CN111189472A - MEMS gyroscope combination calibration method - Google Patents

MEMS gyroscope combination calibration method Download PDF

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CN111189472A
CN111189472A CN201811362982.3A CN201811362982A CN111189472A CN 111189472 A CN111189472 A CN 111189472A CN 201811362982 A CN201811362982 A CN 201811362982A CN 111189472 A CN111189472 A CN 111189472A
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error
mems
calibration method
mems gyroscope
gyro
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杨星辉
申燕超
梁文华
王汝弢
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Beijing Automation Control Equipment Institute BACEI
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Beijing Automation Control Equipment Institute BACEI
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    • 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 belongs to a gyro calibration compensation technology, and particularly relates to an MEMS gyro combination calibration method, which comprises the steps of calibrating a scale coefficient error and a non-orthogonal error, adopting clockwise and anticlockwise rotation to counteract earth rotation and gyro zero offset, estimating the gyro zero offset, determining MEMS gyro outputs at two different static positions, establishing a model, and calculating a gyro constant zero position by adopting least square fitting. The method can realize the calibration of the error parameters, and can finish the calibration of the main error parameters of the MEMS gyroscope combination, including the calibration of the gyroscope constant value zero offset, the calibration coefficient error and the non-orthogonal error, only by using one right-angle vertical plane.

