CN114088118B - Calibration compensation method for MEMS gyroscope by forward and reverse rotation method - Google Patents
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Abstract
The invention provides a calibration compensation method for a MEMS gyroscope by a forward and backward rotation method, which can ensure that the precision of the calibrated MEMS gyroscope is very high. Firstly, establishing a static error model expression of the MEMS gyroscope; placing the turntable at a vertical upward position, fixing the MIMU on the turntable, and measuring error angles alpha and beta of the turntable and the MIMU; when the rotating speed input value of the turntable is omega and the rotating speed input value of the turntable is omega, respectively carrying out forward rotation and reverse rotation, the output expressions of the y-axis gyroscope and the z-axis gyroscope can be obtained; the positive rotation and the negative rotation are respectively used for measuring 3 groups of data, and the positive and negative rotation measurement results are added to obtain zero offset of the MEMS gyroscope; subtracting the positive and negative rotation measurement results, calculating all parameters in a static error model of the MEMS gyroscope, obtaining an error equation of the MEMS gyroscope, and completing the calibration of the gyroscope; finally, experimental inspection is carried out on the turntable, so that the precision of the calibrated MEMS gyroscope can be seen to be very high.
Description
Technical Field
The invention relates to the technical field of micro-mechanical inertial measurement, in particular to a calibration and compensation method of a MEMS gyroscope by a forward and reverse rotation method.
Background
With the development of micro-electromechanical system (MEMS) technology, micro Inertial Measurement Units (MIMU) are increasingly applied to various fields such as measurement, navigation, etc. by virtue of their small size, low power consumption and strong overload resistance. Compared with a measuring unit formed by a high-precision inertial sensor such as a laser gyro, an optical fiber gyro and the like, the gyro in the MIMU has larger drift and cannot sense the rotation angular velocity of the earth. And the calibration of the inertial device error determines the accuracy of the system. Therefore, how to quickly and accurately calibrate MIMU inertial devices has been a key technology for MIMU integration and application.
Error compensation of MEMS inertial devices is an important means to improve their accuracy. Many of the leading research institutions in MEMS technology focus on the research of MEMS gyroscopes and accelerometer error modeling and error compensation methods. Such as the California university MEMS Laboratory in the united states, has conducted extensive analysis of manufacturing process errors and has proposed some compensation methods. When the MEMS inertial device and IMU errors are compensated, an error model of zero offset, zero offset instability, scale factor errors, misalignment angles, random noise and the like is established to carry out model parameter identification, and then compensation is carried out. However, the input values are not considered at the same time to respectively perform the calibration during the forward rotation and the reverse rotation, so that the precision of the MEMS gyroscope calibrated by the existing calibration compensation method is not high.
Disclosure of Invention
In view of the above, the invention provides a calibration and compensation method for a positive and negative rotation MEMS gyroscope, which can enable the precision of the calibrated MEMS gyroscope to be very high.
The technical scheme for realizing the invention is as follows:
a calibration and compensation method of a MEMS gyroscope by a forward and backward rotation method comprises the following steps:
step one, establishing a static error calibration model of the MEMS gyroscope according to a mathematical model of the zero point error, the scale factor error and the installation error of the MIMU;
step two, placing the turntable at a vertical upward position, fixing the MIMU on the turntable, and measuring the error angle between the turntable and the MIMU;
thirdly, when the rotating speed input value of the turntable is omega, respectively carrying out forward rotation and reverse rotation, obtaining output expressions of the y-axis gyroscope and the z-axis gyroscope; the positive rotation and the negative rotation respectively measure 3 groups of data, and the measurement results of the positive rotation and the negative rotation are added to obtain zero offset of the MEMS gyroscope; and subtracting the forward and reverse rotation measurement results to obtain all parameters in the static error model of the MEMS gyroscope, and obtaining an error equation of the MEMS gyroscope to finish the calibration of the gyroscope.
