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CN114061576A - A calibration and compensation method for multi-position MEMS accelerometer - Google Patents

A calibration and compensation method for multi-position MEMS accelerometer Download PDF

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CN114061576A
CN114061576A CN202111492787.4A CN202111492787A CN114061576A CN 114061576 A CN114061576 A CN 114061576A CN 202111492787 A CN202111492787 A CN 202111492787A CN 114061576 A CN114061576 A CN 114061576A
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mems accelerometer
accelerometer
error
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calibration
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李传军
李兴城
赵良玉
张扬
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Beijing Institute of Technology BIT
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C21/00—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00
    • G01C21/10—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration
    • G01C21/12—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning
    • G01C21/16—Navigation; Navigational instruments not provided for in groups G01C1/00 - G01C19/00 by using measurements of speed or acceleration executed aboard the object being navigated; Dead reckoning by integrating acceleration or speed, i.e. inertial navigation
    • G01C21/183—Compensation of inertial measurements, e.g. for temperature effects
    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices

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Abstract

The invention provides a calibration compensation method for an MEMS accelerometer by a multi-position method, which can greatly reduce the measurement error of the MEMS accelerometer. Firstly, establishing a static error model expression of the MEMS accelerometer; fixing the MIMU on one surface of the cube, and placing the cube on a horizontal table according to the orientation condition of the MEMS accelerometer; obtaining an average value after each position is sufficiently sampled, obtaining accelerometer output at each position, and calculating each parameter of the MEMS accelerometer static error model so as to obtain an MEMS accelerometer static error equation; approximately resolving the values of the installation error angles alpha and beta of the MEMS accelerometer according to the position of the turntable and the small angle; finally, experimental examination is carried out on the turntable, and the error of the calibrated MEMS accelerometer is obviously reduced.

