Three-self-inertial-unit rapid alignment and inertial error parameter calibration integrated method

Abstract

The invention relates to an integrated method for rapid alignment and inertial error parameter calibration of three self-inertial units, which belongs to the technical field of inertial navigation and comprises the following steps: S1, based on an initial carrier solidification coordinate system, performing coarse alignment on the three self-inertial units to obtain an initial alignment attitude matrix; s2, constructing a closed-loop Kalman filter based on a random closed-loop control system; and S3, inputting inertial device output of the three self-inertial units and the initial alignment attitude matrix obtained in the step S1 into the closed-loop Kalman filter constructed in the step S2, performing fine alignment on the three self-inertial units, and calibrating and compensating inertial error parameters. According to the method, high-precision initial alignment of the three-self-inertia unit is realized, inertial error parameters can be calibrated and compensated during alignment, the alignment and calibration processes are integrated, the alignment and calibration time of the three-self-inertia unit is shortened, and the navigation precision of the three-self-inertia unit is improved.

Description

Technical Field

[0001] The present invention belongs to the technical field of inertial navigation, and particularly relates to an integrated method for rapid alignment of a three-self inertial assembly and calibration of inertial error parameters. Background Art

[0002] The three-self inertial assembly is equipped with a two-axis turntable, and can perform "self-testing", "self-alignment", and "self-calibration" without disassembly, greatly reducing the maintenance cost. As a safe, reliable, passive, and high-precision attitude and position measurement device, due to its outstanding advantages, it has been rapidly popularized and applied on a large scale, especially in the fields of aviation, aerospace, navigation, etc. For example, the invention patent with the publication number CN110995083A provides a high-reliability locking control method and control system for three-self inertial assembly products, the invention patent with the publication number CN113503895A discloses a method for estimating the size of accelerometers of a three-self inertial assembly based on Kalman filtering, the invention patent with the publication number CN114285343A provides a method and system for multi-turn rotation control of a rotating mechanism of three-self inertial assembly products, and the invention patent with the publication number CN118092873A discloses a method for designing the navigation software architecture of a three-self inertial assembly based on a multi-core processor.

[0003] However, the "self-alignment" and "self-calibration" processes of the existing three-self inertial assembly are separated, resulting in long alignment and calibration times and low accuracy. Summary of the Invention

[0004] In view of the deficiencies of the prior art, the purpose of the present invention is to provide a simple and high-precision integrated method for rapid alignment of a three-self inertial assembly and calibration of inertial error parameters to solve or improve the defects existing in the prior art.

[0005] To achieve the above purpose, the present invention adopts the following technical solutions: An integrated method for rapid alignment of a three-self inertial assembly and calibration of inertial error parameters, comprising the following steps: S1. Based on the initial carrier solidification coordinate system, perform rough alignment on the three-self inertial assembly to obtain an initial alignment attitude matrix; S2. Construct a closed-loop Kalman filter based on a random closed-loop control system; S3. Input the output of the inertial devices of the three-self inertial assembly and the initial alignment attitude matrix obtained in step S1 into the closed-loop Kalman filter constructed in step S2 to perform fine alignment on the three-self inertial assembly, and calibrate and compensate the inertial error parameters.

[0006] Preferably, the specific steps of step S1 are as follows: S11. Construct the following coordinate systems: The navigation coordinate system is the n - system, the vehicle coordinate system is the b - system, the geocentric inertial coordinate system is the i - system, the earth coordinate system is the e - system, the initial navigation coordinate system is the n0 - system, the initial inertial coordinate system is the i0 - system, the initial earth coordinate system is the e0 - system, and the initial vehicle fixed coordinate system is the i b0 - system; S12. Based on the constructed coordinate systems, perform rough alignment on the three - axis inertial measurement unit (IMU) based on the initial vehicle fixed coordinate system to obtain the initial alignment attitude matrix as follows: In the formula, is the initial alignment attitude matrix, is the attitude transformation matrix from the i0 - system to the n - system, is the attitude transformation matrix from the i b0 - system to the i0 - system, is the attitude transformation matrix from the b - system to the i b0 - system; Among them, In the formula, ω ie is the earth's angular velocity of rotation, t is the alignment time, L t is the local latitude at time t; Among them, In the formula, is the integral of the gravitational acceleration in the i0 - system from t0 to t1, t0 is the initial time of alignment, t1 is the intermediate time of alignment from the initial time to the current time, t2 is the current time of alignment, g n is the gravitational acceleration, and T represents the transpose of the matrix; ui 0 (t2) is the integral of the gravitational acceleration in the i0 - system from t0 to t2, t0 is the initial time of alignment, and t2 is the current time of alignment; is the integral of the gravitational acceleration in the i b0 - system from t0 to t1; is the integral of the gravitational acceleration in the i b0 - system from t0 to t2; Among them, is obtained by solving through the following formula: In the formula, is the derivative with respect to relative time, is the three-dimensional angular rate vector of the carrier relative to the inertial system measured by the gyroscope in the three-axis inertial assembly. The symbol × represents the skew-symmetric matrix of the vector. represents the vector and the corresponding skew-symmetric matrix.

