High-precision calibration method for rotation modulation inertial navigation residual drift

Abstract

The invention belongs to the technical field of inertial navigation, relates to a high-precision calibration method for residual drift of a rotation modulation inertial navigation system, and is suitable for a long-endurance flight environment of an aircraft. According to the method, a mathematical model of the longitude and latitude navigation error of the rotary inertial navigation geographical system and the sky-direction residual drift, the north-direction residual drift and the sky-direction mathematical platform error angle of the geographical system is established, and the long-endurance navigation test of eight positions at the azimuth angle interval of 0-360 degrees and 45 degrees is designed; accurate identification of sky-direction and north-direction residual drifts and alignment course errors in different directions is realized. The method has the advantages of high residual drift identification precision, obvious improvement of long-endurance navigation performance, strong autonomy and easy realization.

Description

Technical Field

[0001] The invention belongs to the technical field of inertial navigation and relates to a high-precision calibration method for residual drift of a rotationally modulated inertial navigation. Background Art

[0002] The rotational modulation inertial navigation system uses the alternating symmetrical and orderly rotation of the rotating mechanism to drive the IMU components to rotate in sequence, so that the constant errors of the three-axis gyroscope and accelerometer are automatically compensated in the geographic system, which greatly improves the long-duration navigation performance of the inertial navigation system. However, due to the combined influence of various factors such as gyro drift changes, carrier maneuvers, magnetic fields, and temperature fields, according to the results of engineering practice, it is found that the gyro drift cannot be fully modulated, and there is still a certain amount of equivalent geographic system residual drift. This residual drift restricts the further improvement of the performance of the rotational modulation inertial navigation system and is one of the problems that urgently need to be tackled and solved. Summary of the invention

[0003] The purpose of the present invention is to provide a high-precision calibration method for residual drift of a rotating modulated inertial navigation system, which can further improve the long-duration navigation performance of the rotating inertial navigation system.

[0004] Technical solution of the present invention: In order to achieve the above-mentioned purpose of the invention, according to the first aspect of the present invention, a high-precision calibration method for the residual drift of a rotational modulated inertial navigation is proposed. Aiming at the residual drift error unique to the rotational inertial navigation, a simplified nine-dimensional Kalman filter model is designed, and the filtering process is performed at eight different positions respectively. Finally, the filtering results at each position are fitted by Fourier series to obtain the fitting coefficients of the three drifts.

[0005] The specific steps include:

[0006] Step 1: After the rotation modulation inertial navigation is aligned, it enters the navigation state, collects the real-time update values ​​of longitude and latitude during the navigation process, and records the heading angle ψ at the end of the alignment;

[0007] Step 2: Based on the real-time updated values ​​of longitude and latitude, a simplified nine-dimensional Kalman filter model is used to estimate the celestial residual drift, the north residual drift, and the celestial mathematical platform error angle. The inertial navigation attitude angle is set to (0,0,0), and the attitude matrix is ​​always a unit matrix. By deleting the three-axis gyro drift and the three-axis added zero bias state quantity, and adding the two-dimensional state quantity of the geographic system north drift and the geographic system celestial drift, the accurate separation of the geographic system drift and the alignment heading error is achieved.

[0008] Step 3: Rotate the turntable 45° and perform steps 1 to 2;

[0009] Step 4: Repeat steps 1 to 3 to enable the system to complete single position drift estimation at the heading angles ψ+K×45°, K=1, 2, ..., 7 respectively;

[0010] Step 5: Using the 8 sets of azimuth angles and the estimated values ​​of the celestial residual drift and the northward residual drift, Fourier series is used for fitting to obtain the final calibration values ​​of the celestial residual drift and the northward residual drift;

[0011] Step 6: During navigation, the angular velocity compensation is calculated using the celestial and north residual drift calibration values ​​and the aircraft system's real-time heading angle and added to the gyro's original data. Strapdown calculation is then performed to update the velocity, position, and attitude to obtain long-duration, high-precision navigation results.

