CN1818555A - Microinertia measuring unit precisive calibration for installation fault angle and rating factor decoupling - Google Patents

Abstract

The precise calibration method of the micro-inertial measurement unit decoupling the installation error angle and the scale factor is used to accurately calibrate all the error coefficients in the MIMU. Firstly, the overall error model of the MIMU is established to separate the installation error angle and the scale factor of the accelerometer and gyroscope. coupling. The 10-position static calibration test is carried out, and the constant value offset of the accelerometer and gyroscope is calculated by the position error cancellation method, and the scale factor and installation error angle of the accelerometer are separated. Through the 3-direction positive and negative rate tests, the least square method and iterative method are used to calculate the gyroscope installation error angle, the scale factor under low dynamic conditions, and the error items related to the gyroscope output and specific force. Finally, the interpolation method is used to calculate the gyroscope height in sections Dynamic scale factor. This method is simple, fast, and high-precision. The experimental equipment does not need to point north. It realizes the decoupling of the gyroscope and accelerometer scale factors and the installation error angle in the MIMU. The calibrated installation error angle can provide guidance for further installation and adjustment of the MIMU. .

Description

Accurate Calibration Method of Micro-IMU Decoupled from Mounting Error Angle and Scale Factor

technical field

The invention relates to a MIMU accurate calibration method decoupling the installation error angle and the scale factor, which is used for calculating various error coefficients in the MIMU overall error model, and is especially suitable for MIMU calibration with a large installation error angle, and the method is also applicable It is used in flexible gyroscope inertial measurement unit (IMU) and liquid floating gyroscope IMU.

Background technique

The MIMU composed of three orthogonally arranged micro-electromechanical gyroscopes and accelerometers is the core component of the micro-inertial navigation system. Its accuracy determines the navigation accuracy of the micro-inertial navigation system. The deterministic system error in the MIMU error source accounts for about About 90% of the total error, so the separation, calibration and compensation of deterministic system errors are decisive for improving the accuracy of MIMU.

At present, the calibration of MIMU basically adopts traditional calibration methods, mainly including multi-position static calibration, dynamic rate calibration, and dynamic and static hybrid calibration. Among them, the static calibration is to use the acceleration of gravity of the earth and the angular rate of the earth's rotation to solve the MIMU error coefficient on each axis. This method includes various calibration methods such as 12 positions and 24 positions, which can accurately calibrate the error coefficient of the accelerometer in the MIMU, but the gyroscope The calibration accuracy is very low; the dynamic rate calibration method improves the error calibration accuracy of the gyroscope in the MIMU, but only part of the error coefficient can be calibrated; the dynamic and static hybrid calibration method overcomes the shortcomings of the static and dynamic calibration methods, and can not only calibrate out All error coefficients, while improving the calibration accuracy, has become the mainstream direction of MIMU calibration.

The existing dynamic and static hybrid calibration methods have been widely used in the calibration of MIMU, and they are all based on the existing error model design. The angular velocity channel error model in the existing MIMU error model is:

${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; xy</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; xz</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; xx</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; xy</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; xz</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}$

${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; yx</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; yz</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; yx</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; yy</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; yz</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}$

${\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 1</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; K</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}\mathrm{<span\; class="notranslate">\; 2</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}^{\mathrm{<span\; class="notranslate">\; 2</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; zx</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; zy</span>}}{\mathrm{<span\; class="notranslate">\; \&omega;</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; zx</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; x</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; zy</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; the\; y</span>}}<span\; class="notranslate">\; +</span>{\mathrm{<span\; class="notranslate">\; D.</span>}}_{\mathrm{<span\; class="notranslate">\; zz</span>}}{\mathrm{<span\; class="notranslate">\; f</span>}}_{\mathrm{<span\; class="notranslate">\; z</span>}}<span\; class="notranslate">\; )</span>$

Among them, ω _x , ω _y and ω _z represent the analog voltage values output by the x, y and z axis gyroscopes in the MIMU respectively; ω _x , ω _y and ω _z represent the actual angular velocity input by the x, y and z axes respectively; K _t1 , K _t2 are the primary and secondary items of the gyroscope scale factor respectively; M _yx , M _xz , M _zx are the installation error items; D _x , D _y , D _z represent the x, y, z axis gyroscope constant deviation D _ij represents the error item related to the i-axis gyroscope output and the j-axis specific force; f _x , f _y and f _z represent the actual specific force of the x-, y-, and z-axis input, respectively. The acceleration channel error model in the existing MIMU error model is:

f _x ＝k _ax (f _x +B _x +I _xy f _y +I _xy f _z )

f _y ＝k _ay (f _y +B _y +I _yx f _x +I _yz f _z )

f _z ＝k _az (f _z +B _z +I _zy f _y +I _zx f _x )

Where f _x , f _y and f _z represent the analog voltage values output by the x, y and z axis accelerometers in the MIMU respectively; k _ax , k _ay , k _az represent the scale factors of the x, y and z axis accelerometers; I _ij Represents the installation error term between the i-axis accelerometer and the j-axis; B _x , By _y , and B _z represent the constant value offsets of the x, y, and z-axis accelerometers. The gyroscope and accelerometer installation error items in the above-mentioned angular velocity and acceleration channel error models are actually the coupling coefficients of the scaling factor and the installation error angle, so the existing dynamic and static hybrid calibration methods cannot accurately calculate the installation error angle, and thus cannot be used for further correction. The installation error angle provides guidance information. At the same time, this method does not calculate the gyroscope scale factor under negative rotation speed, which leads to the asymmetry error of the gyroscope scale factor. In addition, the calibration test equipment used in this method requires north-seeking, thus increasing Test difficulty and workload.