[0007] Preferably, the specific steps of step S2 are as follows: S21. Construct the state variables of the 33-dimensional closed-loop Kalman filter as follows: In the formula, X is the state variable of the 33-dimensional closed-loop Kalman filter. is the three-dimensional attitude error, δv n is the three-dimensional velocity error, δP is the three-dimensional position error, X g is the nine-dimensional inertial error parameter of the gyroscope, X a is the twelve-dimensional inertial error parameter of the accelerometer, δl b is the three-dimensional external lever arm error where the rotation center of the indexing mechanism does not coincide with the sensitive center of the inertial measurement unit; S22. Construct the state equation of the 33-dimensional closed-loop Kalman filter as follows: In the formula, is the derivative of X with respect to time, F’ is the state transition matrix of the 33-dimensional closed-loop Kalman filter, G’ is the control input matrix of the 33-dimensional closed-loop Kalman filter, and u is the control input vector; In the formula, F is the state transition matrix of the 30-dimensional closed-loop Kalman filter, 0 30×3 is a 30-row 3-column zero matrix, 0 3×30 is a 3-row 30-column zero matrix, 0 3×3 is a 3-row 3-column zero matrix; G is the control input matrix of the 30-dimensional closed-loop Kalman filter, 0 3×6 is a 3-row 6-column zero matrix; In the formula, F 11 is the first block matrix of F, F 12 is the second block matrix of F, F 13 is the third block matrix of F, F 14 is the fourth block matrix of F, F 21 is the fifth block matrix of F, F 22 is the sixth block matrix of F, F 23 is the seventh block matrix of F, F 25 is the eighth block matrix of F, F 32 is the ninth block matrix of F, F 33The tenth block matrix of F, 0 3×12 Is a zero matrix of 3 rows and 12 columns, 0 3×9 Is a zero matrix of 3 rows and 9 columns, 0 9×3 Is a zero matrix of 9 rows and 3 columns, 0 9×9 Is a zero matrix of 9 rows and 9 columns, 0 9×12 Is a zero matrix of 9 rows and 12 columns, 0 12×3 Is a zero matrix of 12 rows and 3 columns, 0 12×9 Is a zero matrix of 12 rows and 9 columns, 0 12×12 Is a zero matrix of 12 rows and 12 columns; In the formula, Is the three-dimensional angular rate vector of the navigation system where the carrier is located relative to the inertial system. The symbol × represents taking the skew-symmetric matrix of the vector, Represents the vector The corresponding skew-symmetric matrix; In the formula, L is the local geographical latitude, h is the local geographical height, R M Is the local Earth meridian radius, R N Is the local Earth prime vertical radius; In the formula, v E Is the eastward velocity, v N Is the northward velocity; In the formula, Is the transformation matrix from the body frame to the navigation frame, Is the component of the gravity vector on the x-axis of the body frame, Is the component of the gravity vector on the y-axis of the body frame, Is the component of the gravity vector on the z-axis of the body frame, I2 is the 2×2 identity matrix, I3 is the 3×3 identity matrix, 0 1×2 Is a zero matrix of 1 row and 2 columns, 0 2×1 Is a zero matrix of 2 rows and 1 column; In the formula, f b Is the three-dimensional specific force vector of the carrier relative to the inertial system measured by the accelerometer in the triple redundant inertial measurement unit. The symbol × represents taking the skew-symmetric matrix of the vector, Represents the vector The corresponding skew-symmetric matrix; In the formula, Is the angular rate vector of the Earth's rotation relative to the inertial system, is the angular rate vector of the navigation system relative to the Earth, and the symbol × represents the skew-symmetric matrix of the vector. represents the vector corresponding skew-symmetric matrix, v n is the vehicle velocity vector, v n × represents the vector v n corresponding skew-symmetric matrix; In the formula, 0 3×3 is a 3×3 zero matrix, 0 24×3 is a 24×3 zero matrix; S23. The observation equation of the 33-dimensional closed-loop Kalman filter is constructed as follows: Z = HX + V; In the formula, Z is the measurement vector, H is the observation matrix, H = [0 3×3 I3 0 3×3 0 3×21 , 0 3×21 is a 3×21 zero matrix, and V is the observation noise; S24. The feedback compensation form of the filtering estimation result of the 33-dimensional closed-loop Kalman filter is constructed as follows: In the formula, is the filtering result of the transformation matrix from the vehicle coordinate system to the navigation system, is the filtering result of the vehicle velocity vector, is the filtering result of the latitude, δL is the measurement error of the latitude, λ is the local geographical longitude, and δλ is the measurement error of the longitude, is the filtering result of the altitude, δh is the measurement error of the altitude, K g is the scale factor matrix of the gyroscope, is the filtering result of the scale factor matrix of the gyroscope, δK g is the measurement error of the scale factor matrix of the gyroscope, ε is the zero bias of the gyroscope, is the filtering result of the zero bias of the gyroscope, δε is the measurement error of the zero bias of the gyroscope, K a is the scale factor matrix of the accelerometer, is the filtering result of the scale factor matrix of the accelerometer, δK a is the measurement error of the scale factor matrix of the accelerometer, is the zero bias of the accelerometer, is the filtering result of the zero bias of the accelerometer, is the measurement error of the zero bias of the accelerometer.