Description

MEMS gyroscope combination calibration method
Technical Field
The invention belongs to a gyro calibration compensation technology, and particularly relates to an MEMS gyro combination calibration method.
Background
Compared with the traditional medium-high precision inertial sensor, the low-precision MEMS inertial device has the particularity mainly represented by poor zero-bias repeatability and stability of the MEMS. Secondly, since the cost of the MEMS inertial device system is usually much lower than the high precision calibration equipment used in the laboratory, it is not possible to prepare a series of expensive experimental calibration equipment for a low precision MEMS sensor for engineering applications.
Disclosure of Invention
The invention aims to provide a MESM gyroscope combination calibration method, which realizes the calibration of model parameters.
The technical scheme of the invention is as follows:
a calibration method for an MEMS gyroscope combination comprises the following steps:
1) calibrating scale coefficient errors and non-orthogonal errors, and adopting clockwise and anticlockwise rotation to counteract earth rotation and gyro zero offset;
1.1) marking the initial position of the MEMS triaxial gyroscope combination hexahedron;
1.2) slightly rotating the hexahedron 360 degrees clockwise around a rotating shaft vertical to a horizontal plane, and then rotating the hexahedron 360 degrees anticlockwise to ensure that the hexahedron rotates around the same shaft by a known angle, namely delta theta in the whole process;
1.3) determining the error equation of a surface
Figure BDA0001865804540000011
Figure BDA0001865804540000012
Figure BDA0001865804540000021
mijIs an element of the symmetric matrix M;
wherein Km＝diag(Kmx,Kmy,Kmz) The error of the scale factor is calculated,
Figure BDA0001865804540000022
a non-orthogonal error matrix, wherein rho, phi and lambda are angle errors in three directions;
1.4) installing the MEMS gyroscope group at different positions in a six-sided shell, repeating the steps 1.2 and 1.3, simultaneously solving an equation set, and solving Km＝diag(Kmx,Kmy,Kmz) The error of the scale factor is calculated,
Figure BDA0001865804540000023
six unknown parameters in the non-orthogonal error matrix;
2) estimating zero offset error
2.1) estimating the zero offset ω of the gyro using the following equationie
Figure BDA0001865804540000024
2.2) obtaining the outputs of the MEMS gyroscope at two different static positions is
Figure BDA0001865804540000025
And
Figure BDA0001865804540000026
the two expressions are respectively substituted into the expression in 2.1), and the two expressions are subtracted to obtain the following expression
Figure BDA0001865804540000027
And 2.3) substituting data of different static positions into a formula of 2.2), and calculating a constant zero position of the gyroscope by adopting least square fitting.
2. The calibration method of the MEMS gyroscope assembly of claim 1, wherein the measurement model of the MEMS triaxial gyroscope assembly is:
Figure BDA0001865804540000028
the above formula is inverse operation to obtain
Figure BDA0001865804540000029
Wherein the content of the first and second substances,
Figure BDA0001865804540000031
the measurement vector is output for the MEMS gyroscope combination,
Figure BDA0001865804540000032
external angular velocity input, vmIs the measurement noise.
In the step 1): given a smooth plane and a reference, the combined hexahedron with the MEMS three-axis gyroscope is placed on a horizontal plane close to the initial position of the reference mark.
The smooth horizontal floor tile plane of the laboratory and the side-placed square stool plane perpendicular to the horizontal plane are selected as the smooth plane and the reference respectively.
In the step 1: and 2.3) selecting 10-100 groups of data of different static positions and substituting the data into a formula 2.2).
In the step 1.2), the position of the rotated hexahedron on the square stool surface coincides with the initial mark position, that is, the rotation of 360 degrees around the rotation axis vertical to the horizontal plane is illustrated.
The rotating operation in the rotating process of repeating 1.2) and 1.3) in the step 1.4) is opposite to the direction sequence of the last time.
The invention has the following remarkable effects: compared with the prior laboratory traditional method that the gyro combination calibration can be completed by means of a position turntable and a rate turntable with certain precision, the invention provides a simple, practical and easy-to-operate outfield calibration method, reasonable design of experimental arrangement scheme steps and an effective solving algorithm are used for realizing calibration of error parameters, and the calibration of main error parameters of the MEMS gyro combination, including the calibration of gyro constant value zero offset, scale coefficient errors and non-orthogonal errors, can be completed by only one right-angle vertical plane.
Detailed Description
The present invention is described in further detail below.
The measurement model of a general MEMS three-axis gyroscope combination can be expressed as:
Figure BDA0001865804540000033
the formula (2) is obtained by performing an inverse operation on the formula (1). The calibration process is actually the identification and calculation of these parameters.
Figure BDA0001865804540000041
Wherein the content of the first and second substances,
Figure BDA0001865804540000042
the measurement vector is output for the MEMS gyroscope combination,
Figure BDA0001865804540000043
external angular velocity input, vmIs measuring noise, Km＝diag(Kmx,Kmy,Kmz) Error of scale coefficient, b0A matrix of constant-value errors is formed,
Figure BDA0001865804540000044
is a non-orthogonal error matrix.
Step 1, calibrating scale coefficient errors and non-orthogonal errors, and adopting clockwise and anticlockwise rotation to counteract earth rotation and gyro zero offset
1.1) setting a smooth plane and a reference straight line, such as selecting a smooth horizontal floor tile plane of a laboratory and a side-placed square stool plane vertical to the horizontal plane, placing a combined hexahedron provided with an MEMS three-axis gyroscope on the horizontal plane close to the square stool plane and on the square stool plane and marking the initial position of the combined hexahedron;
1.2) firstly clockwise slightly rotating the hexahedron by 360 degrees around the rotating shaft of the vertical horizontal plane, namely the position of the rotated hexahedron on the square stool surface is coincided with the initial marking position, namely, the rotating shaft of the vertical horizontal plane is rotated by one circle, then clockwise rotating the hexahedron by 360 degrees, and the angular speed is when clockwise rotating along the same shaft:
Figure BDA0001865804540000045
wherein the content of the first and second substances,
Figure BDA0001865804540000046
for gyroscope output data, superscript '+' indicates clockwise rotation;
Figure BDA0001865804540000047
representing the angular velocity of the manually rotated housing;
Figure BDA0001865804540000048
to representThe rotational angular velocity of the earth;
Figure BDA0001865804540000049
is a direction cosine matrix of the navigation system to the platform system. Integration is performed at both ends of equation (3), and a clockwise rotation hexahedron 360 ° can be obtained, and during integration when rotating clockwise along the same axis:
Figure BDA00018658045400000410
1.3) counterclockwise rotation of the hexahedron by 360 °, the integral obtained when rotating counterclockwise along the same axis is determined:
Figure BDA0001865804540000051
1.4) obtained by subtracting the formulae (4) and (5)
Figure BDA0001865804540000052
The notations (3) and (4) show that the angular velocity of the rotating housing need not be constant, but need to be guaranteed to rotate about the same axis through a known angle, Δ θ, throughout the process. The difference between the clockwise angle minus the counterclockwise angle after rotation should be 360 ° - (-360 °) to 720 ° -)
1.5) taking module values at two ends of the formula (6) to obtain:
Figure BDA0001865804540000053
the two ends are squared simultaneously and then finished to obtain:
Figure BDA0001865804540000054
after the matrix form of formula (8) is expanded, it can be written as:
Figure BDA0001865804540000055
wherein
Figure BDA0001865804540000056
mijIs an element of the symmetric matrix M:
Figure BDA0001865804540000057
if equation (9) is written in the form of a general equation:
Figure BDA0001865804540000058
1.6) and so on, selecting other five surfaces of the hexahedron, repeating the steps 1.2 and 1.3, solving the equation set simultaneously, and solving Km＝diag(Kmx,Kmy,Kmz) The error of the scale factor is calculated,
Figure BDA0001865804540000061
six unknown parameters in the non-orthogonal error matrix;
the rotation operation of the step 2) is firstly carried out clockwise rotation, then the step 3) is carried out anticlockwise rotation, the rotation operation of the lower part is just opposite to the operation of the upper part, and the rotation operation of the lower part is firstly carried out anticlockwise rotation;
step 2, estimating zero offset error
2.1) estimating zero offset ω of the gyroieFor a static MEMS gyroscope, according to equation (2): ,
Figure BDA0001865804540000062
the two sides are squared simultaneously to obtain
Figure BDA0001865804540000063
2.2) at two different static positions we obtain the output of the MEMS gyroscope
Figure BDA0001865804540000064
And
Figure BDA0001865804540000065
respectively substituting the two formulas into formula (12) and subtracting to obtain the following formula
Figure BDA0001865804540000066
2.3) on the basis of the scale coefficient error and the non-orthogonal error which are obtained in the prior art, when enough static position data are acquired, the zero offset error can be obtained by adopting total least square or general least square.
And substituting data (at least ten groups of data) of different static positions into a formula (13), and performing least square fitting to calculate a gyro constant zero position.

