Gaussian measurement noise;

[0065] S4, using the estimated angular velocity of each axis at each moment, establish an adaptive Kalman filter for random drift error estimation, and perform random drift error and deterministic error compensation on the xyz axis respectively; the random error drift compensation method is: select 400 data points in the static state for preprocessing of the data of each axis, remove the linear trend term, and then use the GM (1, 1) model to remove the nonlinear trend term, and normalize the data. The preprocessed data is a zero-mean stationary random sequence with normality. According to the AIC criterion, the optimal ARMA (2, 1) model is established; the equation is

[0066]

[0067] Using ARMA model coefficients and θ j The constructed adaptive Kalman filter is as follows:

[0068] X IIk =A II X IIk-1 +W IIk

[0069] Z IIk =H II X IIk +V IIk

[0070] Among them, the system state variable X IIk =[x k x k-1 ] T , x k is the random drift error estimate. System noise variable W IIk =a k , H II =[1 0], G0=1,

[0071] The adaptive parameter update process in the adaptive Kalman filter is:

[0072]

[0073] q IIk =q IIk-1 +γQ IIk-1 D k e IIk

[0074]

[0075] Among them, P IIk，k-1 is the covariance matrix, e IIk is the estimation error, q Ik and QIk are the mean and variance of the time-varying system noise, R IIk-1 is the measurement noise variance, γ=(1-b) / (1-b k+1 ), b is the forgetting factor;

[0076] S5, taking the estimated angular rate after random drift error compensation at each moment as a reference, establish a deterministic error estimation Kalman filter and perform compensation; considering the zero bias, scale factor and installation error of the MEMS gyroscope, the error model is constructed as follows:

[0077] ω m =S g ω t +b g

[0078] Among them, ω m =[ω mx ω my ω mz ] T is the orthogonal three-axis output of the uncalibrated array MEMS gyroscope in frame b, ω t =[ω x ω y ω z ] T is the actual angular velocity of the carrier, b g is the bias of the MEMS gyroscope, s g is the coefficient matrix. g and g It can be expressed as

[0079]

[0080] The state equation and observation equation of the Kalman filter for deterministic error compensation are:

[0081]

[0082] S6, estimating and obtaining twelve error parameters at the moment, first obtaining the value of the angular rate estimation after compensating the random drift error estimation at the current sampling moment, and substituting the value into the filter of the deterministic error estimation as a reference to obtain the deterministic error angular rate;

[0083] S7, using the random drift error and deterministic error estimation method to estimate the current sampling angular rate, and obtain the final calibration result.

[0084] Furthermore, this method uses 17 MEMS chips to construct an array MEMS inertial navigation system;

[0085] Furthermore, each of the 17 MEMS chips is an inertial measurement unit (IMU) including a three-axis accelerometer and a three-axis MEMS gyroscope; there are nine chips on the front, eight of which are evenly arranged in a circle, and the angle between adjacent chips is 45°; the eight chips on the back and the eight chips arranged in a circle on the front are in corresponding positions.

[0086] Furthermore, the product is placed on a turntable to simulate different motion states to verify the calibration accuracy of the present invention. The turntable operates as follows:

[0087] 1) Stationary - 10° / s reverse rotation around x-axis - Stationary - 10° / s forward rotation around x-axis - Stationary - 10°, 1Hz oscillation - Stationary;

[0088] 2) stationary - reverse rotation around the y-axis 10° / s - stationary - forward rotation around the y-axis 10° / s - stationary - 10°, 1Hz oscillation - stationary;

[0089] 3) Stationary - Reverse rotation around z-axis 10° / s - Stationary - Forward rotation around z-axis 10° / s - Stationary - 10°, 1Hz oscillation - Stationary.

[0090] The sampling rate is 100Hz. After the invention calibrates the waveform as follows Figure 2 As shown, the blue line is the measured value of the three-axis output fused from the output of each MEMS gyroscope, and the red line is the rotation speed calibrated using the method proposed by the invention.

[0091] The above shows and describes the basic principles and main features of the present invention and the advantages of the present invention. It is obvious to those skilled in the art that the present invention is not limited to the details of the above exemplary embodiments, and the present invention can be implemented in other specific forms without departing from the spirit or basic features of the present invention. Therefore, from any point of view, the embodiments should be regarded as exemplary and non-restrictive. The scope of the present invention is limited by the appended claims rather than the above and the description, and it is intended that all changes falling within the meaning and scope of the equivalent elements of the claims are included in the present invention. Any figure mark in the claims should not be regarded as limiting the claims involved.