[0008] Preferably, the specific steps of step S3 are as follows: Input the inertial device output of the three-self inertial unit and the initial alignment attitude matrix obtained in step S1 into the closed-loop Kalman filter constructed in step S2 for Kalman filtering and solution, so as to realize the precise alignment of the three-self inertial unit and obtain the calibration result of inertial error parameters; compensate the navigation result in the form of feedback compensation of the filtering estimation result constructed in step S24 with the calibration result of inertial error parameters.

[0009] Compared with the prior art, the present invention has the following beneficial effects: The integrated method for rapid alignment of the three-self inertial unit and calibration of inertial error parameters of the present invention realizes the high-precision initial alignment of the three-self inertial unit, and can also calibrate and compensate inertial error parameters during alignment, integrating the two processes of alignment and calibration, reducing the alignment and calibration time of the three-self inertial unit, improving the navigation accuracy of the three-self inertial unit, and solving the problem that the "self-alignment" and "self-calibration" processes of the existing three-self inertial unit are separated, resulting in long alignment and calibration time and low accuracy.

[0010] Using the method of the present invention, the alignment time of the three-self inertial unit is 3 minutes, and the alignment result starts to be displayed at 40 seconds. The two horizontal angles can converge quickly, and the oscillation amplitude is relatively small. The heading angle reaches within the theoretical accuracy of 1.2′ of the three-self inertial unit at about 80s and continues to converge within this range; at the same time, the accelerometer zero bias, gyro assembly installation error, and accelerometer installation error can converge quickly, and the gyro drift, gyro scale factor, and accelerometer scale factor converge after about 1 hour; for 3.5h of navigation, the maximum speed error is 0.3m / s, and the maximum position error is 0.5nm / 3.5h; it proves the correctness and accuracy of the method provided by the present invention, can well shorten the alignment and calibration time of the three-self inertial unit, improve the navigation accuracy of the three-self inertial unit, and has good practicability. Description of the Drawings

[0011] In order to more clearly illustrate the technical solutions in the present invention or the prior art, the following will briefly introduce the drawings required for use in the description of the embodiments or the prior art. Obviously, the drawings in the following description can also be obtained by those of ordinary skill in the art according to these drawings without creative efforts.

[0012] Figure 1 It is a schematic flow chart of an integrated method for rapid alignment of a three-self inertial unit and calibration of inertial error parameters of the present invention.

[0013] Figure 2 It is a schematic diagram of the roll angle after rough alignment obtained by the three-self inertial unit in Experimental Example 1 of the present invention for step S1 verification.

[0014] Figure 3It is a schematic diagram of the pitch angle after coarse alignment obtained by verifying step S1 with the three inertial units in Experimental Example 1 of the present invention.

[0015] Figure 4 It is a schematic diagram of the heading angle after coarse alignment obtained by verifying step S1 with the three inertial units in Experimental Example 1 of the present invention.