Contents of the invention

The technical solution problem of the present invention is: overcome the deficiency of existing MIMU calibration method, propose a kind of micro inertial measurement unit accurate calibration method of installation error angle and scale factor decoupling, this method is simple, quick, high precision, and experimental equipment does not need It needs to be pointed out that the decoupling of the scale factor of the gyroscope and accelerometer in the MIMU and the installation error angle has been realized.

The technical solution of the present invention is: the precise calibration method of the micro-inertial measurement unit decoupled from the installation error angle and the scale factor, which is characterized in that it is realized through the following steps:

(1) Based on the MIMU error characteristics, the coupling problem between the scale factor and the installation error angle is considered, and the overall error model of the MIMU is established;

(2) Use a biaxial position table or a turntable (without pointing to the north) to conduct a 10-position static calibration test;

(3) According to the static calibration test data, the constant value offset of the accelerometer and gyroscope is calculated by the symmetrical position error cancellation method, and the accelerometer scale factor and installation error angle are calculated by the acceleration channel decoupling method;

(4) Use a single-axis rate turntable (no need to point north) and three-sided tooling to conduct positive and negative rate tests in 3 directions;

(5) According to the experimental data of the positive and negative rates in 3 directions, the least square method and the cyclic iteration method are used to separate the gyroscope scale factor and the installation error angle coupling in the MIMU successively, and calculate the scale factor and gyroscope installation error in the low dynamic condition of the gyroscope Angle, combined with the static calibration test data to solve the error terms related to the gyroscope output and specific force, and use the interpolation method to accurately calculate the scale factor of the gyroscope under high dynamic conditions.

The 10-position static calibration test method in the described step (2) is: set the x, y, z axes of MIMU to coincide with the celestial direction of the geographical coordinate system respectively and horizontally rotate 180 ° 6 positions around the celestial axis; set the x of the MIMU Any axis of , y, and z coincides with the geographic coordinate system and horizontally rotates 180°2 around the geographic axis; set the z-axis of the MIMU to be in the geographic horizontal plane, and the x, y axes are respectively 45° to the geographic coordinate system. The included angle and the y-axis of the MIMU are in the geographic horizontal plane, and the x and z-axes form 45° included angles with the geographic coordinate system and 2 positions respectively, achieving a total of 10 static positions.

The acceleration channel decoupling method in the described step (3) is to utilize the z axis of MIMU in the geographic horizontal plane, and the x and y axes respectively form a 45 ° angle with the geographical coordinate system sky direction and the y axis of MIMU in the geographic horizontal plane, The x and z axes form an included angle of 45° with the geographical coordinate system at 2 positions respectively. According to the acceleration channel error model, the input and output state equations of the accelerometers of each axis are listed, combined with the input and output state equations of the accelerometers of each axis at the other 8 positions, through The phase division method and the inverse trigonometric function method first calculate the accelerometer installation error angle, then calculate the accelerometer scale factor, and finally realize the decoupling of the acceleration channel.

The interpolation method of the step (5) calculates the scale factor method under the high dynamic situation of the gyroscope in sections: utilize the installation error angle obtained to calculate the scale factor of each interpolation speed point under the high dynamic situation, and adopt the linear interpolation method to divide The section calculates the scale factor for high dynamic conditions of the gyroscope.

The principle of the invention is: according to the error mechanism that the accelerometer scale factor and the installation error angle affect the output of the accelerometer, the MIMU acceleration channel error model is established. According to the error mechanism of the gyroscope scale factor, the installation error angle, and the error items related to the gyroscope output and specific force affecting the gyroscope output, an angular velocity channel error model is established. Using the principle that the errors of the MIMU at the symmetrical position are partly the same and partly opposite, the separation of errors is realized by simple addition or subtraction, and the constant value bias of the accelerometer and gyroscope is calculated. Using the principle of changing one installation error angle and keeping other error items unchanged, the interference of other error items is eliminated by phase division, and the coupling between the accelerometer scale factor and the installation error angle is separated. In the dynamic calibration test, the gyroscope sensitive to the earth's rotation angular rate in the MIMU horizontal plane integrates to zero during the whole rotation process to eliminate the calibration error caused by the earth's rotation angular rate. Using the principle that the angular rate input in the dynamic calibration test is much larger than the errors of the gyroscope, the scale factor of the gyroscope and the coupling coefficient of the installation error angle are accurately calibrated. Using the successive approximation principle of the cyclic iteration method, the coupling between the scale factor of the gyroscope and the installation error angle is separated.

