A non-orthogonal error calibration method for a dual-axis rotary inertial navigation system rotation mechanism

Abstract

The present application relates to the technical field of inertial navigation, in particular to a non-orthogonal error calibration method for a two-axis rotary inertial navigation system rotation mechanism, which is suitable for non-orthogonal error calibration of a two-axis rotary inertial navigation system rotation mechanism and carrier attitude extraction; the method comprises: establishing a non-orthogonal error model for the two-axis rotary inertial navigation system rotation mechanism; starting the two-axis rotary inertial navigation system, rotating according to a prescribed path, and collecting data; then, according to the non-orthogonal error model of the rotation mechanism, constructing a non-orthogonal error calibration method for the two-axis rotary inertial navigation system based on a particle swarm optimization algorithm; finally, using the calibration result, decoupling the attitude of an inertial measurement unit from the rotation mechanism to obtain high-precision carrier attitude information. The non-orthogonal error calibration problem of the two-axis rotary inertial navigation system can be effectively solved, and high-precision error calibration and carrier attitude extraction can be realized.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation technology, specifically to a non-orthogonal error calibration method for the indexing mechanism of a dual-axis rotating inertial navigation system, applicable to the non-orthogonal error calibration of the indexing mechanism of a dual-axis rotating inertial navigation system and the extraction of carrier attitude. Background Technology

[0002] An Inertial Navigation System (INS) consists of an Inertial Measurement Unit (IMU), a housing, control circuitry, and a navigation computer. The INS uses the IMU to measure the angular velocity and acceleration of a vehicle, and then the navigation computer calculates the vehicle's attitude, velocity, and position from the angular velocity and acceleration. Because the INS is based on Newton's second law and relies on integral calculations, errors inevitably accumulate over time.

[0003] Strapdown inertial navigation systems (INS) are directly fixed to the vehicle. Therefore, the attitude, velocity, and position calculated by the strapdown INS are the attitude, velocity, and position of the vehicle. Rotating INS, on the other hand, uses a rotation mechanism to periodically rotate the inertial measurement unit (IMU), canceling out positive and negative constant errors within the IMU to achieve high-precision navigation and positioning. Its onboard rotation modulation system can eliminate navigation errors introduced by constant errors in inertial devices, installation errors, and calibration factor errors. Unlike strapdown INS, rotating INS cannot directly calculate the vehicle's attitude information because the IMU is constantly rotating periodically relative to the vehicle.

[0004] In certain applications of rotating inertial navigation systems (INS), high requirements are placed on the carrier's attitude, such as in high-dynamic airborne rotating INS systems and angular motion isolation in long-endurance rotating INS systems. Therefore, researching high-precision carrier attitude calculation techniques for rotating INS systems has significant practical implications. To extract carrier attitude information from a rotating INS system, it is essential to accurately decouple it from the attitude of the indexing mechanism. However, in practical dual-axis rotating INS systems, non-orthogonal errors inevitably exist in the installation between the inertial measurement unit (IMU) and the indexing mechanism, and non-orthogonal errors also exist in the inner and outer frames of the dual-axis indexing mechanism during installation. Therefore, if non-orthogonal errors are not considered, directly extracting the carrier attitude will result in a large attitude error. To obtain high-precision carrier attitude information, the non-orthogonal errors of the indexing mechanism must be calibrated and compensated. Summary of the Invention

[0005] This invention proposes a non-orthogonal error calibration method for the rotation mechanism of a dual-axis rotating inertial navigation system, which can effectively solve the problem of non-orthogonal error calibration of dual-axis rotating inertial navigation systems and achieve high-precision error calibration and carrier attitude extraction.

[0006] The technical solution adopted in this invention is a non-orthogonal error calibration method for the rotation mechanism of a dual-axis rotating inertial navigation system, the method comprising:

[0007] A non-orthogonal error model of the indexing mechanism of a dual-axis rotating inertial navigation system is established; the dual-axis rotating inertial navigation system is started, rotated along a specified path, and data is collected; then, based on the non-orthogonal error model of the indexing mechanism, a non-orthogonal error calibration method for the dual-axis rotating inertial navigation system based on particle swarm optimization algorithm is constructed; finally, using the calibration results, the attitude of the inertial measurement unit is decoupled from the indexing mechanism to obtain high-precision carrier attitude information.