Claims

1. A method for calibrating a micro-array MEMS gyroscope in an external field, characterized in that: The following steps are involved: S1, power on, initialize the microcomputer inertial sensor; S2, converting the output of the micro-array MEMS gyroscope into a three-axis output of the carrier coordinate system; S3, combining the maneuvering target tracking theory, establishes the Kalman filter for angular velocity tracking, and estimates the angular velocity of each axis at each moment; S4, using the estimated angular velocity of each axis at each moment, an adaptive Kalman filter for random drift error estimation is established, and random drift error and deterministic error compensation are performed on the xyz axis respectively; S5, using the estimated angular velocity after random drift error compensation at each moment as a reference, establishing a deterministic error estimation Kalman filter and performing compensation; S6, estimating and obtaining twelve error parameters at the moment, first obtaining the value of the angular rate estimation after compensating the random drift error estimation at the current sampling moment, and substituting the value into the filter of the deterministic error estimation as a reference to obtain the deterministic error angular rate; S7, using the random drift error and deterministic error estimation method to estimate the current sampling angular rate, and obtain the final calibration result.

2. The method for calibrating a micro-array MEMS gyroscope in an external field online according to claim 1, characterized in that: The step S2 converts the output of the micro-array MEMS gyroscope into a three-axis output of the carrier coordinate system, and the specific process is as follows: First, construct the carrier coordinate system (b system) as "xyz" and determine the sensitive axis of the i-th sensor in the array in the carrier coordinate system and O b Z b The angle between the axes is α i , in X b O b Y b Projection on the plane and O b X b The angle between the axis and the i , then the output of the sensitive axis of the n sensors is expressed in the b system as M=HX+υ Where, υ is the measurement noise; Using the least squares method to fuse the array MEMS sensor output into three-axis output Where ω is the sensitive axis output of the redundant MEMS gyroscope, is the three-axis angular velocity of system b relative to the geographic coordinate system (xyz).

3. The method for calibrating a micro-array MEMS gyroscope in an external field online according to claim 2, characterized in that: In step S3, the system state space equation is established in combination with the maneuvering target tracking theory as follows: X Ik =A I X Ik-1 +W Ik Z Ik =H I X IIk +V Ik in, H I = [1 0], system noise W Ik is zero and has a variance of The white noise sequence, V Ik The mean is zero and the variance is R Ik Gaussian measurement noise.

4. The method for calibrating a micro-array MEMS gyroscope in an external field online according to claim 3, characterized in that: The random error drift compensation method in step S4 is: 400 data points are selected from each axis data in a static state for preprocessing, and after removing the linear trend term, the nonlinear trend term is removed by using the GM (1, 1) model, and the data is normalized. The preprocessed data is a zero-mean stationary random sequence with normality. According to the AIC criterion, the optimal ARMA (2, 1) model is established; the equation is: Using ARMA model coefficients and θ j The constructed adaptive Kalman filter is as follows: X IIk =A II X IIk-1 +W IIk Z IIk =H II X IIk +V IIk Among them, the system state variable X IIk =[x k x k-1 ] T , x k is the random drift error estimate. System noise variable W IIk =a k , H II =[1 0], G0=1, The adaptive parameter update process in the adaptive Kalman filter is: q IIk =q IIk-1 +γQ IIk-1 D k e IIk Among them, P IIk，k-1 is the covariance matrix, e IIk is the estimation error, q Ik and Q Ik are the mean and variance of the time-varying system noise, R IIk-1 is the measurement noise variance, γ=(1-b) / (1-b k+1 ), b is the forgetting factor.

5. The method for calibrating a micro-array MEMS gyroscope in an external field online according to claim 4, characterized in that: The step S5 considers the zero bias, scale factor and installation error of the MEMS gyroscope and constructs the error model as follows: oh m =S g oh t +b g Among them, ω m =[ω mx ω my ω mz ] T is the orthogonal three-axis output of the uncalibrated array MEMS gyroscope in frame b, ω t =[ω x ω y ω z ] T is the actual angular velocity of the carrier, b g is the bias of the MEMS gyroscope, S g is the coefficient matrix. g and g It can be expressed as The state equation and observation equation of the Kalman filter for deterministic error compensation are:

6. The method for calibrating a micro-array MEMS gyroscope in an out-of-field online manner according to claim 5, characterized in that: This method uses 17 MEMS chips to build an array MEMS inertial navigation system.

7. The method for calibrating a micro-array MEMS gyroscope in an external field online according to claim 6, characterized in that: Each of the 17 MEMS chips is an inertial measurement unit (IMU) including a three-axis accelerometer and a three-axis MEMS gyroscope; there are nine chips on the front, eight of which are evenly arranged in a circle, and the angle between adjacent chips is 45°; the eight chips on the back and the eight chips arranged in a circle on the front are in corresponding positions.

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