In the first step, the static error model of the MEMS gyroscope is as follows:
in which W is o ＝[W x W y W z ] T Output value for gyroscope; b (B) g ＝[B gx B gy B gz ] T Zero drift for the gyroscope; s is S gx ，S gy ，S gz Is marked with a scaleFactor coefficient; k (K) gx1 ，K gx2 ，K gy1 ，K gy2 ，K gz1 ，K gz2 Is the installation error coefficient; omega= [ omega ] x ω y ω z ] T Values are entered for the gyroscope.
When the rotational speed input value of the turntable is omega, respectively performing forward rotation and reverse rotation, obtaining output expressions of the y-axis gyroscope and the z-axis gyroscope, wherein the output expressions are as follows:
W y+ ＝B gy +K gy1 ω-S gy ωα+K gy2 ωβ
W y- ＝B gy -K gy1 ω+S gy ωα-K gy2 ωβ
W z+ ＝B gz +K gz1 ω-K gz2 ωα+S gz ωβ
W z- ＝B gz -K gz1 ω+K gz2 ωα-S gz ωβ。
wherein, zero offset of MEMS gyroscope is:
wherein K is gy2 And K gz2 Approximately 0,S gy And S is gz Approximately 1, K gy1 And K gz1 The values of (2) are:
values of the remaining parameters:
wherein, still include the following step:
calibrating the MEMS gyroscope based on the physical experiment;
and fifthly, checking the calibration result of the MEMS gyroscope by using a turntable.
The beneficial effects are that:
firstly, establishing a static error model expression of an MEMS gyroscope; placing the turntable at a vertical upward position, fixing the MIMU on the turntable, and measuring error angles alpha and beta of the turntable and the MIMU; when the rotating speed input value of the turntable is omega and the rotating speed input value of the turntable is omega, respectively carrying out forward rotation and reverse rotation, the output expressions of the y-axis gyroscope and the z-axis gyroscope can be obtained; the forward rotation and the reverse rotation are respectively used for measuring 3 groups of data, the forward rotation and the reverse rotation are added, the zero offset of the MEMS gyroscope can be obtained, the forward rotation and the reverse rotation are subtracted, all parameters in a static error model of the MEMS gyroscope can be calculated, an error equation of the MEMS gyroscope is obtained, and the calibration of the gyroscope is completed; finally, experimental inspection is carried out on the turntable, so that the precision of the calibrated MEMS gyroscope can be seen to be very high.
Drawings
FIG. 1 is a general flow chart of the present invention.
FIG. 2 is a schematic diagram of an experimental MIMU according to the present invention.
Fig. 3 shows the output values of the MEMS gyroscope of the present invention.
Detailed Description
The invention will now be described in detail by way of example with reference to the accompanying drawings.
The positive and negative rotation method of the invention is a method that the turntable rotates positively and reversely at a fixed rotation speed respectively, and then redundant parameters are eliminated according to the established error model, so that the error model is calculated, and the calibrated MEMS gyroscope has high precision. Referring to fig. 1, which is a general execution flow chart of the invention, the invention designs a calibration and compensation method of a positive and negative rotation method MEMS gyroscope, comprising the following steps:
step one, establishing a static error model of the MEMS gyroscope according to a mathematical model of the zero point error, the scale factor error and the installation error of the MIMU:
in which W is o ＝[W x W y W z ] T Output value for gyroscope; b (B) g ＝[B gx B gy B gz ] T Zero drift for the gyroscope; s is S gx ，S gy ，S gz Is a scale factor coefficient; k (K) gx1 ，K gx2 ，K gy1 ，K gy2 ，K gz1 ，K gz2 Is the installation error coefficient; omega= [ omega ] x ω y ω z ] T Values are entered for the gyroscope.
And secondly, placing the turntable at a vertical upward position, fixing the MIMU on the turntable, and measuring error angles alpha and beta of the turntable and the MIMU. Then when the turntable rotation speed input value is omega= [ omega 00] T The actual input of the gyroscope is shown in the following equation.