[0008] The specific steps are as follows:

[0009] S1: Establish a non-orthogonal error model for the rotation mechanism of a dual-axis rotating inertial navigation system.

[0010] First, we define the coordinate system:

[0011] The IMU coordinate system, or S-frame for short, has three axes that coincide with the sensitive axes of the three orthogonally mounted laser gyroscopes in the IMU.

[0012] The inner frame coordinate system, abbreviated as in system: The inner frame coordinate system is fixedly connected to the inner frame of the dual-axis indexing mechanism. The Z-axis of the inner frame coordinate system... in The axis coincides with the inner axis of the dual-axis indexing mechanism. The IMU is mounted on the inner frame. The spatial relative position between the IMU coordinate system and the inner frame coordinate system remains unchanged. There is a fixed installation offset angle between the IMU coordinate system and the inner frame coordinate system.

[0013] The outer frame coordinate system, or out system for short: The outer frame coordinate system is fixedly connected to the outer frame of the dual-axis indexing mechanism. The X-axis of the outer frame coordinate system... out The shaft coincides with the outer rotating shaft of the dual-axis indexing mechanism;

[0014] Inner frame zero coordinate system, abbreviated as in0 system: When the rotation angle of the inner axis of the dual-axis indexing mechanism is 0, the position of the inner frame coordinate system is the inner frame zero coordinate system. The spatial relative position between the inner frame zero coordinate system and the outer frame remains unchanged, and there is a fixed installation offset angle between the inner frame zero coordinate system and the outer frame coordinate system.

[0015] The carrier coordinate system, abbreviated as b system: The xyz axes of the carrier coordinate system point to the right, front and top of the carrier respectively. The carrier is fixed to the inertial navigation system. When the rotation angle of the outer axis of the dual-axis rotation mechanism is 0, the outer frame coordinate system coincides with the carrier coordinate system.

[0016] Navigation coordinate system, abbreviated as n-system: The x, y, and z axes of the navigation coordinate system are defined to point to geographic east, north, and sky, respectively;

[0017] S1.1 Constructing a non-orthogonal error model between the IMU coordinate system and the coordinate system of the inner frame of the translation mechanism.

[0018] Define θ x ,θ y ,θ z Let be the non-orthogonal error angle between the IMU coordinate system and the inner frame coordinate system. Then, the attitude transfer matrix from the IMU coordinate system to the inner frame coordinate system is:

[0019]

[0020] Since the non-orthogonal error angle is usually very small (Jiang Yifu, Li Sihai, Yan Gongmin, Xie Bo. A method for extracting carrier navigation information based on dual-axis rotation modulation inertial measurement [J]. Chinese Journal of Inertial Technology, 2022, 30(03):304-308+315.), based on the small angle assumption, sinθ≈θ, cosθ≈1, and ignoring higher-order terms, the attitude transfer matrix from the IMU coordinate system to the inner frame coordinate system is simplified to:

[0021]

[0022] S1.2 Constructing a non-orthogonal error model between the inner frame zero-position coordinate system and the outer frame coordinate system of the indexing mechanism.

[0023] Define η x ,η y ,η z Let be the non-orthogonal error angle between the inner frame zero-position coordinate system and the outer frame coordinate system. Then, the attitude transfer matrix from the inner frame zero-position coordinate system to the outer frame coordinate system is:

[0024]

[0025] Since the non-orthogonal error angle is usually very small, based on the small angle assumption, sinη≈η, cosη≈1, and ignoring higher-order terms, the attitude transfer matrix from the inner frame zero coordinate system to the outer frame coordinate system simplifies to:

[0026]

[0027] S1.3 Constructing a carrier attitude transfer model for a dual-axis rotating inertial navigation system

[0028] According to the matrix chain multiplication rule, the carrier attitude transfer model of the dual-axis rotating inertial navigation system is as follows:

[0029]

[0030] In the formula This is the attitude transition matrix from the vehicle coordinate system to the navigation coordinate system, which is the vehicle attitude; This is the attitude transfer matrix from the IMU coordinate system to the navigation coordinate system, which is the attitude of the IMU. It is directly obtained by the IMU measurement and the navigation computer. Let be the attitude transfer matrix from the inner frame coordinate system to the IMU coordinate system. in express transpose; This represents the attitude transfer matrix from the outer frame coordinate system to the inner frame zero-position coordinate system. Let α be the attitude transfer matrix from the inner frame coordinate system to the inner frame zero coordinate system, and α be the rotation angle of the inner frame. Let β be the attitude transfer matrix from the carrier coordinate system to the outer frame coordinate system, and β be the rotation angle of the outer frame. and They are respectively:

[0031]

[0032] S2: Start the dual-axis rotating inertial navigation system, rotate along the prescribed path, and collect data.

