A fast alignment method for rotation-modulated inertial navigation system based on group-affine property

Abstract

The present application relates to the technical field of inertial navigation, in particular to a fast alignment method of a rotation modulation inertial navigation system based on group affine property, which is suitable for the fast alignment of an inertial navigation system in a carrier such as an airplane, an unmanned aerial vehicle, a rocket, a ship, etc. and the inertial navigation thereof. On the basis of multi-position alignment of the rotation modulation inertial navigation system, the method abandons the traditional alignment idea of "coarse alignment + fine alignment", designs an alignment state model satisfying the group affine property based on the Lie group theory, and the state model can realize initial alignment of any large initial misalignment angle in combination with Kalman filtering and can quickly converge in a short time.

Description

Technical Field

[0001] This invention relates to the field of inertial navigation technology, specifically to a rapid alignment method for a rotation modulation inertial navigation system based on group affine properties, applicable to rapid alignment and inertial navigation of inertial navigation systems in aircraft, unmanned aerial vehicles, rockets, ships and other launch vehicles. Background Technology

[0002] An inertial navigation system (INS) is an autonomous navigation system that relies entirely on its own inertial devices to complete navigation tasks. It measures the angular velocity and acceleration of a vehicle relative to inertial space and calculates the vehicle's real-time attitude, velocity, and position information. Aircraft, unmanned aerial vehicles, rockets, ships, and other land, sea, and air transport equipment are typically equipped with INS to provide autonomous navigation information. In long-endurance aircraft applications, reliable navigation information is essential to ensure the aircraft can accurately execute its missions. For GNSS-denied environments, navigation methods such as integrated navigation that utilize external sensors to suppress inertial navigation errors are no longer feasible. Pure inertial navigation performance is challenged, and a rotation-modulated inertial navigation system capable of continuously providing high-precision navigation information over long endurance is the optimal choice.

[0003] The initial alignment process of a rotation-modulated inertial navigation system (INS) is crucial throughout the entire navigation process, directly affecting subsequent navigation accuracy. Initial alignment has always been a key research issue in the field of INS. In some application scenarios of rotation-modulated INS, there are high requirements for the speed of initial alignment to ensure rapid response capabilities; however, alignment speed and accuracy are contradictory. Furthermore, the traditional "coarse alignment + fine alignment" scheme has the following problems: 1) The allocation of coarse and fine alignment time: If the fine alignment time is allocated too short within a finite time, the convergence of the Kalman filter estimate will be worse; if the coarse alignment time is allocated too short, it will be more susceptible to base sway interference, which will also affect the convergence of fine alignment; 2) Parameter setting issues: In long-term alignment, even if the initial variance matrix setting of the Kalman filter is inaccurate, it can gradually converge. However, in short-term rapid alignment, the initial variance matrix setting will significantly affect the alignment accuracy. The different coarse alignment accuracies under different base sway interference conditions mean that the initial variance matrix setting lacks universality. Summary of the Invention

[0004] To address the alignment time allocation and parameter setting issues in the initial alignment of a rotating modulation inertial navigation system (INS), and to achieve high accuracy in a short time, this invention proposes a fast alignment method for INS based on group affine properties. This method, building upon multi-position alignment of the INS, abandons the traditional "coarse alignment + fine alignment" approach. Based on Lie group theory, it designs an alignment state model that satisfies group affine properties. This state model, combined with Kalman filtering, can achieve initial alignment with arbitrarily large initial misalignment angles and converges rapidly in a short time.

[0005] The technical solution adopted in this invention is as follows: A fast alignment method for a rotation modulation inertial navigation system based on group affine properties, comprising the following steps:

[0006] S1: Define the coordinate system, power on the inertial navigation system, the inertial navigation system's rotation mechanism executes a specific rotation sequence, and the inertial measurement unit (IMU) collects data from the gyroscope and accelerometer and transmits it to the navigation computer in real time.