[0016] Figure 5 It is a schematic diagram of the gyro drift estimation curve obtained by verifying the method of the present invention with the three inertial units in Experimental Example 2 of the present invention.

[0017] Figure 6 It is a schematic diagram of the accelerometer zero bias estimation curve obtained by verifying the method of the present invention with the three inertial units in Experimental Example 2 of the present invention.

[0018] Figure 7 It is a schematic diagram of the gyro scale factor estimation curve obtained by verifying the method of the present invention with the three inertial units in Experimental Example 2 of the present invention.

[0019] Figure 8 It is a schematic diagram of the accelerometer scale factor estimation curve obtained by verifying the method of the present invention with the three inertial units in Experimental Example 2 of the present invention.

[0020] Figure 9 It is a schematic diagram of the gyro assembly installation error estimation curve obtained by verifying the method of the present invention with the three inertial units in Experimental Example 2 of the present invention.

[0021] Figure 10 It is a schematic diagram of the accelerometer assembly installation error estimation curve obtained by verifying the method of the present invention with the three inertial units in Experimental Example 2 of the present invention.

[0022] Figure 11 It is a schematic diagram of the heading angle curve after fine alignment obtained by verifying the method of the present invention with the three inertial units in Experimental Example 2 of the present invention.

[0023] Figure 12 It is a schematic diagram of the velocity error curve obtained by verifying the method of the present invention with the three inertial units in Experimental Example 2 of the present invention.

[0024] Figure 13 It is a schematic diagram of the position error curve obtained by verifying the method of the present invention with the three inertial units in Experimental Example 2 of the present invention. Detailed implementation manners

[0025] To make the objectives, technical solutions, and advantages of the present invention clearer, the technical solutions in the present invention will be clearly and completely described below with reference to the accompanying drawings in the present invention. Apparently, the described embodiments are some, but not all, of the embodiments of the present invention. All other embodiments obtained by those of ordinary skill in the art based on the embodiments in the present invention without creative efforts shall fall within the protection scope of the present invention. To make the above features and advantages of the present invention more obvious and understandable, specific embodiments are given below and detailed descriptions are made in conjunction with the accompanying drawings as follows.

[0026] As Figure 1 shown, an embodiment of the present invention provides an integrated method for rapid alignment of a three-self inertial unit and calibration of inertial error parameters, including the following steps: S1. Based on the initial carrier-fixed coordinate system, perform rough alignment on the three-self inertial unit to obtain an initial alignment attitude matrix; S2. Construct a closed-loop Kalman filter based on a random closed-loop control system; S3. Input the output of the inertial devices of the three-self inertial unit and the initial alignment attitude matrix obtained in step S1 into the closed-loop Kalman filter constructed in step S2 to perform fine alignment on the three-self inertial unit and calibrate and compensate the inertial error parameters.

[0027] In this embodiment, the specific steps of step S1 are as follows: S11. Construct the coordinate systems as follows: The navigation coordinate system is the n coordinate system, the carrier coordinate system is the b coordinate system, the geocentric inertial coordinate system is the i coordinate system, the earth coordinate system is the e coordinate system, the initial navigation coordinate system is the n0 coordinate system, the initial inertial coordinate system is the i0 coordinate system, the initial earth coordinate system is the e0 coordinate system, and the initial carrier-fixed coordinate system is the i b0 coordinate system; S12. Based on the constructed coordinate systems, perform rough alignment on the three-self inertial unit based on the initial carrier-fixed coordinate system to obtain an initial alignment attitude matrix, as follows: In the formula, is the initial alignment attitude matrix, is the attitude transformation matrix from the i0 coordinate system to the n coordinate system, is the attitude transformation matrix from the i b0 coordinate system to the i0 coordinate system, is the attitude transformation matrix from the b coordinate system to the i b0 coordinate system; Among them, In the formula, ω ie is the earth's angular velocity of rotation, t is the alignment time, and L t is the local latitude at time t; Among them, In the formula, is the integral of the acceleration due to gravity in the i0 system from t0 to t1, where t0 is the initial alignment time, t1 is the intermediate time from the initial alignment time to the current time, t2 is the current alignment time, and g n is the acceleration due to gravity, and T represents the transpose of a matrix; is the integral of the acceleration due to gravity in the i0 system from t0 to t2, where t0 is the initial alignment time and t2 is the current alignment time; is the integral of the acceleration due to gravity in the i b0 system from t0 to t1; is the integral of the acceleration due to gravity in the i b0 system from t0 to t2; Among them, is obtained by solving through the following formula: In the formula, is the derivative with respect to relative time, is the three-dimensional angular rate vector of the carrier relative to the inertial system measured by the gyroscopes within the three-axis inertial measurement unit. The symbol × represents taking the skew-symmetric matrix of a vector, represents the vector corresponding skew-symmetric matrix.