ω i ＝[ω -ωα ωβ] T
Step three, when the rotational speed input value of the turntable is omega, respectively carrying out forward rotation and reverse rotation, obtaining the output of the y-axis gyroscope and the z-axis gyroscope, wherein the output of the y-axis gyroscope and the z-axis gyroscope are as follows:
W y+ ＝B gy +K gy1 ω-S gy ωα+K gy2 β
W y- ＝B gy -K gy1 ω+S gy ωα-K gy2 ωβ
W z+ ＝B gz +K gz1 ω-K gz2 ωα+S gz ωβ
W z- ＝B gz -K gz1 ω+K gz2 ωα-S gz ωβ
if the data of each measurement 3 groups are forward rotated and reverse rotated, the measurement results of the forward rotation and the reverse rotation are added, and zero offset of the MEMS gyroscope can be obtained:
because of both installation errors and scale factor errorsVery small, so the following assumptions are made first in the intermediate calculation process: k in the formula gy2 And K gz2 Approximately 0,S gy And S is gz Approximately 1, then K can be obtained by subtracting the positive and negative rotation measurement results gy1 And K gz1 The values of (2) are:
and continuously subtracting the forward and reverse rotation measurement results to obtain the value of the residual parameter:
thus, all parameters in the static error model of the MEMS gyroscope are calculated, and the calibration of the gyroscope is completed.
And step four, calibrating the MEMS gyroscope based on the physical experiment.
The experimental calibration MIMU consists of a MEMS triaxial accelerometer and two uniaxial MEMS gyroscopes, and the structure of the MIMU is shown in figure 2.
The turntable and MIMU are maintained in a state in which the mounting error between the two is measured, i.e., the turntable is vertically upward at this time. The control turntable rotates for more than 1 minute at +/-360 degrees/s, +/-1080 degrees/s and +/-2160 degrees/s respectively, and the output value of the MEMS gyroscope is collected at the sampling frequency of 200Hz, and the result is shown in figure 3.
As can be seen from fig. 3, the y, z-axis gyroscope exhibits significant sinusoidal fluctuations due to the coupling of the x-axis roll information. Along with the increase of the rotating speed of the turntable, the absolute values of data output by the y-axis gyroscope and the z-axis gyroscope are larger and larger, which is caused by the installation error between the MIMU and the turntable, and the influence of the larger rotating speed is more obvious, so that the error compensation has an important effect.
And selecting a section of more stable data from the measured results to obtain a mean value, wherein the obtained result is shown in table 1. Table 1 shows the gyroscope output for forward and reverse rotation at a fixed rotational speed.
Then, substituting the data in table 1 into the MEMS gyroscope static error model, each parameter in the MEMS gyroscope static error model can be calculated, and the error equation is obtained as follows:
fifthly, checking a calibration result of the accelerometer by using the turntable, and collecting output values of the gyroscope when the rotating speeds of the turntable are respectively +720 degrees/s, +/-1440 degrees/s and +/-1800 degrees/s in order to ensure that the installation error angle of the MIMU and the turntable is kept unchanged and the turntable is kept in a vertical and upward state. Then, the calibration result is written into the control unit of the MIMU, and the output value of the gyroscope is measured under the same condition, and the result obtained by comparing the two is shown in the table 2. Table 2 shows MEMS gyroscope output values before and after calibration.
It can be seen from table 2 that the calibrated MEMS gyroscope output values are very accurate. The maximum values of the y-axis and z-axis outputs before calibration were-6.8678 DEG/s and-13.0737 DEG/s, respectively. But after calibration the output became-0.089 deg./s and-0.0421 deg./s. Thus, the experiment has higher accuracy for the calibration of the MIMU and in actual measurement the effect of its deterministic error can be disregarded for the compensated MEMS gyroscope.