[0007] S1.1 Define the coordinate system:

[0008] Define the geocentric inertial coordinate system as the inertial reference coordinate system, denoted as the i-system; define the geocentric geofixed coordinate system (ECEF) as the e-system; define the “East-North-Sky” geographic coordinate system as the navigation coordinate system, denoted as the n-system; define the x, y, and z axes of the carrier coordinate system as pointing to the right-front-up directions of the carrier, denoted as the b-system; define the x, y, and z axes of the IMU coordinate system as corresponding to the sensitive axes of the three gyroscopes, denoted as the s-system.

[0009] S1.2 Inertial Navigation System Power On, Set Initial Alignment Time T a Start the navigation computer timer and initialize time k = 0;

[0010] S1.3IMU acquires the gyroscope output angular velocity at time k. Comparison with accelerometer output And and It is transmitted to the navigation computer in real time.

[0011] "~" indicates that the gyroscope output angular velocity and the accelerometer output specific force include measurement errors.

[0012] After power-on, S1.4 The indexing mechanism synchronously executes the dual-position indexing sequence:

[0013] 1) The stationary position of the indexing mechanism T a / 2-180 / ω-0.5×ω / a seconds;

[0014] 2) The rotation mechanism around the axial axis rotates 180° at an angular velocity of ω;

[0015] 3) The indexing mechanism is stationary (T) a / 2-180 / ω-0.5×ω / a seconds;

[0016] Among them, T a ω is the initial alignment time, in seconds; in engineering applications, it is typically set to 300 or 600 seconds. ω is the angular velocity of the indexing mechanism, in ° / s. a is the angular acceleration of the indexing mechanism, in ° / s².2 .

[0017] S2: The navigation computer receives the angular velocity output from the gyroscope in real time. Comparison with accelerometer output Then, inertial navigation calculations are performed:

[0018] S2.1 Initialize navigation parameters, as follows:

[0019] S2.1.1 Define the navigation parameters at time k: The attitude matrix of the IMU is The velocity vector is v e (k), with position vector p e (k), the auxiliary velocity vector is

[0020] The superscript "e" indicates that this parameter is in the Earth-centered Earth-fixed coordinate system (e-system), and the same applies below.

[0021] S2.1.2 The attitude matrix at time k=0 Perform initialization:

[0022]

[0023] S2.1.3 The velocity vector v at k=0 e (0) Perform initialization:

[0024] v e (0) = [0 0 0] T (2)

[0025] The superscript "T" indicates matrix transpose.

[0026] S2.1.4 The position vector p at time k=0 e (0) Perform initialization:

[0027] p e (0)=[L0 λ0 h0] T (3)

[0028] In the formula, L0 represents the latitude of the inertial navigation system at the initial position, λ0 represents the longitude of the inertial navigation system at the initial position, and h0 represents the altitude of the inertial navigation system at the initial position.

[0029] S2.1.5 The auxiliary velocity vector at time k=0 Perform initialization:

[0030]

[0031] Let be the projection of the rotational angular velocity of the e-frame relative to the i-frame into the e-frame. Earth's rotation rate ω ie =15° / h; Represents the calculation vector The antisymmetric matrix, and so on;

[0032] S2.2 Navigation computer timer update: k = k + 1;

[0033] S2.3 Perform inertial navigation calculations in the geocentric-fixed coordinate system, as follows:

[0034] S2.3.1 Perform attitude update:

[0035]

[0036] In the formula I 3×3 It is a 3×3 identity matrix; φ(k) is the equivalent rotation vector at time k, which is generated by the angular velocity output by the gyroscope. The calculation process can be found in the reference [Straight-through inertial navigation algorithm and integrated navigation principle / Yan Gongmin, Weng Jun, eds. - Xi'an: Northwestern Polytechnical University Press, 2019.8]; φ(k) is the modulus of φ(k), i.e. φ(k)=|φ(k)|; (φ(k)×) represents the antisymmetric matrix of the calculated vector φ(k).