[0012] In a possible embodiment, in step 2, the state variables of the simplified nine-dimensional Kalman filter model are as follows: K =[δφ,δλ,δV E ,δV N ,φ E ,φ N ,φ U ,D N ,D U ] T

[0013] Among them, δφ is the latitude error, δλ is the longitude error, δV E is the eastward velocity error, δV N is the north velocity error, φ E is the east declination angle, φ N is the north declination angle, φ U is the celestial declination angle, and D N Geography Department Northward Residual Drift, D U It is the residual drift of the geographical system;

[0014] The state matrix F is a 7×7 matrix, where the element F(i,j) in the i-th row and j-th column of the F matrix is ​​defined as follows, and all undefined elements are 0;

[0015]

[0016] F(3,6)=-f U ;

[0017]

[0018]

[0019] Where R is the radius of the earth, h is the local height, ω ie is the angular rate of the Earth's rotation. n ,ω u are the north and celestial components of the Earth's rotation angular velocity; φ is the local latitude; V E V is the eastward velocity in the geographic system; N is the north velocity in the geographic system; f EIt is the eastward force of the geographical system; f N It is the north direction relative force of the geographical system; f U For the geography department, the sky direction is compared; It is the first row and first column element of the attitude transformation matrix of the aircraft system relative to the geographic system;

[0020] The measurement matrix H has a dimension of 4×9, and all elements except the following are 0:

[0021] H(1,1)=1,H(2,2)=1,H(3,3)=1,H(4,4)=1

[0022] The Kalman filter P matrix is ​​initialized to a 9×9 dimensional matrix:

[0023] P=diag(6e-8,6e-8,0.25,0.25,3e-4,3e-4,6e-2,1e-12,1e-12)

[0024] The Kalman filter Q matrix is ​​initialized to a 25×25 dimensional matrix:

[0025] Q=diag(0,0,5e-5,5e-5,5e-13,5e-13,5e-13,0,0);

[0026] Kalman filter R matrix:

[0027] R=diag(2.47e-2,2.47e-2,1,1).

[0028] In one possible embodiment, in step 2, the attitude matrix only sets the diagonal elements to 1: The remaining elements of the attitude matrix are set to 0: By setting the rotating inertial navigation attitude matrix to a constant value, the attitude matrix change caused by the rotation is prevented from affecting the geographic system drift estimation.

[0029] In a possible embodiment, in step 2, the Kalman filter estimation value at the first hour of the celestial deflection angle is taken as As the result of the celestial deflection estimation, take the Kalman filter estimation value of the north drift and celestial drift at the 6th hour As the estimated results of northward drift and celestial drift At the same time, the equivalent eastward drift is calculated using the estimated celestial deflection angle: in, is the estimated eastward drift.

[0030] In a possible embodiment, in step 5, after completing the drift measurement test at 8 different azimuth angles, Fourier series fitting is performed using each set of heading angles and drift estimation values ​​according to the following formula;

[0031]

[0032] in, are the estimated residual drifts in the east, north and sky directions of the ith test position respectively; A E , B E are the Fourier fitting coefficients of the first eastward residual drift and the second eastward residual drift; A N , B N are the Fourier fitting coefficients of the first northward residual drift and the second northward residual drift; A U , B U They are the Fourier fitting coefficients of the residual drift on the first day and the Fourier fitting coefficients of the residual drift on the second day.

[0033] In a possible embodiment, in step 6, the gyro angle increment correction value is calculated using the following formula:

[0034] in, is the gyro angle increment correction value, is the attitude transformation matrix of the IMU system relative to the geographic system; ψ b is the real-time heading angle of the aircraft system, and DT is the calculation period.

[0035] In a possible embodiment, in step 6, the gyro angle increment output value is:

[0036] in, It is the output after gyro angle increment correction. The raw output of the gyro angle increment.

[0037] In a possible embodiment, the solution period is 0.0025 s.