The advantage of the present invention compared with prior art is:

(1) The present invention is based on the complete error model design of the MIMU, solves the coupling problem between the installation error angle and the scale factor, and calibrates the installation error angle of the accelerometer and gyroscope in the MIMU, which can provide guidance for further correction of the installation error angle. It overcomes the disadvantage that the error model adopted by the existing calibration method cannot separate the scale factor and the coupling of the installation error angle.

(2) All the calibration test equipment adopted in the present invention do not need to seek north, which reduces the test requirements and difficulty, and improves the calibration efficiency.

(3) Compared with the existing calibration method, the calibration method involved in the present invention is simple, has clear physical meaning, small workload, short time, and less pollution to the calibration result by gyroscope drift.

(4) The least square method and the loop iteration method are used to calculate the scale factor of the gyroscope under low dynamic conditions, which reduces the calculation amount when working under low dynamic conditions, and the interpolation method is used to calculate the scale of the gyroscope under high dynamic conditions factor, which reduces the non-linear error of the scaling factor under high dynamic conditions. Moreover, the method uses positive and negative velocity experimental data, and reduces the asymmetry error of the scaling factor compared with the existing dynamic and static mixed calibration method.

Description of drawings

Fig. 1 is the flow chart of the MIMU accurate calibration method decoupling the installation error angle and the scale factor of the present invention;

Fig. 2 is a schematic diagram of the relationship between the biaxial position platform coordinate system and the geographic coordinate system northeast sky involved in the present invention;

Fig. 3 is the speed turntable coordinate system that the present invention relates to and the relation schematic diagram between this coordinate system and geographical coordinate system northeast sky;

4 is a schematic diagram of the MIMU coordinate system involved in the present invention;

Fig. 5 is a schematic diagram of the 10-position static calibration test steps in the present invention.

Detailed ways

The specific implementation steps of the technical solution of the present invention are as shown in Figure 1. First, each coordinate system used in the specific implementation process is defined. Figure 3 is the relationship between the rate turntable coordinate system O _T X _T Y _T Z _T and the coordinate system and the geographic coordinate system northeast sky; Figure 4 is the MIMU coordinate system oxyz, the specific implementation steps are as follows:

1. Based on the characteristics of MIMU installation error angle, poor resolution, large drift, non-linear scale factor and large asymmetry error, a complete error model of MIMU is established, and the installation error angle is used to replace the installation error in the existing error model coefficient, which separates the coupling of the scale factor from the installation error angle. The angular velocity channel error model of MIMU is:

ω _x , ω _y and ω _z in formulas (1) to (3) respectively represent the analog voltage values output by the x-, y- and z-axis gyroscopes in the MIMU; ω _x , ω _y and ω _z represent x, y, The actual angular velocity input by the z-axis; K _x , K _y , K _z represent the scale factors of the x-, y-, and z-axis gyroscopes respectively;  _ij represents the installation error angle of the i-axis gyroscope towards the j-axis; D _x , D _y , D _z represents the constant value bias of the x, y, z axis gyroscope respectively; D _ij represents the error item related to the i-axis gyroscope output and the j-axis ratio force; f _x , f _y and f _z represent the x, y, z axis respectively Enter the actual specific force. The MIMU acceleration channel error model is:

f _x ＝k _ax [cos(θ _xy )cos(θ _xz )f _x +sin(θ _xz )f _y +sin(θ _xz )f _z ]+B _x (4)

f _y ＝k _ay [cos(θ _yx )cos(θ _yz )f _y +sin(θ _yx )f _x +sin(θ _yz )f _z ]+B _y (5)

f _z ＝k _az [cos(θ _zy )cos(θ _zx )f _z +sin(θ _zy )f _y +sin(θ _zx )f _x ]+B _z (6)

In formulas (4) to (6), f _x , f _y and f _z respectively represent the analog voltage values output by the accelerometers in the x, y and z axes of the MIMU; k _ax , k _ay and k _az represent the x, y and z axes Accelerometer scale factor; θ _ij represents the installation error angle of the i-axis accelerometer to the j-axis; B _x , B _y , B _z represent the constant value bias of the x, y, z-axis accelerometer.

2. Use a dual-axis position table (without seeking north) to perform a 10-position static calibration test, as shown in Figure 6. The specific steps are as follows:

(1) Install the MIMU horizontally on the dual-axis position platform, rotate the outer frame of the position platform so that the Z axis of the position platform coordinate system coincides with the celestial direction of the geographic coordinate system, and rotate the inner frame to ensure that the MIMU coordinate system oxyz coincides with the position platform coordinate system OXYZ, This position is the first position. After the position station is completely stabilized, start the MIMU to preheat it for 20 to 30 minutes, and then record the output data of the MIMU at this position for 1 to 5 minutes;

(2) Rotate the inner frame of the positioning table 180° clockwise (looking down on the positioning table), so that the x, y, and z axes of the MIMU coincide with the -X, -Y, and Z axes of the positioning table coordinate system, and this position is the second position. After the position station is completely stabilized, record the MIMU output data at the position for 1 to 5 minutes;