[0037] S2.3.2 performs a speed update:

[0038]

[0039] In the formula T is the specific force value output by the accelerometer. s The sampling time interval for IMU data; Let be the gravitational force vector at time k; and the auxiliary velocity vector at time k-1. With the velocity vector v at time k-1 e The relationship between (k-1), the gravitational vector at time k-1 The gravitational vector g at time k-1 e The relationships between (k-1) are as follows:

[0040]

[0041]

[0042] S2.3.3 performs a location update:

[0043]

[0044] S3: Construct a fast alignment state model for a rotation modulation inertial navigation system that satisfies the group affine property.

[0045] Based on Lie group theory, if the state variables of a dynamic system are defined in a Lie group space and satisfy the condition of global state variable independence, then its corresponding state model satisfies the group affine property. Based on the group affine property, a linear state model in a Lie group space can accurately reflect the propagation process of a nonlinear state model. This means that a linear state model satisfying the group affine property can be established to solve the nonlinear state model. For details on Lie group theory and the group affine property, please refer to [Barrau A. Non-linear state error based extended Kalman filters with applications to navigation [D]. Mines Paristech, 2015.]. The core idea of ​​this invention is to abandon the coarse alignment process in the traditional "coarse alignment + fine alignment" scheme to fully utilize alignment data and shorten alignment time. However, this will cause the initial misalignment angle to be too large, and the alignment model will decay from a linear state model to a nonlinear state model, leading to Kalman filter failure. By constructing a state model for fast alignment of a rotating modulation inertial navigation system that satisfies the group affine property, the problem of Kalman filter failure caused by the nonlinear model will be effectively solved. Specifically:

[0046] S3.1 Constructing a state model for rapid alignment of a rotation modulation inertial navigation system that satisfies group affine properties

[0047]

[0048] In the formula, X k Z is the 18-dimensional state vector at time k. k Φ is the 3D measurement vector at time k; k|k-1 G is the one-step state transition matrix from time k-1 to time k; k|k-1 Assign a system noise matrix H from time k-1 to time k. k The measurement matrix at time k; w k-1 The system noise matrix at time k-1; v k Let w represent the observation noise matrix at time k. k-1 The settings can be found in the reference [Strapdown Inertial Navigation Algorithm and Integrated Navigation Principle / Yan Gongmin, Weng Jun, eds. — Xi'an: Northwestern Polytechnical University Press, 2019.8];

[0049] S3.1.1 Constructing an 18-dimensional state vector X k :

[0050]

[0051] In the formula, This represents the attitude error of the IMU at time k, and the subscript "lg" indicates that the type of this error is a left-invariant error that satisfies the group affine property. This represents the velocity error of the IMU at time k; ε represents the position error of the IMU at time k; s (k) represents the gyroscope drift of the IMU at time k. L represents the zero bias of the IMU's accelerometer at time k. s (k) represents the inner arm error of the IMU at time k; the definition of left invariant error can be found in the reference [Barrau A. Non-linear state error-based extended Kalman filters with applications to navigation[D]. MinesParistech, 2015.].

[0052] S3.1.2 Constructing the 3D Measurement Vector Z k :

[0053]

[0054] In the formula, v e (k) represents the velocity vector at time k:

[0055]

[0056] To measure velocity, since the alignment of the rotationally modulated inertial navigation system is performed while the vehicle remains stationary,

[0057] S3.1.3 Construct the one-step state transition matrix Φ from time k-1 to time k. k|k-1 :

[0058]

[0059] In the formula I 18×18 I represents an 18×18 identity matrix. 3×3 Represents a 3×3 identity matrix, O 3×3 This represents a 3×3 zero matrix.