[0038] Beneficial technical effects of the present invention:

[0039] Aiming at the problem that the long-time navigation performance of rotating inertial navigation is seriously restricted by residual drift, the present invention establishes a simplified 9-dimensional Kalman state filter based on the equivalent drift action mechanism, and performs high-precision calibration calculation of the residual drift of the rotating inertial navigation by designing an eight-position turntable test, which has the advantages of high precision and strong practicality. It can effectively solve the problem of the influence of the residual drift of the rotating inertial navigation, and can be widely used in various rotating inertial navigation long-time navigation fields, including airborne, land-based and vehicle-mounted. BRIEF DESCRIPTION OF THE DRAWINGS

[0040] Figure 1 Schematic diagram of three robots using single-line laser radar to collect environmental information in a preferred embodiment of the present invention;

[0041] Figure 2 A schematic diagram comparing the northward residual drift of the preferred embodiment of the present invention and the comparative example;

[0042] Figure 3 Schematic diagram comparing the celestial residual drift of the preferred embodiment of the present invention and the comparative example. DETAILED DESCRIPTION

[0043] In order to make the purpose, technical solution and advantages of the present invention more clear, the embodiments of the present invention are described in detail below. It should be noted that the embodiments and features in the embodiments of the present application can be combined with each other arbitrarily without conflict.

[0044] Embodiment 1:

[0045] A high-precision calibration method for residual drift of rotational modulation inertial navigation system, such as Figure 1 As shown, the following steps are included:

[0046] Step 1. The rotating inertial navigation system is fixedly installed on the single-axis azimuth turntable. After power-on initialization, the rotating frame returns to zero. After alignment is completed, it enters the navigation state. Collect the longitude and latitude update values ​​during the navigation process, and record the heading angle ψ at the end of alignment.

[0047] Step 2: Use the real-time updated values ​​of longitude and latitude to calculate the longitude and latitude navigation errors, and use the established Kalman filter model to estimate the celestial residual drift, the north residual drift, and the celestial mathematical platform error angle. The Kalman filter state variables are reduced to 9 dimensions: X K =[δφ,δλ,δV E ,δV N ,φ E ,φ N ,φ U ,D N ,D U ] T

[0048] Among them, δφ is the latitude error, δλ is the longitude error, δV E is the eastward velocity error, δV N is the north velocity error, φ E is the east declination angle, φ N is the north declination angle, φ U is the celestial declination angle, and D N Geography Department Northward Residual Drift, D U It is the residual drift of the geographic system.

[0049] The state matrix F is a 7×7 matrix, where the element F(i,j) in the i-th row and j-th column of the F matrix is ​​defined as follows, and all undefined elements are 0.

[0050]

[0051] F(3,6)=-f U ;

[0052]

[0053]

[0054] Where R is the radius of the earth, h is the local height, ω ie is the angular rate of the Earth's rotation. n ,ω u is the north and celestial components of the Earth's rotation angular velocity. φ is the local latitude. V E V is the eastward velocity in the geographic system; N is the north velocity in the geographic system; f E It is the eastward force of the geographical system; f N It is the north direction relative force of the geographical system; f U It is a comparison of the geographical direction. It is the first row and first column element of the attitude transformation matrix of the aircraft system relative to the geographic system.

[0055] The measurement matrix H has a dimension of 4×9, and all elements except the following are 0:

[0056] H(1,1)=1,H(2,2)=1,H(3,3)=1,H(4,4)=1

[0057] The Kalman filter P matrix is ​​initialized to a 9×9 dimensional matrix:

[0058] P=diag(6e-8,6e-8,0.25,0.25,3e-4,3e-4,6e-2,1e-12,1e-12)

[0059] The Kalman filter Q matrix is ​​initialized to a 25×25 dimensional matrix:

[0060] Q=diag(0,0,5e-5,5e-5,5e-13,5e-13,5e-13,0,0);

[0061] Kalman filter R matrix:

[0062] R=diag(2.47e-2,2.47e-2,1,1)

[0063] Step 3: Rotate the turntable 45° and perform steps 1 to 2.