(3) Rotate the outer frame of the position table 90° counterclockwise (viewing the position table from the -X axis), so that the x, y, and z axes of the MIMU coincide with the -X, Z, and Y axes of the position table coordinate system, and the position is In the third position, after the position station is completely stabilized, record the MIMU output data for 1 to 5 minutes at this position;

(4) Rotate the inner frame of the positioning table 180° counterclockwise, so that the x, y, and z axes of the MIMU coincide with the X, Z, and -Y axes of the positioning table coordinate system respectively. This position is the fourth position, and the positioning table is completely stabilized. After that, record the MIMU output data for 1 to 5 minutes at this position;

(5) Rotate the inner frame of the positioning table 90° counterclockwise, and then rotate the outer frame of the positioning table 90° clockwise, so that the x, y, and z axes of the MIMU coincide with the Z, -Y, and X axes of the positioning table coordinate system respectively. It is the 5th position. After the position station is completely stabilized, record the MIMU output data at this position for 1 to 5 minutes;

(6) Rotate the inner frame of the positioning table 180° clockwise, so that the x, y, and z axes of the MIMU coincide with the Z, Y, and -X axes of the positioning table coordinate system respectively. This position is the sixth position, and the positioning table is completely stabilized. After that, record the MIMU output data for 1 to 5 minutes at this position;

(7) Rotate the outer frame of the positioning table 180° clockwise, so that the x, y, and z axes of the MIMU coincide with the -Z, -Y, and -X axes of the positioning table coordinate system respectively. This position is the seventh position. When the positioning table is completely After stabilization, record MIMU output data at this position for 1 to 5 minutes;

(8) Rotate the inner frame 180° counterclockwise so that the x, y, and z axes of the MIMU coincide with the -Z, Y, and X axes of the position table coordinate system respectively. This position is the 8th position. After the position table is completely stabilized, Record MIMU output data for 1 to 5 minutes at this position;

(9) Rotate the inner frame 180° clockwise, and then rotate the outer frame of the position stage 135° counterclockwise, so that the z-axis of the MIMU coincides with -X of the position stage coordinate system, and the y-axis is 45° from the Z axis of the position stage coordinate system. , the x-axis is at 45° from the Z-axis of the coordinate system of the position table, which is the 9th position. After the position table is completely stabilized, record data for 1 to 5 minutes at this position;

(10) Rotate the outer frame of the position stage 45° counterclockwise, then rotate the inner frame of the position stage 90° counterclockwise, and rotate the outer frame 45° counterclockwise again, so that the y-axis of the MIMU coincides with the coordinate system -X of the position stage, and the x-axis is at The coordinate system of the position stage is 45° from the Z axis to the Y axis, and the z axis is located at 45° from the Z axis to the Y axis of the stage coordinate system. , So far, the 10-position static test has been completed.

3. Using the 10-position static calibration test data, calculate the constant value bias of the gyroscope and all error coefficients of the accelerometer.

(1) According to the 1st to 8th positions in the static 10-position calibration test, the symmetrical position error cancellation method is used to calculate the constant value offset of the accelerometer and gyroscope in the MIMU.

The fifth position, that is, the x, y, and z axes in the MIMU coordinate system coincide with the Z, -Y, and X axes of the position station coordinate system respectively. Assume that the angle between the Y axis of the position station coordinate system and the north direction of the geographic coordinate system is ψ. The MIMU acceleration channel output is:

f _x5 ＝k _ax cos(θ _xy )cos(θ _xz )·g+B _x (7)

f _y5 ＝k _ay sin(θ _yx )g+B _y (8)

f _y5 ＝k _az sin(θ _zx )g+B _z (9)

In the formula, f _ij represents the analog voltage output of the i-axis accelerometer when the MIMU is in the jth position, and g represents the acceleration of gravity. The MIMU angular velocity channel output is:

(10)

(11)

(12)

In the formula, ω _ij represents the analog voltage output of the i-axis gyroscope when the MIMU is in the jth position, and φ represents the latitude of the local position.

The sixth position, that is, the x, y, and z axes in the MIMU coordinate system coincide with the Z, Y, and -X axes of the MIMU coordinate system respectively. The output of the MIMU accelerometer channel at this position is:

f _x6 ＝k _ax cos(θ _xy )cos(θ _xz )·g+B _x (13)

f _y6 = k _ay sin(θ _yx )g+B _y (14)

f _z6 ＝k _az sin(θ _zx )g+B _z (15)

After changing from the 5th position to the 6th position, the initial deviation angle in the horizontal direction changes from Ψ to Ψ+180°, because sin(ψ+180°)=-sin(ψ), cos(ψ+180°)=-cos (ψ), the output of the 6th position angular velocity channel is:

(16)

(17)

(18)