Claims (7)

1. A calibration method for an MEMS gyroscope combination is characterized by comprising the following steps:
1) calibrating scale coefficient error and non-orthogonal error, and adopting clockwise and anticlockwise rotation to offset earth rotation and gyro zero-offset
1.1) marking the initial position of the MEMS triaxial gyroscope combination hexahedron;
1.2) slightly rotating the hexahedron 360 degrees clockwise around a rotating shaft vertical to a horizontal plane, and then rotating the hexahedron 360 degrees anticlockwise to ensure that the hexahedron rotates around the same shaft by a known angle, namely delta theta in the whole process;
1.3) determining the error equation of a surface
Figure FDA0001865804530000011
Figure FDA0001865804530000012
Figure FDA0001865804530000013
mijIs an element of the symmetric matrix M;
wherein Km＝diag(Kmx,Kmy,Kmz) The error of the scale factor is calculated,
Figure FDA0001865804530000014
a non-orthogonal error matrix, wherein rho, phi and lambda are angle errors in three directions;
1.4) installing the MEMS gyroscope group at different positions in a six-sided shell, repeating the steps 1.2 and 1.3, simultaneously solving an equation set, and solving Km＝diag(Kmx,Kmy,Kmz) The error of the scale factor is calculated,
Figure FDA0001865804530000015
six unknown parameters in the non-orthogonal error matrix;
2) estimating zero offset error
2.1) estimating the zero offset ω of the gyro using the following equationie
Figure FDA0001865804530000016
2.2) obtaining the outputs of the MEMS gyroscope at two different static positions is
Figure FDA0001865804530000017
And
Figure FDA0001865804530000018
the two expressions are respectively substituted into the expression in 2.1), and the two expressions are subtracted to obtain the following expression
Figure FDA0001865804530000021
And 2.3) substituting data of different static positions into a formula of 2.2), and calculating a constant zero position of the gyroscope by adopting least square fitting.
2. The calibration method of the MEMS gyroscope assembly of claim 1, wherein the measurement model of the MEMS triaxial gyroscope assembly is:
Figure FDA0001865804530000022
the above formula is inverse operation to obtain
Figure FDA0001865804530000023
Wherein the content of the first and second substances,
Figure FDA0001865804530000024
the measurement vector is output for the MEMS gyroscope combination,
Figure FDA0001865804530000025
external angular velocity input, vmIs the measurement noise.
3. The calibration method for the MEMS gyroscope combination as claimed in claim 1, wherein in the step 1): given a smooth plane and a reference, the combined hexahedron with the MEMS three-axis gyroscope is placed on a horizontal plane close to the initial position of the reference mark.
4. The calibration method of the MEMS gyroscope combination as claimed in claim 3, wherein: the smooth horizontal floor tile plane of the laboratory and the side-placed square stool plane perpendicular to the horizontal plane are selected as the smooth plane and the reference respectively.
5. The calibration method for the MEMS gyroscope combination as claimed in claim 1, wherein in the step 1: and 2.3) selecting 10-100 groups of data of different static positions and substituting the data into a formula 2.2).
6. A calibration method for a MEMS gyroscope assembly as claimed in claim 1, wherein in step 1.2), the position of the rotated hexahedron on the square bench surface coincides with the initial mark position, i.e. it describes a 360 ° turn around the rotation axis in the vertical horizontal plane.
7. The calibration method for the MEMS gyroscope combination as claimed in claim 1, wherein the rotation operation in the rotation process of step 1.4) repeated 1.2) and 1.3) is in reverse order of the previous direction.
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CN112611400A (en) * 2021-01-08 2021-04-06 中国船舶重工集团公司第七0七研究所 Single-shaft turntable-based inertial measurement unit on-site calibration method
CN112665586A (en) * 2020-12-11 2021-04-16 陕西华燕航空仪表有限公司 Method for improving precision of MEMS gyroscope

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Cited By (2)

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Publication number Priority date Publication date Assignee Title
CN112665586A (en) * 2020-12-11 2021-04-16 陕西华燕航空仪表有限公司 Method for improving precision of MEMS gyroscope
CN112611400A (en) * 2021-01-08 2021-04-06 中国船舶重工集团公司第七0七研究所 Single-shaft turntable-based inertial measurement unit on-site calibration method

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