[0028] In this embodiment, the specific steps of step S2 are as follows: S21. Construct the thirty-three-dimensional closed-loop Kalman filter state variables as follows: In the formula, X is the thirty-three-dimensional closed-loop Kalman filter state variable, is the three-dimensional attitude error, and δv n is the three-dimensional velocity error, δP is the three-dimensional position error, X g is the nine-dimensional inertial error parameter of the gyroscope, X a is the twelve-dimensional inertial error parameter of the accelerometer, and δl b is the three-dimensional external lever arm error where the rotation center of the indexing mechanism does not coincide with the sensitive center of the inertial measurement unit; S22. Construct the state equation of the thirty-three-dimensional closed-loop Kalman filter as follows: In the formula, is the derivative of X with respect to time, F’ is the state transition matrix of the 33-dimensional closed-loop Kalman filter, G’ is the control input matrix of the 33-dimensional closed-loop Kalman filter, and u is the control input vector; Wherein, F is the state transition matrix of the 30-dimensional closed-loop Kalman filter, 0 30×3 is a 30-row and 3-column zero matrix, 0 3×30 is a 3-row and 30-column zero matrix, 0 3×3 is a 3-row and 3-column zero matrix; G is the control input matrix of the 30-dimensional closed-loop Kalman filter, 0 3×6 is a 3-row and 6-column zero matrix; Wherein, F 11 is the first block matrix of F, F 12 is the second block matrix of F, F 13 is the third block matrix of F, F 14 is the fourth block matrix of F, F 21 is the fifth block matrix of F, F 22 is the sixth block matrix of F, F 23 is the seventh block matrix of F, F 25 is the eighth block matrix of F, F 32 is the ninth block matrix of F, F 33 is the tenth block matrix of F, 0 3×12 is a 3-row and 12-column zero matrix, 0 3×9 is a 3-row and 9-column zero matrix, 0 9×3 is a 9-row and 3-column zero matrix, 0 9×9 is a 9-row and 9-column zero matrix, 0 9×12 is a 9-row and 12-column zero matrix, 0 12×3 is a 12-row and 3-column zero matrix, 0 12×9 is a 12-row and 9-column zero matrix, 0 12×12 is a 12-row and 12-column zero matrix; Wherein, is the three-dimensional angular rate vector of the navigation system where the carrier is located relative to the inertial system, and the symbol × represents taking the skew-symmetric matrix of the vector, represents the vector corresponding skew-symmetric matrix; Wherein, L is the local geographic latitude, h is the local geographic height, R M is the local Earth meridian radius, R N is the local Earth prime vertical radius; where \(v\) E is the eastward velocity, and \(v\) N is the northward velocity; where is the transformation matrix from the vehicle frame to the navigation frame, is the component of the gravity vector along the \(x\)-axis of the vehicle frame, is the component of the gravity vector along the \(y\)-axis of the vehicle frame, is the component of the gravity vector along the \(z\)-axis of the vehicle frame, \(I_2\) is the \(2\times2\) identity matrix, \(I_3\) is the \(3\times3\) identity matrix, \(0\) 1×2 is the \(1\times2\) zero matrix, and \(0\) 2×1 is the \(2\times1\) zero matrix; where \(f\) b is the three-dimensional specific force vector of the vehicle relative to the inertial frame measured by the accelerometers in the triple redundant inertial measurement unit. The symbol \(\times\) represents the skew-symmetric matrix of the vector, represents the skew-symmetric matrix corresponding to the vector ; where is the angular rate vector of the Earth relative to the inertial frame, is the angular rate vector of the navigation frame relative to the Earth. The symbol \(\times\) represents the skew-symmetric matrix of the vector, represents the skew-symmetric matrix corresponding to the vector , and \(v\) n is the vehicle velocity vector. \(v\) n \(\times\) represents the skew-symmetric matrix corresponding to the vector \(v\) n ; where \(0\) 3×3 is the \(3\times3\) zero matrix, and \(0\) 24×3 is the \(24\times3\) zero matrix; S23. The observation equation of the 33-dimensional closed-loop Kalman filter is constructed as follows: \(Z = HX+V\); where \(Z\) is the measurement vector, \(H\) is the observation matrix, and \(H = [0\) 3×3 \(I_3\ 0\) 3×3 \ 0\) 3×21 , \(0\) 3×21 is the \(3\times21\) zero matrix, and \(V\) is the observation noise; S24. The feedback compensation form of the filtering estimation result of the 33-dimensional closed-loop Kalman filter is constructed as follows: where is the filtering result of the transformation matrix from the carrier system to the navigation system, is the filtering result of the carrier velocity vector, is the filtering result of the latitude, δL is the measurement error of the latitude, λ is the local geographic longitude, and δλ is the measurement error of the longitude, is the filtering result of the altitude, δh is the measurement error of the altitude, K g is the scale factor matrix of the gyroscope, is the filtering result of the scale factor matrix of the gyroscope, δK g is the measurement error of the scale factor matrix of the gyroscope, ε is the zero bias of the gyroscope, is the filtering result of the zero bias of the gyroscope, δε is the measurement error of the zero bias of the gyroscope, K a is the scale factor matrix of the accelerometer, is the filtering result of the scale factor matrix of the accelerometer, δK a is the measurement error of the scale factor matrix of the accelerometer, is the zero bias of the accelerometer, is the filtering result of the zero bias of the accelerometer, is the measurement error of the zero bias of the accelerometer.

