CN1908584A

CN1908584A - Method for determining initial status of strapdown inertial navigation system

Info

Publication number: CN1908584A
Application number: CN 200610112526
Authority: CN
Inventors: 房建成; 宫晓琳; 盛蔚; 杨胜; 徐帆; 刘百奇
Original assignee: Beihang University
Current assignee: Beihang University
Priority date: 2006-08-23
Filing date: 2006-08-23
Publication date: 2007-02-07
Anticipated expiration: 2026-08-23
Also published as: CN100516775C

Abstract

The initial attitude determination method for SINS comprises: rotating the SINS from initial position to any one position round arbitrary 3D axis; according to SINS output on first position and the relation of earth rotational angular velocity and acceleration of gravity, determining the initial attitude primarily; then, using Kalman filter to estimate the gyro constant drift and other values for more accurate initial attitude. This invention improves observability and precision.

Description

Initial attitude determination method for strapdown inertial navigation system

Technical Field

The invention relates to a method for determining the initial attitude of a Strapdown Inertial Navigation System (SINS), which can be used for determining the initial attitude of various high-and-medium-precision strapdown inertial navigation systems, and is particularly suitable for the conditions that no indexing mechanism exists during the installation of an airborne SINS, or the indexing mechanism has low precision and limited rotation angle.

Background

The basic principle of a Strapdown Inertial Navigation System (SINS) is that according to a mechanical law relative to an inertial space proposed by Newton, a gyroscope and an accelerometer are used for measuring linear motion and angular motion parameters of a carrier relative to the inertial space, and under a given motion initial condition, a computer is used for carrying out integral operation to continuously provide position, speed and attitude information in real time. The SINS completely depends on self inertia sensitive elements and does not depend on any external information to measure navigation parameters, so the SINS has the advantages of good concealment, no limitation by weather conditions, no signal loss, no interference and the like, is a completely autonomous and all-weather navigation system, and is widely applied to the fields of aviation, aerospace, navigation and the like. According to the basic principles of SINS, the SINS must obtain initial information, including initial position, velocity, and attitude, before navigation positioning is resolved. The initial position and speed information of the SINS are easier to obtain than the initial attitude, and the accuracy after the initial attitude is determined is the initial accuracy when the SINS enters the navigation working state. Therefore, it is an important step to make a fast and accurate initial attitude determination when the SINS starts to work.

The initial attitude determination of the existing strapdown inertial navigation system can be divided into two stages of coarse alignment and fine alignment. In the coarse alignment stage, the output of a gyroscope and an accelerometer at a single position or two positions (fixed two positions or any two positions) is directly introduced into a computer under the condition of a static base, and the initial attitude of the carrier is calculated. In this method, errors of the gyroscope and the accelerometer and external interference factors are often ignored, but these factors cause errors, so the initial attitude calculation accuracy is not high. Particularly, when the outputs of the gyroscope and the accelerometer which are fixed at two positions are adopted for calculation, the SINS is required to rotate 180 degrees or 90 degrees around the Z axis, so that the SINS needs to be installed on an indexing mechanism, the 180-degree or 90-degree rotation is realized by using the indexing mechanism, the engineering use is very inconvenient, the precision of the indexing mechanism is not high, the rotation angle cannot be accurately measured, and the precision of initial attitude determination is reduced. Due to the limitation of the installation position of the SINS in specific engineering, the rotation angle cannot meet the requirement of 180 degrees or 90 degrees, and at the moment, the existing method for determining the initial posture of fixing two positions cannot be applied. In addition, when the gyroscope and the accelerometer at any two positions are used for output, an arcsine function, errors of the gyroscope and the accelerometer, measurement errors and the like are required to be calculated, so that the calculation result is easy to be unstable, and an imaginary number phenomenon occurs. Thus, the time for determining the initial attitude is multiplied, and the accuracy of the initial attitude calculation cannot be guaranteed.

And the fine alignment stage is carried out on the basis of coarse alignment, and data output by the gyroscope and the accelerometer are processed by using a state space method of a modern control theory. When data of a single position is processed, the observability of an azimuth misalignment angle is poor, the convergence rate is low, the required time is long, and errors of a gyroscope and an accelerometer cannot be observed, so that better estimation cannot be performed, the purpose of improving the accuracy of an initial attitude cannot be achieved, and the calibration of the gyroscope and the accelerometer cannot be realized while the initial attitude is calculated. When data of two fixed positions are processed, as described above, the conventional method for determining the initial posture of the two fixed positions has the limitation of a rotation angle, has high requirements on the precision of a steering mechanism, and cannot be applied to specific engineering.

Disclosure of Invention

The technical problem to be solved by the invention is as follows: the method overcomes the defects of the prior art and provides an accurate and convenient method for determining the initial attitude of the strapdown inertial navigation system.