Simultaneous equations (7) to (18), list the average output of the acceleration channel in the MIMU at positions 5 and 6 as:

f _x6/5 ＝( f _x6 + f _x5 )/2＝k _ax cos(θ _xy )cos(θ _xz )·g+B _x (19)

f _y6/5 ＝( f _y6 + f _y5 )/2＝ _kay sin(θ _yx )g+B _y (20)

f _z6/5 ＝( f _z6 + f _z5 )/2＝k _az sin(θ _zx )g+B _z (21)

In the formula, f _ij/k represents the average value of the analog voltage output of the i-axis accelerometer at the j and k positions of the MIMU, and the symmetrical position cancellation method is used to eliminate the influence of the earth's rotation angular rate ω _ie on the axial gyroscope in the horizontal plane, and the MIMU The average output of the middle angular velocity channel at positions 5 and 6 is:

ω _x6/5 ＝( ω _x6 + ω _x5 )/2＝K _x cos( _xy )cos( _xz )sin(φ)ω _ie +D _x +D _xx g (22)

ω _y6/5 ＝( ω _y6 + ω _y5 )/2＝K _y sin( _yx )sin(φ)ω _ie +D _y +D _yx g (23)

ω _z6/5 ＝( ω _z6 + ω _z5 )/2＝K _z sin( _zx )sin(φ)ω _ie +D _z +D _zx g (24)

In the formula, ω _ij/k represents the average value of the analog voltage output of the i-axis gyroscope at the j and k positions of the MIMU. Similarly, the average value of the acceleration channel output in the MIMU at positions 1 to 4 and 7 to 8 can be obtained as:

f _x2/1 ＝( f _x2 + f ₁ )/2＝k _ax sin(θ _xz )·g+B _x (25)

f _y2/1 ＝( f _y2 + f _y1 )/2＝ _kay sin(θ _yz )g+B _y (26)

f _z2/1 ＝( f _z2 + f _z1 )/2＝k _az cos(θ _zy )cos(θ _zx )g+B _z (27)

f _x4/3 ＝( f _x4 + f ₃ )/2＝k _ax sin(θ _xy )·g+B _x (28)

f _y4/3 ＝( f _y4 + f _y3 )/2＝ _kay cos(θ _yz )cos(θ _yx )g+B _y (29)

f _z4/3 ＝( f _z4 + f _z3 )/2＝k _az sin(θ _zy )g+B _z (30)

f _x8/7 ＝( f _x8 + f _x7 )/2＝k _ax cos(θ _xy )cos(θ _xz )·(-g)+B _x (31)

f _y8/7 ＝( f _y8 + f _y7 )/2＝ _kay sin(θ _yx )(-g)+B _y (32)

f _z8/7 ＝( f _z8 + f _z7 )/2＝k _az sin(θ _zx )(-g)+B _z (33)

The average value of the angular velocity channel output in the MIMU at positions 1~4, 7~8 is:

ω _x2/1 ＝( ω _x2 + ω _x1 )/2＝K _x sin( _xz )sin(φ)ω _ie +D _x +D _xz g (34)

ω _y2/1 ＝( ω _y2 + ω _y1 )/2＝K _y sin( _yz )sin(φ)ω _ie +D _y +D _yz g (35)

ω _z2/1 ＝( ω _z2 + ω _z1 )/2＝K _z cos( _zy )cos( _zx )sin(φ)ω _ie +D _z +D _zz g (36)

ω _x4/3 ＝( ω _x4 + ω _x3 )/2＝K _x sin( _xy )sin(φ)ω _ie +D _x +D _xy g (37)

ω _y4/3 ＝( ω _y4 + ω _y3 )/2＝K _y cos( _yx )cos( _yz )sin(φ)ω _ie +D _y +D _yy g (38)

ω _z4/3 ＝( ω _z4 + ω _z3 )/2＝K _z sin( _zy )sin(φ)ω _ie +D _z +D _zy g (39)

ω _x8/7 ＝( ω _x8 + ω _x7 )/2＝K _x cos( _xy )cos( _xz )sin(φ)(-ω _ie )+D _x +D _xx (-g) (40)

ω _y8/7 ＝( ω _y8 + ω _y7 )/2＝K _y sin( _yx )sin(φ)(-ω _ie )+D _y +D _yx (-g) (41)

ω _z8/7 ＝( ω _z8 + ω _z7 )/2＝K _z sin( _zx )sin(φ)(-ω _ie )+D _z +D _zx (-g) (42)

Simultaneous equations (19) and (31), (20) and (32), (21) and (33), the constant biases of the accelerometers in the x, y, and z directions of the MIMU are obtained respectively:

B _x ＝( f _x6/5 + f _x8/7 )/2 (43)

B _y =( f _y6/5 + f _y8/7 )/2 (44)

B _z ＝( f _z6/5 + f _z8/7 )/2 (45)

Simultaneous equations (22) and (40), (23) and (41), (24) and (42), the constant value offsets of the x-, y-, and z-axis gyroscopes in the MIMU are respectively obtained as follows:

D _x ＝( ω _x6/5 + ω _x8/7 )/2 (46)

D _y =( ω _y6/5 + ω _y8/7 )/2 (47)

D _z ＝( ω _z6/5 + ω _z8/7 )/2 (48)

(2) According to the acceleration channel data recorded in the 10-position static calibration test, the acceleration channel decoupling method is used to calculate the installation error angle and scale factor of the accelerometer in the MIMU.

