A method for double-position calibration of zero bias error of inertial system in the field

Abstract

The present invention relates to an outdoor dual-position calibration method for zero bias error of an inertial system, wherein an IMU is rotated approximately 180° around an azimuth axis, and the index change is tracked through a gyro output, and the tracking attitude matrix and the second position alignment attitude matrix are used to perform a difference to solve the platform misalignment angle, thereby obtaining an analytical solution for the zero bias of a gyro and an accelerometer. The method does not rely on the index accuracy and the north reference, is not affected by the initial heading angle, can calibrate the zero bias of a gyro and an accelerometer simultaneously, and improves the accuracy, reliability and adaptability of the dual-position calibration method to outdoor environments. Compared with the background technology, the technology of the present invention is not affected by the initial heading angle, avoids the appearance of singular values, improves the calibration accuracy of the gyro drift to 0.01° / h, and can calibrate the zero bias of an accelerometer simultaneously.

Description

Technical Field

[0001] The invention belongs to the technical field of inertial navigation, and relates to an outfield dual-position calibration method for an inertial system zero bias error, and in particular to an outfield zero bias error calibration method for an inertial navigation system. Background Art

[0002] Inertial devices have time-limited effects. As they are used for a longer time, the bias parameters of gyroscopes and accelerometers will change due to factors such as internal stress release and external environment. In order to ensure long-term navigation accuracy, the inertial navigation system usually needs to be returned to the manufacturer after a certain period of use, and recalibrated in the laboratory using equipment such as a high-precision turntable. If the zero bias error is quickly calibrated under field conditions using a method that does not rely on the indexing accuracy and north reference, the calibration time can be shortened, the transportation cost can be reduced, and the speed and mobility of maintenance can be improved. Affected by observability, the field dual-position calibration method based on the Kalman filter is difficult to estimate the celestial gyro bias in a short period of time.

[0003] The document "Inertial Instrument Test and Data Analysis, National Defense Industry Press, 2012, first edition, p220-221" discloses a dual-position drift measurement method that does not rely on a high-precision turntable. This method forms a dual position by approximately 180° rotation around the IMU azimuth axis, and establishes a set of equations based on the angular rate output at the two positions to solve the azimuth misalignment angle, thereby achieving accurate calibration of the three-axis gyro drift. The method described in the document can be applied to gyro bias calibration under field conditions, but the accelerometer bias error is not calibrated, and when the initial heading angle is near 90° and 270°, singular values ​​will appear in the azimuth misalignment angle calculation, resulting in a decrease in the accuracy of gyro drift calibration. Summary of the invention

[0004] Technical issues to be solved

[0005] In order to avoid the shortcomings of the prior art, the present invention proposes an outfield dual-position calibration method for zero bias error of an inertial system, which improves the outfield environment adaptability and calibration accuracy of the dual-position drift measurement method.

[0006] Technical Solution

[0007] An inertial system zero bias error external field dual position calibration method, characterized by the following steps:

[0008] Step 1: Initial alignment at the first position: Place the inertial navigation system horizontally, record it as the first position, and keep it still for more than 600 seconds in the first position. Record the average angular rate of the three-axis gyro output during this period. And the accelerometer output relative force average And calculate the initial alignment pose matrix for the first position The attitude matrix contains the misalignment angle error

[0009]

[0010] in, N1=U1×E1;

[0011] Step 2: Attitude tracking: Rotate the inertial navigation system 180° around the azimuth axis to reach the second position. During the rotation, use the gyro output data to solve the attitude differential equation and calculate the attitude matrix at the end of the rotation. Recorded as

[0012]

[0013] in: is the attitude matrix solved during the rotation process, and its initial value is is the gyro output angular rate; is the projection of the Earth's rotation angular rate in the inertial navigation coordinate system;

[0014] Step 3: Alignment at the second position: Keep still for more than 600 seconds at the second position and record the average angular rate of the three-axis gyro output during the still period. And the accelerometer output relative force average according to and Calculate the initial alignment pose matrix for the second position Since the rotation is 180°, the attitude matrix contains the misalignment angle error

[0015]

[0016] in, N2=U2×E2;

[0017] Step 4: Calculate the misalignment angle: Based on the attitude tracking matrix and the second position alignment pose matrix Calculate the misalignment angle

[0018]

[0019] Calculate the corrected attitude matrix

[0020]

[0021]

[0022] Step 5: Calculate the gyro and accelerometer bias and inject the calculation results into the inertial navigation system memory parameters to complete the bias error calibration:

[0023] Calculate gyro bias ε b :

[0024]

[0025] Calculating Accelerometer Bias

[0026]

[0027] in: is the projection of the Earth's rotation angular velocity on the northeastern sky geographic coordinate system, g n =[0 0 -g] T , g is the local gravitational acceleration modulus.

[0028] Beneficial Effects

[0029] The invention proposes an outdoor dual-position calibration method for zero bias error of an inertial system, which rotates the IMU approximately 180° around the azimuth axis, tracks the index change through the gyro output, and solves the platform misalignment angle by subtracting the tracking attitude matrix from the second position alignment attitude matrix, thereby obtaining an analytical solution for the zero bias of the gyro and accelerometer. The method does not rely on the index accuracy and north reference, is not affected by the initial heading angle, can calibrate the zero bias of the gyro and accelerometer simultaneously, and improves the accuracy, reliability and adaptability of the dual-position calibration method to outdoor environments. BRIEF DESCRIPTION OF THE DRAWINGS

[0030] Figure 1 It is a diagram of the implementation process of the present invention;

[0031] Figure 2 It is the gyro constant drift calibration error when the initial heading angle is 90° in the background technology;

[0032] Figure 3 is the gyro constant drift calibration error of the method of the present invention when the initial heading angle is 90°;

[0033] Figure 4 It is the accelerometer zero bias calibration error of the method of the present invention when the initial heading angle is 90°. DETAILED DESCRIPTION

[0034] The present invention will now be further described with reference to the embodiments and the accompanying drawings:

[0035] 1. Initial alignment at the first position.