[0029] In this embodiment, the specific steps of step S3 are as follows: Input the inertial device output of the three-self inertial group and the initial alignment attitude matrix obtained in step S1 into the closed-loop Kalman filter constructed in step S2 for Kalman filtering calculation to achieve precise alignment of the three-self inertial group and obtain the calibration result of the inertial error parameters; compensate the navigation result in the form of feedback compensation of the filtering estimation result constructed in step S24 with the calibration result of the inertial error parameters.

[0030] A method for integrating the fast alignment and inertial error parameter calibration of a three-self inertial group in this embodiment realizes the high-precision initial alignment of the three-self inertial group, and can also calibrate and compensate the inertial error parameters during alignment, integrating the two processes of alignment and calibration, reducing the alignment and calibration time of the three-self inertial group, improving the navigation accuracy of the three-self inertial group, and solving the problem that the "self-alignment" and "self-calibration" processes of the existing three-self inertial group are separated, resulting in long alignment and calibration time and low accuracy.

[0031] Experimental example 1: Select a certain three-self inertial group to verify the rough alignment of step S1 of the method of the present invention. Place a certain three-self inertial group on a stationary marble table and perform rough alignment according to step S1 to obtain as Figures 2 to 4The attitude after rough alignment is shown. The alignment time is 3 minutes, and the alignment result starts to be displayed at 40 seconds. The two horizontal angles can converge quickly, and the oscillation amplitude is relatively small. The heading angle reaches within the theoretical accuracy of 1.2′ of the three self-inertial units at about 80 seconds and continues to converge within this range. This method can complete the alignment process in 2 minutes, verifying the effectiveness of step S1 of the method of the present invention.

[0032] Experimental Example 2: A certain three self-inertial unit was selected to verify the method of the present invention. A certain three self-inertial unit was placed on a stationary marble table, and integrated alignment and calibration were performed according to the method of the present invention, obtaining the Figures 5 to 10 calibration results shown. By analyzing the estimated error curve, the zero bias of the accelerometer, the installation error of the gyro assembly, and the installation error of the accelerometer can converge quickly, and the gyro drift, gyro scale factor, and accelerometer scale factor converge after about 1 hour. Then, in order to verify the accuracy of the parameter estimation of this method, the 3.8-hour test data of this test was processed offline. After 10 minutes of alignment, it switched to navigation, including 3 minutes of rough alignment and 6 minutes of closed-loop fine alignment. Figure 11 is the heading angle curve after fine alignment. The heading angle converges within the oscillation range of 2′ after 2 minutes of fine alignment. Figure 12 and Figure 13 are the speed error and position error curves during 3.5 hours of navigation respectively. The maximum speed error is 0.3 m / s, and the maximum position error is 0.5 nm / 3.5 h, indicating that the method of the present invention can accurately estimate the parameters and verifies the effectiveness of the method of the present invention.

[0033] The parts not detailedly disclosed in the present invention belong to the well-known technologies in the art.