At the ninth position, that is, the z-axis in the MIMU coordinate system coincides with the -X-axis of the position table coordinate system, the x-axis is located at 45° from the Z-axis to the -Y-axis, and the y-axis is located at 45° from the Z-axis from the Y-axis. In this position, the MIMU The output of the x, y two-axis accelerometer is:

f _x9 ＝k _ax cos(45°-θ _xz )cos(θ _xz )+B _x (49)

f _y9 ＝k _ay cos(45°-θ _yx )cos(θ _yz )g+B _y (50)

At the 10th position, that is, the y-axis in the MIMU coordinate system coincides with the -X axis of the position table coordinate system, the z-axis is located at 45° from the Z-axis to the -Y-axis, and the x-axis is located at 45° from the Z-axis to the Y-axis. In this position, the MIMU The z-axis accelerometer output is:

f _z10 =k _az cos(θ _zy )cos(45°-θ _zx )g+B _z (51)

Simultaneous formulas (25), (19) and (49), solving the equations to obtain the installation error angle and scale factor of the x-axis accelerometer are:

k _ax =( f _x6/5 -B _x )/cos(θ _xy )cos(θ _xz ) (54)

Simultaneous formulas (26), (29) and (50), solving the equations to obtain the installation error angle and scale factor of the y-axis accelerometer are:

k _ay =( f _y4/3 -B _y )/cos(θ _yx )cos(θ _yz ) (57)

Simultaneous formulas (27), (30) and (51), solving the equations to obtain the installation error angle and scale factor of the z-axis accelerometer are:

k _az ＝( f _z2/1 -B _z )/cos(θ _zx )cos(θ _zy ) (60)

4. Use a single-axis rate turntable (no need to point north) and three-sided tooling to conduct positive and negative rate tests in 3 directions

Carry out the dynamic rate calibration test, look down on the turntable, set the turntable to rotate counterclockwise as forward rotation, and rotate clockwise as reverse rotation. Fix the MIMU horizontally at the center of the single-axis rate turntable through the three-sided orthogonal tooling fixture, so that the z-axis of the MIMU coincides with the Z _T axis of the turntable. After preheating the MIMU with power supply for 20-30 minutes, collect MIMU output data for 1-5 minutes, and then rotate the turntable at 180° to collect MIMU output data for 1-5 minutes. Then set the turntable to rotate forward, record the gyroscope output, and stop; turn the turntable to reverse, record the gyroscope output, and stop. The input angular rate of the turntable changes in order from small to large, input n°/10/s, -n°/10/s, 2n°/10/s, -2n°/10/s, 3n°/ 10/s, -3n°/10/s, ..., n°/s, -n°/s, a total of 20 angular rates, n°/s represents the maximum positive angular rate of the MIMU measurement range, in Under the premise of ensuring the collection of data for the entire rotation cycle, the data output by the MIMU for about 1 to 5 minutes are recorded for each angular rate. Finally, collect MIMU output data for 1 to 5 minutes in a static state, and then collect MIMU output data for 1 to 5 minutes while rotating the turntable at 180°.

In the same way, flip the three-sided orthogonal fixture so that the x-axis and y-axis of the MIMU coincide with the Z _{and T} axes of the turntable respectively, repeat the above work, and complete the positive and negative rate tests in 3 directions.

5. Using the dynamic calibration test data, the least square method and successive iteration method are used to calculate the installation error angle of the gyroscope and the scaling factor of the gyroscope under low and high dynamic conditions.

(1) Calculate the installation error angle of the gyroscope in the MIMU and the scaling factor under low dynamic conditions.

When the z axis of the MIMU coincides with the Z _T axis of the turntable and the turntable rotates at an angular velocity Ω _j , the angular velocity input by the three axes of the MIMU is:

ω _zz = Ω _j + ω _ie sin(φ) (61)

ω _zy ＝ω _ie cos(φ)cos(Ω _j t+ψ _T ) (62)

ω _zx ＝ω _ie cos(φ)sin(Ω _j t+ψ _T ) (63)

Among them, ω _zx , ω _zy and ω _zz are the angular velocities input by the x, y and z axes when the z axis of the MIMU coincides with the Z _T axis of the turntable, respectively; Ω _j represents the input angular velocity of the turntable; t represents the rotation time; ω _ie is the earth Rotation angular velocity; φ is the local latitude; ψ _T is the angle between the y-axis of MIMU and the north direction at the initial moment of rotation. When the turntable rotates for several cycles, all integrals including cos(Ω _j t+ψ) and cos(Ω _j t+ψ) are zero. Let ω _zxj , ω _zyj , ω _zzj be when the z-axis of the MIMU coincides with the Z _T -axis of the turntable, the average value of the output of the gyroscope in the x, y, and z axes at the jth angular rate Ω _j input by the turntable is:

Let the average output of each gyroscope at position 1 be ω _axs1 , ω _zys1 , ω _zzs1 at the beginning of the test position 1, the average output of each gyroscope at position 2 be ω _zxs2 , ω _zys2 , ω _zzs2 , and the output of each gyroscope at position 1 at the end of the test The average values are ω _zxe1 , ω _zye1 , ω _zze1 , and the average values of the output of each gyroscope at position 2 are ω _zxe2 , ω _zye2 , ω _zze2 , and the average values of the x, y, and z-axis gyroscope outputs in the MIMU at the beginning of the test can be obtained ω _zxs , ω _zys , ω _zzs and the average value of each gyroscope output at the end ω _zxe , ω _zye , ω _zze are:

ω _zxs ＝( ω _zxs1 + ω _zxs2 )/2＝K _x sin( _xz )ω _ie sin(φ)+D _x +D _xz g (67)

ω _zys ＝( ω _zys1 + ω _zys2 )/2＝K _y sin( _yz )ω _ie sin(φ)+D _y +D _yz g (68)

ω _zzs =( ω _zzs1 + ω _zzs2 )/2=K _z cos( _zx )cos( _zy )ω _ie sin(φ)+D _z +D _zz g (69)

ω _zxe ＝( ω _zxe1 + ω _zxe2 )/2＝K _x sin( _xz )ω _ie sin(φ)+D _x +D _xz g (70)

ω _zye ＝( ω _zye1 + ω _zye2 )/2＝K _y sin( _yz )ω _ie sin(φ)+D _y +D _yz g (71)

ω _zze ＝( ω _zze1 + ω _zze2 )/2＝K _z cos( _zx )cos( _zy )ω _ie sin(φ)+D _z +D _zz g (72)

To eliminate the influence of the earth's rotation angular rate on the gyroscope, the average values of ω _zxr , ω _zyr , and ω _zzr output by each gyroscope of the MIMU when they are stationary are:

ω _zxr = (ω _zxs + ω _zxe )/2 (73)

ω _zyr = (ω _zys + ω _zye )/2 (74)

_ωzzr = ( _ωzzs + _ωzze )/2 (75)

When the jth input angular rate Ω _j is eliminated, the interference of the earth's rotation angular rate, gyroscope constant bias, gyroscope output and specific force-related error items is eliminated, and the x, y, z gyroscope output values in the MIMU are obtained as :

ω _zzj = ω _zzj - ω _zzr = K _z cos( _zx )cos( _zy )Ω _j (76)

ω _zxj ＝ ω _zxj - ω _zxr ＝K _x sin( _xz )Ω _j (77)

ω _zyj = ω _zyj - ω _zyr = K _y sin( _yz )Ω _j (78)

In the same way, when the x and y axes of the MIMU coincide with the z-axis of the turntable, the z-axis can be obtained after eliminating the interference of the earth's rotation angular rate, the constant bias of the gyroscope, and the error terms related to the output of the gyroscope and the specific force. The gyroscope output values are:

ω _xzj ＝ ω _xzj - ω _xzr ＝K _z sin( _zx )Ω _j (79)

ω _yzj = ω _yzj - ω _yzr = K _z sin( _zy )Ω _j (80)

According to formulas (76), (79) and (80), the coupling coefficient between the scale factor of the z-axis gyroscope in the MIMU and the installation error angle is obtained by the least square method:

The iterative method is used to separate the coupling between the installation error angle and the scaling factor of the gyroscope. The specific steps are as follows:

a. First, take K _z cos( _zx )cos( _zy ) as the initial value K _z ⁰ of the scaling factor in the case of low dynamics of the gyroscope, and set the scaling factor iteration accuracy threshold ε;

b. Substitute the scaling factor K _z ⁱ into equations (82) and (83) respectively to obtain the installation error angles  _zx ⁱ and  _zy ⁱ ;

c. Substitute the installation error angles  _zx ⁱ and  _zy ⁱ into equation (81) to obtain the scaling factor K _z ⁱ ;

d. The scale factor value calculated by two iterations before and after the test, when $\left|\right|K_z^i-K_z^{i-1}\left|\right|\&le;\mathrm{\&epsiv;}$ When , the iteration ends, and K _z ⁱ ,  _zxi ,  _zy ⁱ are respectively used as the scaling factor and the installation error value of the final solved gyroscope under low dynamic conditions, otherwise the calculation returns to step (b) to continue iteration ^;

e. Substituting the obtained K _z ⁱ ,  _zxi ^,  _zy ⁱ , and D _z into equations (34), (39), and (24), it can be obtained that the z-axis gyroscope output is related to the z-axis specific force The error term D _zz , the error term D _zy related to the y-axis specific force, and the error term D _zx related to the x-axis specific force.

According to the above method, the scale factors K _x , K _y , the installation error angles  _xy ,  _xz ,  _yx ,  _yz , and the angular velocity output and axis can be obtained in the same way when the x-axis and y-axis gyroscopes in the MIMU are under low dynamic conditions. Comparing relevant items D _xx , D _xy , D _xz , D _yy , D _yx , D _yz . So far, all calibration coefficients of MIMU are calculated.