[0064] Step 4: Repeat steps (1) to (3) to enable the system to complete single position drift estimation at the heading angle ψ+K×45° (K=1, 2, ..., 7).

[0065] Step 5: In the single-position test, take the Kalman filter estimate at the first hour of the celestial deflection angle As the result of the celestial deflection estimation. Take the Kalman filter estimation value of the north drift and celestial drift at the 6th hour as the estimation result of the north drift and celestial drift. At the same time, use the celestial deflection estimation value to calculate the equivalent east drift: in, is the estimated eastward drift.

[0066] After completing the drift test at eight different azimuth angles, Fourier series fitting was performed using each set of heading angles and drift estimates.

[0067]

[0068] in, A are the estimated values ​​of the residual drift in the east, north and sky directions of the i-th test position respectively. E , B E , A N , B N , A U , B U are the Fourier fitting coefficients of the residual drift in the east, north and celestial directions respectively.

[0069] Step 6: During navigation, use the celestial and north residual drift calibration values ​​and the real-time heading angle of the aircraft system to calculate the angular velocity compensation and add it to the gyro original data, then perform strapdown calculation to update the velocity, position and attitude to obtain long-duration high-precision navigation results. Use the fitting coefficient to calculate the 2.5ms gyro angle increment correction value:

[0070]

[0071] in, is the gyro angle increment correction value, is the attitude transformation matrix of the IMU system relative to the geographic system. b is the real-time heading angle of the aircraft system, and DT is the calculation period of 0.0025s.

[0072] The incremental output value of the gyro angle is:

[0073] in, It is the output after gyro angle increment correction. The raw output of the gyro angle increment.

[0074] Comparative Example

[0075] Step 1. The rotating inertial navigation system is fixedly installed on the single-axis azimuth turntable. After power-on initialization, the rotating frame returns to zero. After alignment is completed, it enters the navigation state. Collect the longitude and latitude update values ​​during the navigation process, and record the heading angle ψ at the end of alignment.

[0076] Step 2: Use the real-time updated values ​​of longitude and latitude to calculate the longitude and latitude navigation errors, and use the Kalman filter model to estimate the residual drift in the sky and the residual drift in the north. The Kalman filter state variable is 25 dimensions:

[0077]

[0078] Note: δφ is the latitude error, δλ is the longitude error, δh is the height error, δV E is the eastward velocity error, δV N is the north velocity error, δV U is the celestial velocity error, φ E is the east declination angle, φ N is the north declination angle, φ U is the celestial declination angle, and D X X-axis gyro drift, D Y is the Y-axis gyro drift, D Z For Z-axis gyro drift, Add zero position to the X axis. Add zero position to the Y axis. Add zero position for Z axis, D N The northward drift of the geographical system, D U is the celestial drift of the geographic system, α XZ For the gyro installation declination angle XZ, α XY For gyro installation declination XY, α YX Installation angle YX, α for gyro ZX Gyro installation declination angle ZX, ε XY To add the installation deflection angle XY, δK GZ is the Z-axis gyro scale coefficient error, δK AX X plus the scale factor error, δK AZ Add the scale factor error to the Z axis.

[0079] The state matrix F is a 25×25 matrix, where the element F(i,j) in the i-th row and j-th column of the F matrix is ​​defined as follows, and all undefined elements are 0.

[0080]

[0081] F(3,6)=1;

[0082]

[0083] F(4,9)=fN ; F(4:6,13:15)=C;

[0084]

[0085] F(5,7)=f U ; F(5,9)=-f E ;

[0086]

[0087] F(7:9,10:12)=C;

[0088]

[0089]

[0090] Note: is the average angular velocity of the IMU Y and Z axes during the filtering period; It is the average specific force of IMU X and Z axis in the filtering period. ie is the Earth's rotation angular velocity. E It is the eastward force of the geographical system; f N It is the north direction relative force of the geographical system; U It is a comparison of the geographical direction.