[0036] Reference Figure 1 , place the inertial navigation system nearly horizontally, record the time period [0, t1] as the first position, keep it still for 600s at the first position, and record the average angular rate of the three-axis gyro output during this period And the accelerometer output relative force average And calculate the initial alignment pose matrix for the first position The attitude matrix contains the misalignment angle error

[0037]

[0038] in, N1=U1×E1.

[0039] 2. Posture tracking.

[0040] The IMU is rotated approximately 180° around the azimuth axis to reach the second position. During the rotation process, the gyro output data is used to update the attitude. The attitude tracking matrix at the end of the rotation is recorded as

[0041] Reference Figure 1 In the time period [t1, t2], the IMU is rotated approximately 180° around the azimuth axis to reach the second position. During the rotation, the attitude differential equation is solved using the gyro output data, and the attitude matrix at the end of the rotation is Recorded as

[0042]

[0043] in: is the attitude matrix solved during the rotation process, and its initial value is is the gyro output angular rate; is the projection of the Earth's rotation angular rate in the inertial navigation coordinate system.

[0044] 3. Align the second position.

[0045] Reference Figure 1 , in the time period [t2, t3], keep still at the second position for 600s, and record the average angular rate of the three-axis gyro output during this time period And the accelerometer output relative force average according to and Calculate the initial alignment pose matrix for the second position Since the rotation is approximately 180°, the attitude matrix contains the misalignment angle error

[0046]

[0047] in, N2=U2×E2.

[0048] 4. Calculation of misalignment angle.

[0049] According to the pose tracking matrix and the second position alignment pose matrix Calculate the misalignment angle

[0050]

[0051] Calculate the corrected attitude matrix

[0052]

[0053]

[0054] 5. Calculation of gyro and accelerometer bias.

[0055] Calculate the gyro constant drift ε by formula (7): b , Formula (8) calculates the accelerometer zero bias The calculation results are injected into the memory parameters of the inertial navigation system to complete the zero bias error calibration.

[0056]

[0057]

[0058] in is the projection of the Earth's rotation angular velocity on the northeastern sky geographic coordinate system, g n =[0 0 -g] T , g is the local gravitational acceleration modulus.

[0059] The specific implementation manner and implementation effect of the present invention are further illustrated below through simulation experiments.

[0060] The simulation conditions are set as follows: the initial position latitude and longitude are [110°; 34°; 400m], the initial pitch, roll and heading angles are [-2°; 1°; 90°], the attitude, pitch and heading angles of the second position after rotation are [0°; 1°; 271°]; the gyro zero bias mean square error is 0.05° / h, the random walk noise is 0.002° / √h, the accelerometer zero bias mean square error is 0.1mg, and the random noise is 0.01mg / √Hz; a total of 100 simulation tests are carried out.

[0061] Figure 2 The gyro drift estimation error obtained by the background technology. In most cases, the three-axis gyro drift estimation error can be kept within the range of 0.01° / h, but some experiments are affected by singular values, resulting in a significant reduction in calibration accuracy, where the maximum estimated error of the x- and y-axis gyro drift exceeds 0.02° / h, and the maximum error of the z-axis gyro drift reaches 1.5° / h.

[0062] Figure 3 The gyro drift estimation error obtained for the improved technology. In 100 simulation experiments, the calibration error of the three-axis gyro drift was kept within 0.01° / h without singular points.

[0063] Figure 4 The accelerometer bias estimation error obtained for the improved technology. In 100 simulation experiments, the calibration error of the triaxial accelerometer bias was kept within 10μg without singular points.

[0064] The effects of the embodiments show that, compared with the background technology, the technology of the present invention is not affected by the initial heading angle, avoids the appearance of singular values, improves the gyro drift calibration accuracy to 0.01° / h, and can calibrate the accelerometer zero bias at the same time.

Claims

1. A method for outdoor dual-position calibration of zero bias error of an inertial system, characterized in that Here are the steps: Step 1: Initial alignment at the first position: Place the inertial navigation system horizontally, record it as the first position, and keep it still for more than 600 seconds in the first position. Record the average angular rate of the three-axis gyro output during this period. And the accelerometer output relative force average And calculate the initial alignment pose matrix for the first position The attitude matrix contains the misalignment angle error in, N1=U1×E1; Step 2: Attitude tracking: Rotate the inertial navigation system 180° around the azimuth axis to reach the second position. During the rotation, use the gyro output data to solve the attitude differential equation and calculate the attitude matrix at the end of the rotation. Recorded as in: is the attitude matrix solved during the rotation process, and its initial value is is the gyro output angular rate; is the projection of the Earth's rotation angular rate in the inertial navigation coordinate system; Step 3: Alignment at the second position: Keep still for more than 600 seconds at the second position and record the average angular rate of the three-axis gyro output during the still period. And the accelerometer output relative force average according to and Calculate the initial alignment pose matrix for the second position Since the rotation is 180°, the attitude matrix includes the misalignment angle error in, N2=U2×E2; Step 4: Calculate the misalignment angle: Based on the attitude tracking matrix and the second position alignment pose matrix Calculate the misalignment angle Calculate the corrected attitude matrix Step 5: Calculate the gyro and accelerometer bias and inject the calculation results into the inertial navigation system memory parameters to complete the bias error calibration: Calculate gyro bias ε b : Calculating Accelerometer Bias in: is the projection of the Earth's rotation angular velocity on the northeastern sky geographic coordinate system, g n =[0 0 -g] T , g is the local gravitational acceleration modulus.

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