[0033] S2.1 The dual-axis rotary inertial navigation system is activated. The navigation computer acquires data measured by the IMU and the angular velocity of the indexing mechanism in real time, and controls the indexing mechanism to rotate in the following sequence:

[0034] 1. Power on and perform static base alignment for 10 minutes to obtain the initial attitude of the IMU.

[0035] 2. Rotate the inner frame 180 degrees clockwise;

[0036] 3. Rotate the outer frame 180 degrees clockwise;

[0037] 4. Rotate the outer frame 180 degrees;

[0038] 5. Rotate the inner frame 180 degrees;

[0039] 6. End data acquisition and power off;

[0040] For the alignment process, please refer to "Straight-through Inertial Navigation Algorithm and Integrated Navigation Principles", edited by Yan Gongmin and Weng Jun, Northwestern Polytechnical University Press, August 2019;

[0041] S3: Constructing a non-orthogonal error calibration method for a dual-axis rotating inertial navigation system based on particle swarm optimization algorithm.

[0042] S3.1 Define the particle format for the particle swarm optimization algorithm.

[0043] Define the position of the i-th particle in the particle swarm as pi p i It contains 6 parameters, for in The attitude transfer matrices from the IMU coordinate system to the inner frame coordinate system in equation (2) are respectively The attitude transfer matrix between the inner frame zero-position coordinate system and the outer frame coordinate system in equation (4) The six misalignment angle error values ​​are determined by the position p of the i-th particle. i The arrangement of the six particle parameters constitutes the following form of nonorthogonal error:

[0044]

[0045]

[0046] In the formula, This indicates that the matrix within the parentheses is composed of the position parameters of the i-th particle;

[0047] S3.2 Constructing the fitness function for the particle swarm optimization algorithm

[0048] Using the root mean square error of the carrier attitude error extracted by the dual-axis rotating inertial navigation system as the fitness, a fitness function of the particle swarm optimization algorithm is constructed, transforming the calibration problem into an optimization problem, which is then solved using the particle swarm optimization algorithm.

[0049] Define the fitness function as follows:

[0050]

[0051] In equation (9), Fit(p) i ) represents the position of the i-th particle at position p i Fitness function at time; This represents the calculated attitude transfer matrix of the carrier at time t relative to the initial time 0. This represents the attitude matrix of the carrier relative to the n-system extracted at time t; Let represent the attitude matrix of the n-frame relative to the carrier at initial time 0; × represents the matrix cross product; since the inertial navigation system remains stationary during calibration, theoretically the attitude of the inertial navigation system at time t remains unchanged relative to time 0. The identity matrix is ​​calculated as follows: That is, the carrier attitude error matrix caused by non-orthogonal errors;

[0052] The calculation process is as follows:

[0053]

[0054] The calculation process is as follows:

[0055]

[0056] In equations (10) and (11), This represents the attitude measured and calculated by the IMU at time t; and According to equations (7) and (8), the i-th particle p i The non-orthogonal error matrix composed of arrangement; The inner frame rotates by an angle α at time t. t At that time, the attitude transfer matrix from the inner frame zero coordinate system to the inner frame coordinate system, The outer frame rotates by an angle β at time t. t At that time, the attitude transfer matrix from the carrier coordinate system to the outer frame coordinate system;

[0057] In equation (9), sum(·) represents the summation function, and Euler(·) represents converting the variables in parentheses into Euler angles; the conversion of the attitude transfer matrix to Euler angles and the strapdown inertial calculation in equation (11) The process can be found in "Stripdown Inertial Navigation Algorithm and Integrated Navigation Principles" edited by Yan Gongmin and Weng Jun, Northwestern Polytechnical University Press, August 2019.

[0058] S3.3 uses the fitness function constructed in S3.2 and employs the particle swarm optimization algorithm for optimization.