[0060] S3.1.4 Construct the system noise distribution matrix G from time k-1 to time k. k|k-1 :

[0061]

[0062] S3.1.5 Construct the measurement matrix H at time k k :

[0063]

[0064] S4: Estimating state quantities for a rapidly aligned state model of a rotation-modulated inertial navigation system based on S3.

[0065] S4.1 Calculate the posterior estimate of the state vector from time k-1 to time k.

[0066]

[0067] In the formula, X represents the 18-dimensional state vector output at time k-1. k-1 The posterior estimate; initial value Represents the state vector X k The one-step prediction from time k-1 to time k, i.e. the prior estimate at time k.

[0068] S4.2 Calculate the mean square error matrix for one-step state prediction from time k-1 to time k:

[0069]

[0070] In the formula, P k-1 Let P represent the mean square error matrix of the posterior state estimate at time k-1. k|k-1 This represents the mean square error matrix for one-step prediction of the state from time k-1 to time k.

[0071] Among them, P k-1 initial value Let T represent the initial value of the mean square error matrix under the n-system projection, and let T represent the mean square error coordinate system transformation matrix.

[0072]

[0073]

[0074] S4.3 Calculate the filter gain K at time k k :

[0075]

[0076] In the formula, the measurement noise covariance matrix R is:

[0077]

[0078] S4.4 Calculate the posterior estimate of the state at time k

[0079]

[0080] S4.5 Calculate the error estimates of each navigation parameter at time k:

[0081] Attitude error estimate for The first to third dimensions are represented as Right now:

[0082]

[0083] Auxiliary speed error estimate for The 4th to 6th dimensions are represented as Right now:

[0084]

[0085] Position error estimate for The 7th to 9th dimensions are represented as Right now:

[0086]

[0087] S4.6 Calculate the mean square error matrix P of the posterior state estimate at time k. k :

[0088] P k =P kk-1 -K k H k P kk-1 (28)

[0089] S5: Use the error estimate obtained from S4.5 to correct the navigation solution result of S2, as follows:

[0090] S5.1 Corrected Attitude Matrix Obtain the corrected attitude matrix

[0091]

[0092] In the formula, Indicates to The formula for matrix exponentiation is as follows:

[0093]

[0094] S5.2 Corrected Auxiliary Velocity Vector Obtain the corrected auxiliary velocity vector

[0095]

[0096] S5.3 Corrected position vector p e (k) yields the corrected position vector.

[0097]

[0098] S6: Determine whether alignment should continue if k < T a When k = T, execute S6.1; a At that time, execute S6.2 to output the corrected high-precision attitude matrix. The alignment is now complete; details are as follows:

[0099] S6.1 When k < T a At that time, perform the following steps:

[0100] S6.1.1 will modify the navigation parameters. and Uncorrected memory in the navigation computer p e (k), that is:

[0101]

[0102]

[0103]

[0104] S6.1.2 will p e (k) P k Stored in the navigation computer's memory; then return to S2.2 and continue execution to S6 to perform the next condition check in S6;

[0105] S6.2 When k = T a At that time, output the corrected attitude matrix. Initial alignment complete.

[0106] Compared with the prior art, the beneficial effects of the present invention are as follows:

[0107] 1. This invention abandons the traditional alignment framework of "coarse alignment + fine alignment", eliminating the need for coarse alignment and the need to consider the time allocation between coarse and fine alignment;

[0108] 2. This invention does not require setting appropriate initial values ​​for the mean square error matrix based on the coarse alignment scheme, thus exhibiting strong versatility;

[0109] 3. This invention saves coarse alignment time, making alignment faster, and achieves better convergence than traditional methods, resulting in higher alignment accuracy within a limited alignment time. Attached Figure Description

[0110] Figure 1 This is a flowchart of the present invention;

[0111] Figure 2 This is for navigation latitude error;

[0112] Figure 3 For navigation longitude error;

[0113] Figure 4 This represents the radial error in navigation. Detailed Implementation

[0114] To illustrate the technical solutions disclosed in this invention in detail, the following description is based on specific embodiments. The specific embodiments described herein are only for explaining this application and are not intended to limit this application.