Description

Multi-position MEMS accelerometer calibration compensation method
Technical Field
The invention relates to the technical field of micro-mechanical inertial measurement, in particular to a calibration compensation method for a multi-position MEMS accelerometer.
Background
With the development of micro-electromechanical system (MEMS) technology, Micro Inertial Measurement Units (MIMUs) are increasingly applied to various fields such as measurement and navigation by virtue of their advantages of 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 gyroscope, a fiber-optic gyroscope and the like, the gyroscope 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 calibrate the MIMU inertia device quickly and accurately is always a key technology for MIMU integration and application.
Error compensation of MEMS inertial devices is an important means to improve their accuracy. Many leading research institutes of MEMS technology focus on the study of MEMS gyroscope and accelerometer error modeling and error compensation methods. For example, the MEMS Laboratory of the university of California in the United states has conducted an in-depth analysis of the errors caused by the manufacturing process, and some compensation methods have been proposed. When compensating errors of the MEMS inertial device and the IMU, establishing error models of zero offset, zero offset instability, scale factor errors, misalignment angles, random noise and the like to identify model parameters, and then compensating.
Measuring the accelerometer in multiple positions in the gravity domain is a common calibration method for calibrating MEMS accelerometers. However, these conventional calibration methods also have high requirements for the calibration environment, such as requiring a high-precision turntable, in order to ensure the level of the platform. However, the actual environment of application is often far from the ideal environment of the laboratory.
Disclosure of Invention
In view of this, the invention provides a calibration compensation method for a multi-position MEMS accelerometer, which can greatly reduce the measurement error of the MEMS accelerometer.
The technical scheme for realizing the invention is as follows:
a multi-position method MEMS accelerometer calibration compensation method comprises the following steps:
step one, establishing a static error model of the MEMS accelerometer according to a mathematical model of a zero error, a scale factor error and an installation error of the MIMU;
fixing the MIMU on one surface of the cube, and placing the cube on a horizontal table according to the orientation condition of the MEMS accelerometer; obtaining output values corresponding to all axes of the MEMS accelerometer according to the position of the MEMS accelerometer on the cube and corresponding input values of the x axis, the y axis and the z axis of the accelerometer, and calculating all parameters of a static error model of the MEMS accelerometer;
thirdly, approximately resolving the value of the installation error angle of the MEMS accelerometer according to the position of the turntable and the small angle;
and step four, calibrating the MEMS accelerometer based on the physical experiment to obtain a calibration result, and completing calibration.
In the first step, a static error model of the MEMS accelerometer is as follows:
Figure BDA0003399935680000021
in the formula, Ao＝[Ax Ay Az]TOutputting a value for the accelerometer; b isa＝[Bax Bay Baz]TIs the null shift of the accelerometer; sax，Say，SazIs the scale factor coefficient; kax1，Kax2，Kay1，Kay2，Kaz1，Kaz2Is a mounting error coefficient; a isi＝[ax ay az]TInputting a value for the accelerometer; axyz is a turntable coordinate system; ox1y1z1Is a MIMU coordinate system.
In the second step, the x-axis output of the MEMS accelerometer is:
Ax1＝Bax+Sax,Ax2＝Bax-Sax,Ax3＝Bax+Kax1
Ax4＝Bax-Kax1,Ax5＝Bax+Kax2,Ax6＝Bax-Kax2
the MEMS accelerometer y-axis output is:
Ay1＝Bay+Kay1,Ay2＝Bay-Kay1,Ay3＝Bay+Say
Ay4＝Bay-Say,Ay5＝Bay+Kay2,Ay6＝Bay-Kay2
the MEMS accelerometer z-axis output is:
Az1＝Baz+Kaz1,Az2＝Baz-Kaz1,Az3＝Baz+Kaz2
Az4＝Baz-Kaz2,Az5＝Baz+Saz,Az6＝Baz-Saz。
wherein, each parameter of the static error model of the MEMS accelerometer is calculated as follows:
Figure BDA0003399935680000031
Sax＝(Ax1-Ax2)/2,Kax1＝(Ax3-Ax4)/2,Kax2＝(Ax5-Ax6)/2
Kay1＝(Ay1-Ay2)/2,Say＝(Ay3-Ay4)/2,Kay2＝(Ay5-Ay6)/2
Kaz1＝(Az1-Az2)/2,Kaz2＝(Az3-Az4)/2,Say＝(Az5-Az6)/2。
in the third step, the turntable coordinate system and the MIMU coordinate system are obtained by rotating the coordinate systems, and the rotation equation is as follows:
Figure BDA0003399935680000032
wherein, alpha, beta and gamma are installation error angles, ai＝[1 -α β]TSubstituting into the static error model of the MEMS accelerometer to solve the installation error angle alpha between the MIMU and the low-precision rotary tableAnd the value of β.
Wherein, still include the following step: and step five, the calibration result of the accelerometer is checked by using the rotary table, the rotary table is respectively inclined to different angles, the output values of the MEMS accelerometer before and after calibration are respectively measured, and the inclined angle at the moment is calculated according to the output values, so that the error of the accelerometer before and after calibration is measured.
Has the advantages that:
the invention firstly establishes a static error model expression of the MEMS accelerometer. The MIMU is fixed to one face of the cube and the cube is placed on a horizontal table according to the orientation condition of the MEMS accelerometer. And (3) obtaining an average value after each position is sufficiently sampled to obtain accelerometer output at each position, so that each parameter of the MEMS accelerometer static error model can be calculated, and the MEMS accelerometer static error equation can be obtained. And calculating the values of the installation error angles alpha and beta of the MEMS accelerometer approximately according to the position of the turntable and the small angle. Finally, experimental examination is carried out on the turntable, and the error of the calibrated MEMS accelerometer is obviously reduced.
The present invention measures the error angle using the calibrated MIMU of the accelerometer. When the turntable is vertically arranged upwards, the input value of the accelerometer on the turntable is 100]TAnd g, obtaining an actual input value of the accelerometer, substituting the actual input value into an accelerometer error model expression, and solving the value of the installation error angle between the MIMU and the low-precision rotary table. The invention realizes six-position calibration by combining the horizontal table and the cube and can still ensure the calibration precision of the inertial device.
Drawings