[0091] The measurement matrix H has a dimension of 3×25, and all elements except the following are 0:

[0092] H(1,4)=1,H(2,5)=1,H(3,6)=1

[0093] The Kalman filter P matrix is ​​initialized to a 25×25 dimensional matrix:

[0094] P=diag(6e-8,6e-8,0,0.25,0.25,0,3e-4,3e-4,6e-2,1e-12,1e-12,1e-12,

[0095] 2.5e-5, 2.5e-5, 2.5e-5, 2.35e-15, 2.35e-15,0,…,0)

[0096] The Kalman filter Q matrix is ​​initialized to a 25×25 dimensional matrix:

[0097] Q=diag(0,0,0,5e-5,5e-5,5e-5,5e-13,5e-13,5e-13,0,...,0,0,0);

[0098] Kalman filter R matrix:

[0099] R=diag(4e-2,4e-2,4e-2)

[0100] Step 3: In the single-position test, take the Kalman filter estimate at the 3rd hour of the celestial deflection angle As the result of the celestial deflection estimation. Take the Kalman filter estimation value of the north drift and celestial drift at the third hour as the estimation result of the north drift and celestial drift. At the same time, use the celestial deflection estimation value to calculate the equivalent east drift: in, is the estimated eastward drift.

[0101] Step 4: During navigation, use the estimated values ​​of the residual drift in the celestial direction and the north direction and the real-time heading angle of the aircraft system to calculate the angular velocity compensation and add it to the original gyro data. Then perform strapdown calculation to update the velocity, position and attitude to obtain long-duration high-precision navigation results. Use the fitting coefficient to calculate the 2.5ms gyro angle increment correction value:

[0102]

[0103] in, is the gyro angle increment correction value, is the attitude transformation matrix of the IMU system relative to the geographic system. b is the real-time heading angle of the aircraft system, and DT is the calculation period of 0.0025s.

[0104] The incremental output value of the gyro angle is:

[0105] in, It is the output after gyro angle increment correction. The raw output of the gyro angle increment.

[0106] like Figure 2 As shown, the embodiment and the comparative example have a residual drift of -0.001° / h to the north, such as Figure 3 As shown, by comparing the estimation results of the 0° / h azimuth residual drift, it can be seen that the model used in the embodiment has a fast convergence speed and high estimation accuracy in estimating the residual drift.

[0107] For the purpose of explanation, the above-mentioned specific implementation methods are only exemplary, in order to better enable those skilled in the art to understand this patent, and should not be understood as limiting the scope of this patent; any technical solutions obtained by equivalent substitution or equivalent transformation fall within the protection scope of the present invention.

Claims

1. A high-precision calibration method for residual drift of a rotationally modulated inertial navigation system, characterized in that: The steps include: Step 1: After the rotation modulation inertial navigation is aligned, it enters the navigation state, collects the real-time update values ​​of longitude and latitude during the navigation process, and records the heading angle ψ at the end of the alignment; Step 2: Estimate the residual drift in the celestial direction, the residual drift in the north direction, and the error angle of the mathematical platform in the celestial direction using a simplified nine-dimensional Kalman filter model based on the real-time updated values ​​of longitude and latitude, set the inertial navigation attitude angle to (0,0,0), and the attitude matrix is ​​always the unit matrix; Step 3: Rotate the turntable 45° and perform steps 1 to 2; Step 4: Repeat steps 1 to 3 to enable the system to complete single position drift estimation at the heading angles ψ+K×45°, K=1, 2, ..., 7 respectively; Step 5: Using the 8 sets of azimuth angles and the estimated values ​​of the celestial residual drift and the northward residual drift, Fourier series is used for fitting to obtain the final calibration values ​​of the celestial residual drift and the northward residual drift; Step 6: During navigation, the angular velocity compensation is calculated using the celestial and north residual drift calibration values ​​and the aircraft system's real-time heading angle and added to the gyro's original data. Strapdown calculation is then performed to update the velocity, position, and attitude to obtain long-duration, high-precision navigation results.