[0115] Example 1

[0116] The alignment performance of the proposed method on a real-time system was verified. The performance parameters of the inertial navigation system in the experiment are shown in Table 1.

[0117] Table 1 IMU Performance Parameters

[0118]

[0119] The heading references for the four directions of the turntable are shown in Table 2.

[0120] Table 2 Heading Reference

[0121]

[0122] based on Figure 1 The process, initial alignment time T a =300 seconds, two sets of rapid alignment tests were conducted in four directions.

[0123] In the comparative test, the following four alignment schemes were used:

[0124] Scheme 1 (coarse alignment of inertial frame for 100 seconds + fine alignment of KF for 200 seconds, denoted as IF+KF), Scheme 2 (coarse alignment of compass method for 100 seconds + fine alignment of KF for 200 seconds, denoted as GC+KF), Scheme 3 (optimized alignment for 100 seconds + fine alignment of KF for 200 seconds, denoted as OBA+KF), and the scheme proposed in this invention, Scheme 4 (LSEGAKF alignment for 300 seconds).

[0125] In rapid alignment, the selection of the initial mean square error matrix will affect the alignment result. For horizontal attitude, it is set to 0.01°; for the initial mean square error matrix parameter corresponding to the heading angle, its observability is relatively poor and it directly affects the degree of positioning divergence. Therefore, three different parameter selections were made for each alignment scheme. The parameter selection P corresponding to result 1 and error 1 is shown below. _ψ = (0.1°) 2 Result 2 and error 2 correspond to P _ψ =(1°) 2 Result 3 and error 3 correspond to P _ψ = (0.01°) 2 .

[0126] After alignment, the attitude matrix output by S6.2 was converted into Euler angles, and the alignment accuracy was evaluated using the heading alignment results. The experimental results are shown in Table 3:

[0127] Table 3 Heading Alignment Results and Errors

[0128] Unit: (°)

[0129]

[0130]

[0131] The standard deviation of heading error is shown in Table 4:

[0132] Table 4 Standard Deviation of Heading Error

[0133]

[0134] It is evident that the alignment accuracy error of this invention (Scheme4) is minimal.

[0135] Example 2

[0136] In-vehicle navigation tests were conducted to further verify the alignment accuracy and navigation performance of the proposed alignment algorithm.

[0137] A 300-second rapid alignment test was conducted using the four alignment methods described in Example 1. Navigation errors were compared after alignment. The time allocation for methods Scheme 1-Scheme 3 was 100 seconds for coarse alignment and 200 seconds for fine alignment. The test results are as follows: Figures 2-4 As shown.

[0138] In addition, rapid alignment tests were conducted under different alignment time allocations, and the navigation error comparisons are shown in Table 5.

[0139] Table 5 Comparison of navigation errors under different alignment time allocations

[0140]

[0141] In the table, "C30+F270" means a coarse alignment time of 30 seconds plus a fine alignment time of 270 seconds.

[0142] It is evident that the present invention (LSEGAKF) exhibits the smallest navigation error within 2 hours, which indirectly reflects the highest alignment accuracy of the present invention.