FIG. 1 is a flow chart of the overall implementation of the present invention.
Fig. 2 is a schematic diagram of an angle between the MIMU and the rotating device according to the present invention.
FIG. 3 is a diagram of an experimental MIMU of the present invention.
FIG. 4 is a graph of acceleration output for each position of the present invention.
Detailed Description
The invention is described in detail below by way of example with reference to the accompanying drawings.
The flow chart of the calibration compensation method of the multi-position MEMS accelerometer is shown in FIG. 1, and comprises the following steps:
step one, establishing a static error model of the MEMS accelerometer according to a mathematical model of the zero point error, the scale factor error and the installation error of the MIMU:
Figure BDA0003399935680000041
in the formula, Ao＝[Ax Ay Az]TOutputting a value for the accelerometer; b isa＝[Bax Bay Baz]TIs the null shift of the accelerometer; sax，Say，SazIs the scale factor coefficient; kax1，Kax2，Kay1，Kay2，Kaz1，Kaz2Is a mounting error coefficient; a isi＝[ax ay az]TAn accelerometer input value is entered.
Step two, fix MIMU to one face of the cube and place the cube on a horizontal table so that the accelerometer is oriented as shown in table 1. Table 1 shows the accelerometer positions and the corresponding input values. And after enough samples are sampled at each position, the average value is obtained to obtain the accelerometer output at each position. According to the positions in the table 1 and the corresponding input values of the accelerometer, the x-axis output of the MEMS accelerometer is obtained as follows:
Ax1＝Bax+Sax,Ax2＝Bax-Sax,Ax3＝Bax+Kax1
Ax4＝Bax-Kax1,Ax5＝Bax+Kax2,Ax6＝Bax-Kax2 (1)
the MEMS accelerometer y-axis output is:
Ay1＝Bay+Kay1,Ay2＝Bay-Kay1,Ay3＝Bay+Say
Ay4＝Bay-Say,Ay5＝Bay+Kay2,Ay6＝Bay-Kay2 (2)
the MEMS accelerometer z-axis output is:
Az1＝Baz+Kaz1,Az2＝Baz-Kaz1,Az3＝Baz+Kaz2
Az4＝Baz-Kaz2,Az5＝Baz+Saz,Az6＝Baz-Saz (3)
and obtaining output values of all axes of the MEMS accelerometer according to the position of the MEMS accelerometer on the cube and the corresponding input values of all axes of the accelerometer, so that all parameters of the static error model of the MEMS accelerometer can be calculated.
And (4) respectively adding or subtracting the expressions (1) to (3) to calculate each parameter of the static error model of the MEMS accelerometer, as shown in the following formula.
Figure BDA0003399935680000051
Sax＝(Ax1-Ax2)/2,Kax1＝(Ax3-Ax4)/2,Kax2＝(Ax5-Ax6)/2
Kay1＝(Ay1-Ay2)/2,Say＝(Ay3-Ay4)/2,Kay2＝(Ay5-Ay6)/2
Kaz1＝(Az1-Az2)/2,Kaz2＝(Az3-Az4)/2,Say＝(Az5-Az6)/2
And thirdly, approximately calculating the values of the installation error angles alpha and beta of the MEMS accelerometer according to the position of the turntable and the small angle.
The schematic diagram of the included angle between the MIMU and the rotating device is shown in FIG. 2, wherein Axyz is a turntable coordinate system;Ox1y1z1is an MIMU coordinate system; α, β, γ are mounting error angles. The turntable coordinate system and the MIMU coordinate system can be obtained by rotating the coordinate system, and the rotation equation is as follows:
Figure BDA0003399935680000061
since α, β and γ are all small angles, sin α, sin β and sin γ are approximately α, β and γ; cos α, cos β and cos γ are approximately 1; the product of the two sinusoids is approximately 0, then the above equation can be simplified to equation (4).
Figure BDA0003399935680000062
The installation error angle can generate larger and larger influence on error calibration along with the increase of the rotating speed of the rotary table, so that the error angle is measured by using the calibrated MIMU of the accelerometer in an experiment. When the turntable is vertically arranged upwards, the input value of the accelerometer on the turntable is 100]Tg, substituting formula (4) to obtain the actual input value of the accelerometer
ai＝[1 -α β]T
The above formula is substituted into an accelerometer error model expression, and the values of the installation error angles alpha and beta between the MIMU and the low-precision rotating platform can be solved.
And step four, calibrating the MEMS accelerometer based on the physical experiment.
The MIMU calibrated for the experiment consists of one MEMS triaxial accelerometer and two uniaxial MEMS gyroscopes, the structure of which is shown in fig. 3.
The MIMU was placed on one face of the cube and the cube was placed in six positions, each position collecting 2 minutes of data at a data acquisition rate of 200 Hz. The selection of which successive more stable 10s accelerometer outputs are shown in figure 4.
The outputs of the three-axis MEMS accelerometers at these six positions were averaged separately and the results are reported in table 2. Table 2 shows the acceleration output values at the respective positions. Taking the values in the table 2 as the parameter values of the acceleration static error model, and substituting the parameter values into the MEMS accelerometer error model expression, the MEMS accelerometer static error equation can be obtained as follows:
Figure BDA0003399935680000071
at this moment, fix MIMU on the lower rotary device of laboratory precision to place rotary device vertically upwards, MEMS accelerometer static error equation at this moment is:
Figure BDA0003399935680000072
and calculating to obtain an error angle between the MIMU and the rotating device:
α＝0.0056rad,β＝-0.0121rad
and step five, the calibration result of the accelerometer is checked by using the rotary table, the rotary table is respectively inclined to different angles, the output values of the MEMS accelerometer before and after calibration are respectively measured, and the inclined angle at the moment is calculated according to the output values, so that the error of the accelerometer before and after calibration is measured. The results obtained are shown in Table 3. Table 3 shows the error comparison before and after accelerometer calibration.
It can be seen from table 3 that the error of the MEMS accelerometer becomes significantly smaller. Before calibration, the calculated inclination error can reach 2.6305 degrees at most; after calibration, the calculated inclination error is only 0.3656 degrees at most, and the accelerometer error is only 0.0045m/s at the moment2。
TABLE 1 accelerometer position and corresponding input values
Figure BDA0003399935680000073
TABLE 2 acceleration output values at various positions
Figure BDA0003399935680000081
TABLE 3 accelerometer calibration before and after error comparison
Figure BDA0003399935680000082
In summary, the above description is only a preferred embodiment of the present invention, and is not intended to limit the scope of the present invention. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.