TABLE 1 output of gyroscopes rotating in opposite directions at fixed rotational speeds
Table 2 calibration of MEMS gyroscope output values
In summary, the above embodiments are only preferred embodiments of the present invention, and are not intended to limit the scope of the present invention. Any modification, equivalent replacement, improvement, etc. made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
Claims (1)
1. The MEMS gyroscope calibration compensation method by the forward and backward rotation method is characterized by comprising the following steps of:
step one, establishing a static error calibration model of the MEMS gyroscope according to a mathematical model of the zero point error, the scale factor error and the installation error of the MIMU; the static error model of the MEMS gyroscope is as follows:
in which W is o ＝[W x W y W z ] T Output value for gyroscope; b (B) g ＝[B gx B gy B gz ] T Zero drift for the gyroscope; s is S gx ，S gy ，S gz Is a scale factor coefficient; k (K) gx1 ，K gx2 ，K gy1 ，K gy2 ，K gz1 ，K gz2 Is the installation error coefficient; omega= [ omega ] x ω y ω z ] T Inputting a value for a gyroscope;
step two, placing the turntable at a vertical upward position, fixing the MIMU on the turntable, and measuring the error angle between the turntable and the MIMU;
thirdly, when the rotating speed input value of the turntable is omega, respectively carrying out forward rotation and reverse rotation, obtaining output expressions of the y-axis gyroscope and the z-axis gyroscope; the positive rotation and the negative rotation respectively measure 3 groups of data, and the measurement results of the positive rotation and the negative rotation are added to obtain zero offset of the MEMS gyroscope; subtracting the positive and negative rotation measurement results to obtain all parameters in a static error model of the MEMS gyroscope, and obtaining an error equation of the MEMS gyroscope to finish the calibration of the gyroscope;
when the rotating speed input value of the turntable is omega, respectively carrying out forward rotation and reverse rotation, obtaining output expressions of the y-axis gyroscope and the z-axis gyroscope, wherein the output expressions are as follows:
the zero bias of the MEMS gyroscope is:
K gy2 and K gz2 Approximately 0,S gy And S is gz Approximately 1, K gy1 And K gz1 The values of (2) are:
values of the remaining parameters:
calibrating the MEMS gyroscope based on the physical experiment; the calibrated MIMU consists of an MEMS triaxial accelerometer and two uniaxial MEMS gyroscopes;
maintaining the turntable and the MIMU in a state of measuring an installation error between the turntable and the MIMU, namely, vertically upwards the turntable at the moment; the rotary table is controlled to rotate for more than 1 minute at the rotating speeds of +/-360 degrees/s, +/-1080 degrees/s and +/-2160 degrees/s respectively, and the output value of the MEMS gyroscope is collected at the sampling frequency of 200 Hz;
checking a MEMS gyroscope calibration result by using a turntable, and in order to ensure that the installation error angle of the MIMU and the turntable is kept unchanged, keeping the turntable in a vertical upward state, and collecting output values of the gyroscope when the rotating speeds of the turntable are +/-720 degrees/s, +/-1440 degrees/s and +/-1800 degrees/s respectively; and then writing the calibration result into a control unit of the MIMU, and measuring the output value of the gyroscope under the same condition.
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| CN108534800A (en) * | 2018-03-09 | 2018-09-14 | 中国科学院长春光学精密机械与物理研究所 | A kind of MEMS-IMU warm population parameter calibration compensation method entirely |
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|---|---|---|---|---|
| WO2013131471A1 (en) * | 2012-03-06 | 2013-09-12 | 武汉大学 | Quick calibration method for inertial measurement unit |
| CN103196462A (en) * | 2013-02-28 | 2013-07-10 | 南京航空航天大学 | Compensation method for error calibration of MEMS gyroscope in MIMU |
| CN104101363A (en) * | 2014-07-28 | 2014-10-15 | 中国电子科技集团公司第二十六研究所 | Gyroscope dynamic calibration method for measuring rotary carrier transversal posture |
| CN108132060A (en) * | 2017-11-17 | 2018-06-08 | 北京计算机技术及应用研究所 | A kind of systematic calibration method of Strapdown Inertial Navigation System without benchmark |
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