Claims

1. A fast alignment method for a rotation-modulated inertial navigation system based on group affine properties, characterized in that, This method consists of the following steps: S1: Define the coordinate system, power on the inertial navigation system, the inertial navigation system's rotation mechanism executes a specific rotation sequence, and the inertial measurement unit collects data from the gyroscope and accelerometer and transmits it to the navigation computer in real time; S1.1 Define the coordinate system: Define the geocentric inertial coordinate system as the inertial reference coordinate system, denoted as the i-system; define the geocentric-ground-fixed coordinate system as the e-system; define the "East-North-Sky" geographic coordinate system as the navigation coordinate system, denoted as the n-system; define the x, y, and z axes of the carrier coordinate system as pointing to the right-front-up directions of the carrier, denoted as the b-system; define the x, y, and z axes of the IMU coordinate system as corresponding to the sensitive axes of the three gyroscopes, denoted as the s-system. S1.2 Inertial Navigation System Power On, Set Initial Alignment Time T a Start the navigation computer timer and initialize time k = 0; S1.3 IMU acquires the gyroscope output angular velocity at time k. Comparison with accelerometer output And and Transmitted in real time to the navigation computer; "~" indicates that the gyroscope output angular velocity and accelerometer output specific force include measurement errors; After power-on, S1.4 The indexing mechanism synchronously executes the dual-position indexing sequence: 1) The stationary position of the indexing mechanism T a / 2-180 / ω-0.5×ω / a seconds; 2) The rotation mechanism around the axial axis rotates 180° at an angular velocity of ω; 3) The indexing mechanism is stationary (T) a / 2-180 / ω-0.5×ω / a seconds; Among them, T a The initial alignment time is given in seconds; ω is the angular velocity of the indexing mechanism in ° / s; and a is the angular acceleration of the indexing mechanism in ° / s. 2 ; S2: The navigation computer receives the angular velocity output from the gyroscope in real time. Comparison with accelerometer output Then, inertial navigation calculations are performed: S2.1 Initialize navigation parameters, as follows: S2.1.1 Define the navigation parameters at time k: The attitude matrix of the IMU is The velocity vector is v e (k), with position vector p e (k), the auxiliary velocity vector is The superscript "e" indicates that this parameter is in the geocentric coordinate system, and the same applies below; S2.1.2 The attitude matrix at time k=0 Perform initialization: S2.1.3 The velocity vector v at k=0 e (0) Perform initialization: v e (0)＝[0 0 0] T (2) The superscript "T" indicates matrix transpose; S2.1.4 The position vector p at time k=0 e (0) Perform initialization: p e (0)=[L0 λ0 h0] T (3) In the formula, L0 represents the latitude of the inertial navigation system at the initial position, λ0 represents the longitude of the inertial navigation system at the initial position, and h0 represents the altitude of the inertial navigation system at the initial position. S2.1.5 The auxiliary velocity vector at time k=0 Perform initialization: Let be the projection of the rotational angular velocity of the e-frame relative to the i-frame into the e-frame. Earth's rotation rate ω ie =15° / h; Represents the calculation vector The antisymmetric matrix, and so on; S2.2 Navigation computer timer update: k = k + 1; S2.3 Perform inertial navigation calculations in the geocentric-fixed coordinate system, as follows: S2.3.1 Perform attitude update: In the formula I 3×3 It is a 3×3 identity matrix; Φ(k) is the equivalent rotation vector at time k, which is generated by the angular velocity output by the gyroscope. The calculation shows that Φ(k) is the modulus of Φ(k), i.e., Φ(k) = |Φ(k)|; S2.3.2 performs a speed update: In the formula T is the specific force value output by the accelerometer. s The sampling time interval for IMU data; Let be the gravitational force vector at time k; and the auxiliary velocity vector at time k-1. With the velocity vector v at time k-1 e The relationship between (k-1), the gravitational vector at time k-1 The gravitational vector g at time k-1 e The relationships between (k-1) are as follows: S2.3.3 performs a location update: S3: Construct a fast alignment state model for a rotation modulation inertial navigation system that satisfies the group affine property. By constructing a state model for rapid alignment of a rotation-modulated inertial navigation system that satisfies the group affine property, the problem of Kalman filter failure caused by nonlinear