[0059] Particle Swarm Optimization (PSO) algorithm establishes a swarm of particles, where the position of each particle represents a potential solution. It achieves intelligent problem-solving through simple particle behaviors and information interaction within the swarm. The total number of iterations for each particle's search process is G. The particle's movement is the search process for the optimal solution, and the particle's speed can be dynamically adjusted based on the particle's historical best position and the swarm's historical best position. The position where the i-th particle has the best fitness during the search process is called the individual's optimal position. The position of the particle with the best fitness in the population is called the global optimal position g. best ;

[0060] The position of the i-th particle at the d-th iteration is d = 1, 2, ..., G; Combining equations (9), (10), and (11), the corresponding fitness function is:

[0061]

[0062]

[0063]

[0064] In equations (12) and (13), the subscript d represents the number of iterations of the current particle swarm, and the maximum number of iterations is G; i = 1, 2, ..., N represents the particle number index, and N represents the particle swarm size, which is the total number of particles in a particle swarm; r1 and r2 are random numbers between (0,1); c1 and c2 are learning factors, which respectively characterize the ability of a particle to learn from itself and other particles, and are usually taken as a fixed value of 2; ω is the inertia weight constant, which is used to adjust the diversity of particles, and the value is generally between [0.4, 0.9]. The larger the value of ω, the stronger the global optimization ability; the smaller the value of ω, the stronger the local optimization ability. In order to balance the global optimization ability and the local optimization ability, ω is usually taken as 0.6. Indicates the particle's current velocity. v gmin ,v gmax Let v represent the particle's current minimum and maximum velocities, respectively, determined by the magnitude of the non-orthogonal error angle. The non-orthogonal error angle is typically less than 1°, therefore v can be defined as... gmax =1,v gmin =-1; Considering both computing power and engineering experience, N=50.

[0065] The position of the i-th particle in the d-th iteration is calculated using equation (12). The fitness of the i-th particle can be used to re-evaluate the optimal position of the individual with the best fitness. By calculating the fitness of all particles in the particle swarm at the d-th iteration, the global optimum position g with the best current fitness can be re-evaluated. best .

[0066] The global optimum is determined when the maximum number of iterations (e.g., 150) is reached or the termination condition is met (defined as a fitness value less than 0.01). Fitness Fit(g) best Global minimum; set the global optimal position g. best The six parameters Substituting equations (7) and (8) yields (15) and (16), which are the accurate non-orthogonal errors of the dual-axis rotary inertial navigation positioning mechanism:

[0067]

[0068]

[0069] Substituting equations (15) and (16) into equation (17) yields a high-precision carrier attitude.

[0070]

[0071] In the formula, This is the attitude matrix of the IMU obtained from inertial calculation. and The non-orthogonal error matrices (15) and (16) obtained by calibrating the particle swarm optimization algorithm are shown. The attitude matrix is ​​converted from the real-time rotation angle of the inner frame using equation (6). The real-time rotation angle of the outer frame is converted into an attitude matrix using equation (6). This is the high-precision carrier attitude obtained through real-time compensation.

[0072] The present invention has the following technical effects:

[0073] 1. This invention utilizes the particle swarm optimization algorithm to transform the calibration problem into an optimization problem, which can accurately calibrate the non-orthogonal error of a dual-axis rotating inertial navigation system;

[0074] 2. Compared with traditional error calibration methods based on vector projection, this invention has higher calibration accuracy;

[0075] 3. This invention can calibrate non-orthogonal errors without the need for any external equipment, thus saving costs;

[0076] 4. By accurately calibrating the non-orthogonal error of the dual-axis indexing mechanism, this invention can significantly improve the accuracy of carrier attitude extraction; furthermore, it can improve the navigation accuracy of the dual-axis inertial navigation system.

[0077] 5. This invention can provide technical support for carrier angular motion isolation technology in dual-axis rotating inertial navigation systems. Attached Figure Description

[0078] Figure 1 The spatial relative position of the IMU and the inner frame coordinate system of the translation mechanism;

[0079] Figure 2 The spatial relative position between the inner frame coordinate system and the outer frame coordinate system;

[0080] Figure 3 Flowchart of the Particle Swarm Optimization Algorithm;

[0081] Figure 4 Comparison of attitude errors using different calibration methods. Detailed Implementation

[0082] To illustrate the technical solution disclosed in this invention in detail, further explanation is provided below with reference to specific embodiments.