2. The high-precision calibration method for residual drift of a rotational modulation inertial navigation system according to claim 1, characterized in that: In step 2, the state variables of the simplified nine-dimensional Kalman filter model are as follows: K =[δφ,δλ,δV E ,δV N ,φ E ,φ N ,φ U ,D N ,D U ] T Among them, δφ is the latitude error, δλ is the longitude error, δV E is the eastward velocity error, δV N is the north velocity error, φ E is the east declination angle, φ N is the north declination angle, φ U is the celestial deflection angle, and D N Geography Department Northward Residual Drift, D U It is the residual drift of the geographical system; The state matrix F is a 7×7 matrix, where the element F(i,j) in the i-th row and j-th column of the F matrix is ​​defined as follows, and all undefined elements are 0; F(3,6)=-f U ; Where R is the radius of the earth, h is the local height, ω ie is the angular rate of the Earth's rotation. n ,ω u are the north and celestial components of the Earth's rotation angular velocity; φ is the local latitude; V E V is the eastward velocity in the geographic system; N is the north velocity in the geographic system; f E It is the eastward force of the geographical system; f N It is the north direction relative force of the geographical system; f U For the geography department, the sky direction is compared; It is the first row and first column element of the attitude transformation matrix of the aircraft system relative to the geographic system; The measurement matrix H has a dimension of 4×9, and all elements except the following are 0: H(1,1)=1,H(2,2)=1,H(3,3)=1,H(4,4)=1 The Kalman filter P matrix is ​​initialized to a 9×9 dimensional matrix: P=diag(6e-8,6e-8,0.25,0.25,3e-4,3e-4,6e-2,1e-12,1e-12) The Kalman filter Q matrix is ​​initialized to a 25×25 dimensional matrix: Q=diag(0,0,5e-5,5e-5,5e-13,5e-13,5e-13,0,0); Kalman filter R matrix: R=diag(2.47e-2,2.47e-2,1,1).

3. The high-precision calibration method for residual drift of a rotational modulation inertial navigation system according to claim 2 is characterized in that: In step 2, the attitude matrix only sets the diagonal elements to 1: The remaining elements of the attitude matrix are set to 0:

4. The method for high-precision calibration of residual drift of a rotational modulation inertial navigation system according to claim 3 is characterized in that: In step 2, the Kalman filter estimated value at the first hour of the celestial deflection is taken As the result of the celestial deflection estimation, take the Kalman filter estimation value of the north drift and celestial drift at the 6th hour As the estimated results of northward drift and celestial drift At the same time, the equivalent eastward drift is calculated using the estimated celestial deflection angle: in, is the estimated eastward drift.

5. The high-precision calibration method for residual drift of a rotationally modulated inertial navigation system according to claim 4 is characterized in that: In step 5, after completing the drift test at 8 different azimuth angles, Fourier series fitting is performed using each set of heading angles and drift estimation values ​​according to the following formula; in, are the estimated residual drifts in the east, north and sky directions of the ith test position respectively; A E , B E are the Fourier fitting coefficients of the first eastward residual drift and the second eastward residual drift; A N , B N are the Fourier fitting coefficients of the first northward residual drift and the second northward residual drift; A U , B U They are the Fourier fitting coefficients of the residual drift on the first day and the Fourier fitting coefficients of the residual drift on the second day.

6. The high-precision calibration method for residual drift of a rotationally modulated inertial navigation system according to claim 5, characterized in that: In step 6, the gyro angle increment correction value is calculated using the following formula: in, is the gyro angle increment correction value, is the attitude transformation matrix of the IMU system relative to the geographic system; ψ b is the real-time heading angle of the aircraft system, and DT is the calculation period.

7. The method for high-precision calibration of residual drift of a rotationally modulated inertial navigation system according to claim 6, characterized in that: In step 6, the gyro angle increment output value is: in, It is the output after gyro angle increment correction. The raw output of the gyro angle increment.

8. The high-precision calibration method for residual drift of a rotationally modulated inertial navigation system according to claim 6, characterized in that: The solution period is 0.0025s.

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