(2) Calculating the scale factor of the gyroscope in the MIMU under high dynamic conditions.

Due to the large nonlinear error of the MIMU scale factor under high dynamic conditions, the interpolation method is used to calculate the scale factor of the gyroscope under high dynamic conditions in sections to improve the precision of MIMU.

First, the high and low dynamic critical speed points are set according to the dynamic range of the MIMU angular velocity channel, the nonlinear characteristics of the scale factor, the actual working environment, and the accuracy requirements. Generally, ‖Ω _j ‖=3n°/10/s is used as the high and low dynamic critical speed point. Take each rate greater than 3n°/10/s as the interpolation speed point of high dynamic segmental interpolation, substitute the obtained installation error into equation (76), calculate the scaling factor of each interpolation speed point respectively, and then use linear interpolation Calculating the scaling factor K _zt of the gyroscope in the case of high dynamics in sections by using the method is as follows:

K _z,t =K _z,i +(K _z,i+1 -K _z,i )(Ω _t -Ω _i )/(Ω _i+1 -Ω _i ) (84)

In Equation (84), K _{z, t} represents the scale factor of the z-axis gyroscope under high dynamic conditions, K _{z, i} represents the scale factor of the gyroscope at the i-th speed interpolation point of the z-axis, Ω _i represents the speed of the i-th speed interpolation point, Ω _t represents the calculated initial rotational speed (Ω _i ≤Ω _t ≤Ω _i+1 ).

In the same way, the scale factor of the x-axis and y-axis gyroscope under high dynamic conditions can be obtained. This method not only reduces the nonlinear error of the gyroscope scale factor in the MIMU under high dynamic conditions, but also reduces the calculation amount under low dynamic conditions. .

Although the present invention is a calibration method designed based on MIMU error characteristics, it is not only applicable to MIMU, but also applicable to flexible gyroscope IMU and liquid floating gyroscope IMU.

The content that is not described in detail in the description of the present invention belongs to those skilled in the art

current technology.

Claims (4)

1, the micro inertial measurement unit method for precisely marking of alignment error angle and constant multiplier decoupling zero, its characteristics are to realize through the following steps:

(1) sets up MIMU global error model;

(2) utilize two-axis position platform or turntable to carry out 10 position static demarcating tests;

(3) according to the static demarcating test figure, adopt symmetric position error phase elimination calculating accelerometer, gyroscope often to be worth biasing, utilize acceleration passage decoupling method to calculate accelerometer constant multiplier and alignment error angle;

(4) utilize single shaft rate table and three frocks to carry out the positive and negative speed trial in 3 orientation;

(5) according to the positive and negative speed experimental data in 3 orientation, adopt least square method and cyclic iterative to separate gyroscope constant multiplier and the coupling of alignment error angle among the MIMU one by one, constant multiplier, gyroscope alignment error angle under the low current intelligence of computing gyroscope, find the solution the relevant error term of gyroscope output in conjunction with the static demarcating test figure, and adopt constant multiplier under the high current intelligence of method of interpolation segmentation accurate Calculation gyroscope with specific force.

2, the micro inertial measurement unit method for precisely marking of alignment error angle according to claim 1 and constant multiplier decoupling zero is characterized in that: 10 position static demarcating test methods in the described step (2) are: x, y, the z axle that MIMU is set respectively with the geographic coordinate system sky to overlapping and rotating 180 ° of 6 positions to axle horizontal around the sky; Be provided with x, y, the z of MIMU any one with geographic coordinate system ground to overlaps and around ground to 180 ° of 2 position of axle horizontal rotation; The z axle that MIMU is set in geographical surface level, x, y axle respectively with the geographic coordinate system sky to the y of angle at 45 and MIMU axle in geographical surface level, x, z axle respectively with the geographic coordinate system sky to angle at 45 2 positions, realize totally 10 static position.

3, the micro inertial measurement unit method for precisely marking of alignment error according to claim 1 angle and constant multiplier decoupling zero, it is characterized in that: acceleration passage decoupling method is to utilize the z axle of MIMU in geographical surface level in the described step (3), x, the y axle respectively with the geographic coordinate system sky to the y of angle at 45 and MIMU axle in geographical surface level, x, the z axle respectively with the geographic coordinate system sky to angle at 45 2 positions, list each axis accelerometer input/output state equation according to acceleration channel error model, in conjunction with each axis accelerometer input/output state equation under above-mentioned other 8 position, calculate accelerometer alignment error angle earlier by phase division and inverse trigonometric function method, calculate the accelerometer constant multiplier then, finally realize the decoupling zero of acceleration passage.

4, the micro inertial measurement unit method for precisely marking of alignment error angle according to claim 1 and constant multiplier decoupling zero, it is characterized in that: constant multiplier method under the high current intelligence of method of interpolation segmentation computing gyroscope of described step (5): utilize the alignment error angle of trying to achieve, calculate the constant multiplier of each interpolation rotating speed point under the high current intelligence, adopt constant multiplier under the high current intelligence of linear interpolation method segmentation computing gyroscope.

Images