[0034] Finally, it should be noted that the above embodiments are only used to illustrate the technical solutions of the present invention and are not intended to limit them. Although the present invention has been described in detail with reference to the foregoing embodiments, those of ordinary skill in the art should understand that they can still modify the technical solutions recorded in the foregoing embodiments, or perform equivalent replacements for some of the technical features. However, such modifications or replacements do not cause the essence of the corresponding technical solutions to deviate from the spirit and scope of the technical solutions of the embodiments of the present invention.

Claims

1. An integrated method for rapid alignment of a three-axis inertial measurement unit and calibration of inertial error parameters, characterized in that, It includes the following steps: S1. Based on the initial carrier fixed coordinate system, conduct rough alignment on the three-self inertial group to obtain the initial alignment attitude matrix; S2. Construct a closed-loop Kalman filter based on a random closed-loop control system; S3. Input the output of the inertial devices of the three-self inertial group and the initial alignment attitude matrix obtained in step S1 into the closed-loop Kalman filter constructed in step S2, conduct fine alignment on the three-self inertial group, and calibrate and compensate the inertial error parameters.

2. A method for integrating the rapid alignment of a three-self inertial measurement unit and the calibration of inertial error parameters according to claim 1, characterized in that The specific steps of step S1 are as follows: S11. Construct the coordinate system as follows: The navigation coordinate system is the n-frame, the vehicle body coordinate system is the b-frame, the geocentric inertial coordinate system is the i-frame, the earth coordinate system is the e-frame, the initial navigation coordinate system is the n0-frame, the initial inertial coordinate system is the i0-frame, the initial earth coordinate system is the e0-frame, and the initial vehicle fixed coordinate system is the i b0 -frame; S12. Based on the constructed coordinate system, conduct rough alignment on the three-self inertial group based on the initial carrier fixed coordinate system to obtain the initial alignment attitude matrix as follows: In the formula, is the initial alignment attitude matrix, is the attitude transformation matrix from the i0 system to the n system, is the attitude transformation matrix from the i b0 system to the i0 system, is the attitude transformation matrix from the b system to the i b0 system; Among them, where ω ie is the angular velocity of the Earth's rotation, t is the alignment time, and L t is the local latitude at time t; Among them, In the formula, is the integral of the gravitational acceleration in the i0 system from t0 to t1, where t0 is the initial alignment time, t1 is the intermediate time of the alignment from the initial time to the current time, t2 is the current time of the alignment, and g n is the gravitational acceleration, and T represents the transpose of a matrix; is the integral of the acceleration of gravity in the i0 system from t0 to t2, where t0 is the initial moment of alignment and t2 is the current moment of alignment; is the integral of the acceleration due to gravity in the i b0 system from t0 to t1; is the integral of the acceleration due to gravity in the i b0 system from t0 to t2; Among them, It is obtained by solving through the following formula: wherein, is the derivative with respect to relative time, is the three-dimensional angular rate vector of the carrier relative to the inertial system measured by the gyroscopes within the three-axis inertial measurement unit, and the symbol × represents the skew-symmetric matrix of the vector, represents the vector corresponding skew-symmetric matrix.