[0083] The feasibility and effectiveness of this invention were verified using a dual-axis rotating inertial navigation system independently developed by the National University of Defense Technology.

[0084] Step 1: Place the dual-axis rotating inertial navigation system on the plane, operate according to S2, start the dual-axis rotating inertial navigation system, rotate it along the specified path, and collect data;

[0085] The dual-axis rotary inertial navigation system is activated, and the navigation computer acquires data measured by the IMU and the angular velocity of the indexing mechanism in real time, controlling the indexing mechanism to rotate in the following sequence:

[0086] 1. Power on and perform static base alignment for 10 minutes to obtain the initial attitude of the IMU.

[0087] 2. Rotate the inner frame 180 degrees clockwise;

[0088] 3. Rotate the outer frame 180 degrees clockwise;

[0089] 4. Rotate the outer frame 180 degrees;

[0090] 5. Rotate the inner frame 180 degrees;

[0091] 6. End data acquisition and shut down the computer.

[0092] For the alignment process, please refer to "Stripdown Inertial Navigation Algorithm and Integrated Navigation Principles", edited by Yan Gongmin and Weng Jun, Northwestern Polytechnical University Press, August 2019.

[0093] Step 2: Perform the operation according to S3, and calibrate the non-orthogonal error of the dual-axis rotating inertial navigation system using the particle swarm optimization algorithm;

[0094] Obtain the global optimal position g of the particle best :

[0095] g best =[-0.000279 -0.000963 -0.002212 0.000721 ​​-0.000806 -0.009205]°

[0096] The particle swarm optimization algorithm obtains the global optimal position g through iteration. best It is the optimal solution of the fitness function (12), and the global optimal position g is... best Substituting the six parameters into equations (7) and (8) yields (18) and (19), which are the accurate non-orthogonal errors of the dual-axis rotating inertial navigation positioning mechanism:

[0097]

[0098]

[0099] Step 3: Place the dual-axis rotary inertial navigation system on the marble work platform and perform sixteen-sequence navigation operations to compensate for the non-orthogonal errors obtained from the calibration in step 2 in real time and extract the carrier attitude information.

[0100] The real-time compensation formula for the carrier attitude is:

[0101]

[0102] In the formula, This is the attitude matrix of the IMU obtained from inertial calculation. and The error matrix is ​​non-orthogonal, obtained through calibration in the second step. This is the attitude matrix converted from the real-time rotation angle of the inner frame. This is the attitude matrix converted from the real-time rotation angle of the outer frame. To achieve high-precision carrier attitude after real-time compensation, the error in the carrier attitude information extracted by the dual-axis rotating inertial navigation system is calculated, such as... Figure 4 As shown.

[0103] Figure 4 The traditional method is the one described in the literature (Jiang Yifu, Li Sihai, Yan Gongmin, et al. A method for extracting carrier navigation information based on dual-axis rotation modulation inertial measurement [J]. Journal of Chinese Inertial Technology, 2022, 30(03):304-308+315.DOI:10.13695 / j.cnki.12-1222 / o3.2022.03.004.). Through comparison, it is found that the accuracy of this invention has a significant advantage.