Claims (6)

1. A multi-position method MEMS accelerometer calibration compensation method is characterized by comprising the following steps:
step one, establishing a static error model of the MEMS accelerometer according to a mathematical model of a zero error, a scale factor error and an installation error of the MIMU;
fixing the MIMU on one surface of the cube, and placing the cube on a horizontal table according to the orientation condition of the MEMS accelerometer; obtaining output values corresponding to all axes of the MEMS accelerometer according to the position of the MEMS accelerometer on the cube and corresponding input values of the x axis, the y axis and the z axis of the accelerometer, and calculating all parameters of a static error model of the MEMS accelerometer;
thirdly, approximately resolving the value of the installation error angle of the MEMS accelerometer according to the position of the turntable and the small angle;
and step four, calibrating the MEMS accelerometer based on the physical experiment to obtain a calibration result, and completing calibration.
2. The method for calibration compensation of a multi-position MEMS accelerometer as claimed in claim 1, wherein in said first step, the static error model of the MEMS accelerometer is as follows:
Figure FDA0003399935670000011
in the formula, Ao＝[Ax Ay Az]TOutputting a value for the accelerometer; b isa＝[Bax Bay Baz]TIs the null shift of the accelerometer; sax，Say，SazIs the scale factor coefficient; kax1，Kax2，Kay1，Kay2，Kaz1，Kaz2Is a mounting error coefficient; a isi＝[ax ay az]TInputting a value for the accelerometer; axyz is a turntable coordinate system; ox1y1z1Is a MIMU coordinate system.
3. The multi-position method calibration compensation method for the MEMS accelerometer of claim 2, wherein in the second step, the X-axis output of the MEMS accelerometer is:
Ax1＝Bax+Sax,Ax2＝Bax-Sax,Ax3＝Bax+Kax1
Ax4＝Bax-Kax1,Ax5＝Bax+Kax2,Ax6＝Bax-Kax2
the MEMS accelerometer y-axis output is:
Ay1＝Bay+Kay1,Ay2＝Bay-Kay1,Ay3＝Bay+Say
Ay4＝Bay-Say,Ay5＝Bay+Kay2,Ay6＝Bay-Kay2
the MEMS accelerometer z-axis output is:
Az1＝Baz+Kaz1,Az2＝Baz-Kaz1,Az3＝Baz+Kaz2
Az4＝Baz-Kaz2,Az5＝Baz+Saz,Az6＝Baz-Saz。
4. the method for calibration compensation of a multi-position MEMS accelerometer according to claim 3, wherein the parameters of the static error model of the MEMS accelerometer are calculated as follows:
Figure FDA0003399935670000021
Sax＝(Ax1-Ax2)/2,Kax1＝(Ax3-Ax4)/2,Kax2＝(Ax5-Ax6)/2
Kay1＝(Ay1-Ay2)/2,Say＝(Ay3-Ay4)/2,Kay2＝(Ay5-Ay6)/2
Kaz1＝(Az1-Az2)/2,Kaz2＝(Az3-Az4)/2,Say＝(Az5-Az6)/2。
5. the multi-position method MEMS accelerometer calibration compensation method of claim 1, wherein in step three, the turntable coordinate system and the MIMU coordinate system are obtained by rotation of the coordinate systems, and the rotation equation is as follows:
Figure FDA0003399935670000022
wherein, alpha, beta and gamma are installation error angles, ai＝[1 -α β]TSubstituting into the static error model of the MEMS accelerometer to solve the values of the installation error angles alpha and beta between the MIMU and the low-precision rotary table.
6. The multi-position method MEMS accelerometer calibration compensation method of any one of claims 1-5, further comprising the steps of: and step five, the calibration result of the accelerometer is checked by using the rotary table, the rotary table is respectively inclined to different angles, the output values of the MEMS accelerometer before and after calibration are respectively measured, and the inclined angle at the moment is calculated according to the output values, so that the error of the accelerometer before and after calibration is measured.
CN202111492787.4A 2021-12-08 2021-12-08 A calibration and compensation method for multi-position MEMS accelerometer Pending CN114061576A (en)

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Publication number Priority date Publication date Assignee Title
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CN108592952A (en) * 2018-06-01 2018-09-28 北京航空航天大学 The method for demarcating more MIMU errors simultaneously with positive and negative times of rate based on lever arm compensation
CN109631941A (en) * 2018-12-09 2019-04-16 西安航天精密机电研究所 A kind of Inertial Platform System accelerometer installation error method for precisely marking
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