3. A method for integrating rapid alignment of a three-self inertial measurement unit and calibration of inertial error parameters according to claim 2, characterized in that, The specific steps of step S2 are as follows: S21. Construct the 33-dimensional closed-loop Kalman filter state variables as follows: Where X is the state quantity of a 33-dimensional closed-loop Kalman filter, is the three-dimensional attitude error, δv n is the three-dimensional velocity error, δP is the three-dimensional position error, X g is the nine-dimensional inertial error parameter of the gyroscope, X a is the twelve-dimensional inertial error parameter of the accelerometer, δl b is the three-dimensional external lever arm error where the rotation center of the indexing mechanism does not coincide with the sensitive center of the inertial measurement unit; S22. Construct the state equation of the 33-dimensional closed-loop Kalman filter as follows: In the formula, is the derivative of X with respect to time, F’ is the state transition matrix of the 33-dimensional closed-loop Kalman filter, G’ is the control input matrix of the 33-dimensional closed-loop Kalman filter, and u is the control input vector; where F is the state transition matrix of the 30-dimensional closed-loop Kalman filter, 0 30×3 is a 30-row and 3-column zero matrix, 0 3×30 is a 3-row and 30-column zero matrix, 0 3×3 is a 3-row and 3-column zero matrix; G is the control input matrix of the 30-dimensional closed-loop Kalman filter, 0 3×6 is a 3-row and 6-column zero matrix; where F 11 is the first block matrix of F, F 12 is the second block matrix of F, F 13 is the third block matrix of F, F 14 is the fourth block matrix of F, F 21 is the fifth block matrix of F, F 22 is the sixth block matrix of F, F 23 is the seventh block matrix of F, F 25 is the eighth block matrix of F, F 32 is the ninth block matrix of F, F 33 is the tenth block matrix of F, 0 3×12 is a 3-by-12 zero matrix, 0 3×9 is a 3-by-9 zero matrix, 0 9×3 is a 9-by-3 zero matrix, 0 9×9 is a 9-by-9 zero matrix, 0 9×12 is a 9-by-12 zero matrix, 0 12×3 is a 12-by-3 zero matrix, 0 12×9 is a 12-by-9 zero matrix, 0 12×12 is a 12-by-12 zero matrix; In the formula, is the three-dimensional angular velocity vector of the navigation system where the carrier is located relative to the inertial system, and the symbol × represents taking the skew-symmetric matrix of the vector, represents the vector corresponding skew-symmetric matrix; where L is the local geographical latitude, h is the local geographical altitude, and R M is the local radius of the Earth's meridian circle, and R N is the local radius of the Earth's prime vertical circle; wherein, v E is the eastward velocity, and v N is the northward velocity; In the formula, is the transformation matrix from the vehicle coordinate system to the navigation coordinate system, is the component of the gravity vector on the x-axis of the vehicle coordinate system, is the component of the gravity vector on the y-axis of the vehicle coordinate system, is the component of the gravity vector on the z-axis of the vehicle coordinate system, I2 is the 2×2 identity matrix, I3 is the 3×3 identity matrix, 0 1×2 is the 1×2 zero matrix, 0 2×1 is the 2×1 zero matrix; where f b is the three-dimensional specific force vector of the vehicle relative to the inertial system measured by the accelerometers within the three-axis inertial measurement unit, and the symbol × represents the skew-symmetric matrix of a vector, denotes the vector corresponding skew-symmetric matrix; In the formula, is the angular velocity vector of the Earth relative to the inertial system, is the angular velocity vector of the navigation system relative to the Earth. The symbol × represents the skew-symmetric matrix of the vector, represents the vector corresponding skew-symmetric matrix, v n is the carrier velocity vector, v n × represents the vector v n corresponding skew-symmetric matrix; where 0 3×3 is a 3×3 zero matrix, and 0 24×3 is a 24×3 zero matrix; S23. Construct the observation equation of the 33-dimensional closed-loop Kalman filter as follows: Z = HX + V; where Z is the measurement vector, H is the observation matrix, and H = [0 3×3 I3 0 3×3 0 3×21 , 0 3×21 is a 3-row and 21-column zero matrix, and V is the observation noise; S24. Construct the feedback compensation form of the filtering estimation result of the 33-dimensional closed-loop Kalman filter as follows: In the formula, is the filtering result of the transformation matrix from the carrier coordinate system to the navigation coordinate system, is the filtering result of the carrier velocity vector, is the filtering result of the latitude, δL is the measurement error of the latitude, λ is the local geographic longitude, and δλ is the measurement error of the longitude, is the filtering result of the altitude, δh is the measurement error of the altitude, K g is the scale factor matrix of the gyroscope, is the filtering result of the scale factor matrix of the gyroscope, δK g is the measurement error of the scale factor matrix of the gyroscope, ε is the zero bias of the gyroscope, is the filtering result of the zero bias of the gyroscope, δε is the measurement error of the zero bias of the gyroscope, K a is the scale factor matrix of the accelerometer, is the filtering result of the scale factor matrix of the accelerometer, δK a is the measurement error of the scale factor matrix of the accelerometer, is the zero bias of the accelerometer, is the filtering result of the zero bias of the accelerometer, is the measurement error of the zero bias of the accelerometer.

4. A method for integrating the rapid alignment of a three-axis inertial measurement unit and the calibration of inertial error parameters according to claim 3, characterized in that The specific steps of step S3 are as follows: Input the output of the inertial devices of the three-self inertial group and the initial alignment attitude matrix obtained in step S1 into the closed-loop Kalman filter constructed in step S2 for Kalman filtering calculation to achieve fine alignment of the three-self inertial group and obtain the calibration result of the inertial error parameters; Compensate the navigation result with the calibration result of the inertial error parameters through the feedback compensation form of the filtering estimation result constructed in step S24.

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