models can be effectively solved; specifically as follows: S3.1 Constructing a state model for rapid alignment of a rotation modulation inertial navigation system that satisfies group affine properties In the formula, X k Z is the 18-dimensional state vector at time k. k Φ is the 3D measurement vector at time k; k|k-1 G is the one-step state transition matrix from time k-1 to time k; k|k-1 Assign a system noise matrix H from time k-1 to time k. k The measurement matrix at time k; w k-1 The system noise matrix at time k-1; v k Let k represent the observation noise matrix at time k; S3.1.1 Constructing an 18-dimensional state vector X k : In the formula, This represents the attitude error of the IMU at time k, and the subscript "lg" indicates that the type of this error is a left-invariant error that satisfies the group affine property. This represents the velocity error of the IMU at time k; ε represents the position error of the IMU at time k; s (k) represents the gyroscope drift of the IMU at time k. L represents the zero bias of the IMU's accelerometer at time k. s (k) represents the inner arm error of the IMU at time k; S3.1.2 Constructing the 3D Measurement Vector Z k : In the formula, v e (k) represents the velocity vector at time k: To measure velocity, since the alignment of the rotationally modulated inertial navigation system is performed while the vehicle remains stationary, S3.1.3 Construct the one-step state transition matrix Φ from time k-1 to time k. k|k-1 : In the formula I 18×18 I represents an 18×18 identity matrix. 3×3 Represents a 3×3 identity matrix, 0 3×3 Represents a 3×3 zero matrix; S3.1.4 Construct the system noise distribution matrix G from time k-1 to time k. k|k-1 : S3.1.5 Construct the measurement matrix H at time k k : S4: Estimating state quantities for a rapidly aligned state model of a rotation-modulated inertial navigation system based on S3. S4.1 Calculate the posterior estimate of the state vector from time k-1 to time k. In the formula, X represents the 18-dimensional state vector output at time k-1. k-1 The posterior estimate; initial value Represents the state vector X k The one-step prediction from time k-1 to time k, i.e. the prior estimate at time k; S4.2 Calculate the mean square error matrix for one-step state prediction from time k-1 to time k: In the formula, P k-1 Let P represent the mean square error matrix of the posterior state estimate at time k-1. kk-1 This represents the mean square error matrix for one-step prediction of the state from time k-1 to time k. Among them, P k-1 initial value Let T represent the initial value of the mean square error matrix under the n-system projection, and let T represent the mean square error coordinate system transformation matrix. S4.3 Calculate the filter gain K at time k k : In the formula, the measurement noise covariance matrix R is: S4.4 Calculate the posterior estimate of the state at time k S4.5 Calculate the error estimates of each navigation parameter at time k: Attitude error estimate for The first to third dimensions are represented as Right now: Auxiliary speed error estimate for The 4th to 6th dimensions are represented as Right now: Position error estimate for The 7th to 9th dimensions are represented as Right now: S4.6 Calculate the mean square error matrix P of the posterior state estimate at time k. k : P k =P k|k-1 -K k H k P k|k-1 (28) S5: Use the error estimate obtained from S4.5 to correct the navigation solution result of S2, as follows: S5.1 Corrected Attitude Matrix Obtain the corrected attitude matrix In the formula, Indicates to The formula for matrix exponentiation is as follows: S5.2 Corrected Auxiliary Velocity Vector Obtain the corrected auxiliary velocity vector S5.3 Corrected position vector p e (k) yields the corrected position vector. S6: Determine whether alignment should continue if k < T a When k = T, execute S6.1; a At that time, execute S6.2 to output the corrected high-precision attitude matrix. The alignment is now complete; details are as follows: S6.1 When k < T a At that time, perform the following steps: S6.1.1 will modify the navigation parameters. and Uncorrected memory in the navigation computer p e (k), that is: S6.1.2 will p e (k) P k Stored in the navigation computer's memory; then return to S2.2 and continue execution to S6 to perform the next condition check in S6; S6.2 When k = T a At that time, output the corrected attitude matrix. Initial alignment complete.

2. A fast alignment method for a rotation modulation inertial navigation system based on group affine properties according to claim 1, characterized in that: In S1.4, the initial alignment time T a Set it to 300 seconds or 600 seconds.

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