Claims

1. A method for calibrating non-orthogonal errors of a rotation mechanism of a dual-axis rotation inertial navigation system, characterized in that, The method comprises: The non-orthogonal error model of the two-axis rotary inertial navigation system is established, the two-axis rotary inertial navigation system is started, rotation is performed according to a specified path, and data are collected, then a non-orthogonal error calibration method of the two-axis rotary inertial navigation system based on a particle swarm optimization algorithm is constructed according to the non-orthogonal error model of the rotary mechanism, and finally, the attitude of the inertial measurement unit is decoupled from the rotary mechanism by using the calibration result to obtain high-precision carrier attitude information; The specific steps are as follows: S1: establishing a non-orthogonal error model of a two-axis rotary inertial navigation system rotary mechanism Firstly, the coordinate systems are defined: An IMU coordinate system, referred to as an s system: the three axes of the IMU coordinate system coincide with the sensitive axes of the three laser gyroscopes orthogonally installed in the IMU; Inner frame coordinate system, referred to as in system: the inner frame coordinate system is fixedly connected with the inner frame of the biaxial indexing mechanism, the Z in axis coincides with the inner rotating shaft of the biaxial indexing mechanism, the IMU is installed on the inner frame, the spatial relative position of the IMU coordinate system and the inner frame coordinate system is invariable, and a fixed installation angle exists between the IMU coordinate system and the inner frame coordinate system. Out frame coordinate system, referred to as out system: the out frame coordinate system is fixedly connected with the outer frame of the double-shaft indexing mechanism, the X out axis of the out frame coordinate system coincides with the outer rotation shaft of the double-shaft indexing mechanism; An inner frame zero position coordinate system, referred to as an in0 system: when the rotation angle of the inner frame zero position coordinate system is 0, the position of the inner frame coordinate system is defined as the inner frame zero position coordinate system, the relative position of the inner frame zero position coordinate system to the outer frame is constant, and there is a fixed installation angle between the inner frame zero position coordinate system and the outer frame coordinate system; A carrier coordinate system, referred to as a b system: the x-y-z axes of the carrier coordinate system point to the right-front-up of the carrier, the carrier is fixedly connected with the inertial navigation system, and when the rotation angle of the outer frame of the two-axis rotary mechanism is 0, the outer frame coordinate system coincides with the carrier coordinate system; A navigation coordinate system, referred to as an n system: the x-y-z axes of the navigation coordinate system point to the geographical east-north-sky direction; S1.1: constructing a non-orthogonal error model between the IMU coordinate system and the inner frame coordinate system of the rotary mechanism Define θ x ,θ y ,θ z is the non-orthogonal error angle between the IMU coordinate system and the inner frame coordinate system, and the attitude transfer matrix of the IMU coordinate system to the inner frame coordinate system is: Based on the small-angle assumption, sinθ ≈ θ and cosθ ≈ 1, and high-order terms are ignored, the attitude transfer matrix from the IMU coordinate system to the inner frame coordinate system is simplified as: S1.2: constructing a non-orthogonal error model between the inner frame zero position coordinate system and the outer frame coordinate system of the rotary mechanism Definition of η x ,η y ,η z is the non-orthogonal error angle between the inner frame zero position coordinate system and the outer frame coordinate system, and the attitude transfer matrix of the inner frame zero position coordinate system to the outer frame coordinate system is: Based on the small-angle assumption, sinη ≈ η and cosη ≈ 1, and high-order terms are ignored, the attitude transfer matrix from the inner frame zero position coordinate system to the outer frame coordinate system is simplified as: S1.3: constructing a carrier attitude transfer model of the two-axis rotary inertial navigation system According to the matrix chain multiplication rule, the carrier attitude transfer model of the two-axis rotary inertial navigation system is as follows: In the formula is the attitude transfer matrix of the carrier coordinate system to the navigation coordinate system, that is, the carrier attitude; is the attitude transfer matrix of the IMU coordinate system to the navigation coordinate system, that is, the IMU attitude, which is measured by the IMU and directly obtained through navigation computer solution; is the attitude transfer matrix of the inner frame coordinate system to the IMU coordinate system, wherein represents the transpose of represents the attitude transfer matrix of the outer frame coordinate system to the inner frame zero position coordinate system, is the attitude transfer matrix of the inner frame coordinate system to the inner frame zero position coordinate system, and a is the inner frame rotation angle; is the attitude transfer matrix of the carrier coordinate system to the outer frame coordinate system, and β is the outer frame rotation angle; and are respectively: S2: starting the two-axis rotary inertial navigation system, performing rotation according to a specified path, and collecting data S2.1: starting the two-axis rotary inertial navigation system, collecting the data measured by the IMU and the angle velocity of the rotary mechanism in real time, and controlling the rotary mechanism to perform rotation in the following order:

1. Turn on, do 10 minute stationary base alignment, get initial pose of IMU 2. positive rotation of the inner frame by 180 degrees; 3. positive rotation of the outer frame by 180 degrees; 4. negative rotation of the outer frame by 180 degrees; 5. negative rotation of the inner frame by 180 degrees; 6. ending data collection and shutting down; S3: constructing a non-orthogonal error calibration method of the two-axis rotary inertial navigation system based on a particle swarm optimization algorithm S3.1: defining the particle format of the particle swarm algorithm Let p denote the position of the i-th particle in the swarm i , p i contains 6 parameters, for where correspond to the six misalignment angle errors of the attitude transfer matrix from the IMU coordinate system to the inner frame coordinate system in equation (2) and the attitude transfer matrix from the inner frame zero position coordinate system to the outer frame coordinate system in equation (4) are composed of the 6 particle parameters of the position p i of the i-th particle in the following non-orthogonal error form: wherein denotes that the matrix in the parentheses is compiled from the position parameters of the i-th particle; S3.2: constructing a fitness function of the particle swarm optimization algorithm The root mean square error of the carrier attitude error extracted from the two-axis rotary inertial navigation system is taken as the fitness, the fitness function of the particle swarm optimization algorithm is constructed, the calibration problem is converted into an optimization problem, and the particle swarm optimization algorithm is used for solving; The fitness function is defined as: In formula (9), Fit(p i ) is the fitness function of the i th particle at position p i ; represents the attitude matrix of the carrier relative to the n system extracted at time t; represents the attitude matrix of the n system relative to the carrier at initial time 0; represents matrix cross multiplication; since the inertial navigation system remains stationary during the calibration process, theoretically, the attitude of the inertial navigation system relative to time 0 remains unchanged at time t, is a unit matrix, and the calculated is the attitude error matrix of the carrier caused by the non-orthogonal error; The calculation is: The calculation is: In formula (10) and (11), represents the attitude of the IMU at time t; and is shown according to formula (7) and formula (8), the i-th particle p i arranged into a non-orthogonal error matrix; represents the attitude transfer matrix from the inner frame coordinate system to the inner frame coordinate system when the inner frame rotation angle is α t at time t, represents the attitude transfer matrix from the carrier coordinate system to the outer frame coordinate system when the outer frame rotation angle is β t at time t. In formula (9), sum(·) represents a summation function, and Euler(·) represents conversion of variables in parentheses into Euler angles. S3.3 Using the fitness function constructed in S3.2, a particle swarm optimization algorithm is used for optimization The particle swarm optimization algorithm establishes a population consisting of a plurality of particles, wherein a position of each particle represents a potential solution, and intelligent solution to a problem is achieved through simple behavior of the particles and information exchange within the population; a total iteration number of each particle search process is G, a motion process of the particles is a search process for solving an optimal solution, and a motion speed of the particles can be dynamically adjusted according to a historical optimal position of the particles and a historical optimal position of the population; a position of the i-th particle with the best fitness in the search process is referred to as an individual optimal position A position of a particle with the best fitness in the population is referred to as a global optimal position g best ​ The position of the ith particle at the dth iteration is d = 1, 2,..., G; in conjunction with equations (9), (10), and (11), the corresponding fitness function is: In formula (12) and (13), subscript d is the iteration number of the current particle group, the maximum iteration number is G; i=1, 2, …, N is the particle number sequence number, N is the particle group size, that is, the total number of particles in a particle group; r1, r2 are random numbers between (0, 1); c1, c2 are learning factors, respectively representing the ability of the particle to learn from itself and other particles; ω is an inertia weight constant, used to adjust the diversity of the particle, the larger the value of ω, the stronger the global optimization ability, the smaller the value of ω, the stronger the local optimization ability; represents the current speed of the particle, v gmin ,v gmax respectively represent the current minimum and maximum speeds of the particle, determined by the size of the non-orthogonal error angle; The fitness of the ith particle at the dth iteration is calculated using equation (12) The ith particle is re-evaluated for the best individual optimum position The fitness of all particles in the swarm at the dth iteration is calculated, i.e. the global optimum position g is re-evaluated for the best fitness best ; global optimum position g when the maximum number of iterations is reached or the termination requirement is met best ) global minimum; six parameters of the global optimum position g best Substituting equations (7) and (8) into equations (15) and (16) gives the accurate non-orthogonal errors of the two-axis rotary inertial navigation rotation positioning mechanism:​ Substituting the equations (15) and (16) into the equation (17) gives a high-precision carrier attitude wherein is the IMU's attitude matrix obtained from inertial solution, and are the non-orthogonal error matrices (15), (16) obtained from the particle swarm optimization algorithm calibration.

2. The method of claim 1, wherein: Learning factors c1, c2: take fixed value 2; inertia weight constant ω takes value between [0.4, 0.9]; the current minimum and maximum speed of particles v gmin , gmax v gmax = 1, v gmin = -1; the total number of particles N = 50.

3. The method of claim 1, wherein: The maximum number of iterations is 150 or the termination requirement is met when the set fitness is less than 0.01.

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