The technical solution of the invention is as follows: a method for determining initial attitude of strapdown inertial navigation system,

the method comprises the following specific steps:

(1) SINS preheating preparation, wherein the specific preparation time is different according to different systems;

(2) after the SINS is prepared, keeping the SINS still at an initial position (called as a first position), and collecting gyroscope output and accelerometer output;

(3) calculating a heading angle * for the first location using the relationship of the accelerometer output to gravitational acceleration and the relationship of the gyroscope output to the angular rate of rotation of the earth₁Angle of pitch theta₁And roll angle γ₁；

(4) Rotating the SINS from a first position to any position (called a second position) around a space three-dimensional arbitrary axis by any method without an indexing mechanism, keeping the SINS stationary at the second position, and collecting gyroscope output and accelerometer output;

(5) using kalman filtering technique, *₁、θ₁And gamma₁As initial parameters, the data output by the gyroscope and accelerometer at two positions are processed. Due to the change of the SINS position, a system matrix in the SINS error model is changed, so that the observability of the SINS system is improved, the filtering effect is improved, and an error angle (misalignment angle phi for short) between a geographic coordinate system n' and a real geographic coordinate system n is calculated when the second position is estimated better_x、φ_yAnd phi_z) Gyroscope constant drift and accelerometer constant bias;

(6) using estimated phi_x、φ_yAnd phi_zCalculating a transformation matrix C between a real geographic coordinate system n and a calculated geographic coordinate system n_n′ ⁿ. According to the angular increment or angular speed information output by the gyroscope, a quaternion method is adopted to calculate a conversion matrix C between a carrier coordinate system b and a geographical coordinate system n_b ^n′. From C_n′ ⁿAnd C_b ^n′Calculating a transformation matrix C between the carrier coordinate system b and the real geographic coordinate system n_b ⁿThen from C_b ⁿCalculating a heading angle * for the second location₂Angle of pitch theta₂And roll angle γ₂This is taken as the initial attitude of the SINS.

The principle of the invention is as follows: when the SINS keeps still at a certain position, the output of the accelerometer and the gravity acceleration and the output of the gyroscope and the rotation angular rate of the earth have the following relations:

[\begin{matrix} f_{x 1} \\ f_{y 1} \\ f_{z 1} \end{matrix}] = C_{n}^{b} [\begin{matrix} 0 \\ 0 \\ g \end{matrix}] . . . (1)

wherein f is_x1、f_y1And f_z1And ω_x1、ω_y1And ω_z1The specific force and angular rate of the X-axis, Y-axis and Z-axis outputs of the SINS at the position are respectively; g is the acceleration of gravity; omega_ieThe angular velocity of the earth rotation is the projection of the angular velocity of the earth in the east, north and sky directions, which is omega-0 omega_iecosL ω_iesinL](ii) a L is the local latitude; c_n ^bFor the transformation matrix of the navigation coordinate system to the carrier coordinate system,

C_{n}^{b} = {(C_{b}^{n})}^{T} = [\begin{matrix} C_{11} & C_{13} & C_{13} \\ C_{21} & C_{12} & C_{23} \\ C_{31} & C_{32} & C_{33} \end{matrix}] .

C_n ^bthe heading angle * at this position may be expressed₁Angle of pitch theta₁And roll angle γ₁Using the expressions (1) and (2), * at the position can be calculated₁、β₁And gamma₁. The calculation formula is as follows:

the formula (1) and (2) can be used for obtaining:

C_{13} = \frac{f_{x 1}}{g}

C_{23} = \frac{f_{y 1}}{g}

C_{33} = \frac{f_{z 1}}{g}

C₁₁＝C₂₂C₃₃-C₂₃C₃₂

C₂₁＝-C₁₂C₃₃+C₁₃C₃₂

C₃₁＝C₁₂C₂₃-C₁₃C₂₂

heading angle *₁Angle of pitch theta₁And roll angle γ₁The main value calculation formula of (2) is:

if the heading angle *₁Angle of pitch theta₁And roll angle γ₁Is defined as [0, 2 pi ]]、

[-π，+π]Then *₁、θ₁And gamma₁The true value of (c) can be determined as follows.

θ₁＝θ_{1 main} (5)

* determined by formula (5)₁、θ₁And gamma₁Namely the heading angle, pitch angle and roll angle of the SINS at the position.

Heading angle * determined by equation (1) and equation (2) without taking into account accelerometer bias, gyroscope drift, and measurement errors in accelerometer and gyroscope output information₁Angle of pitch theta₁And roll angle γ₁The true angular relationship between the carrier coordinate system and the local geographical coordinate system cannot be accurately described. Therefore, the initial attitude misalignment angle should be estimated from random errors and random disturbances on this basis, further using modern estimation theory.

Using kalman filtering technique, *₁、θ₁And gamma₁As initial parameters, the error angle between the calculated geographic coordinate system n' and the true geographic coordinate system n can be estimated, and C can be corrected_b ^n′Then, a more accurate initial posture can be obtained. However, when kalman filtering processes outputs of an accelerometer and a gyroscope at a single position, the system is not completely observable, wherein errors of two accelerometers and one gyroscope are not observable, so that the estimation effect is poor, and the purpose of improving the initial attitude precision is not achieved. The SINS is rotated to any position around a space three-dimensional arbitrary axis from the first position, namely the position of the SINS is changed, so that a system matrix in an SINS error model is changed, the observability of the SINS system is improved, the Kalman filtering effect is improved, and the misalignment angle and errors of a gyroscope and an accelerometer are better estimated. Using estimated misalignment angle versus conversion matrix C_b ^n′And correcting to obtain more accurate course angle, pitch angle and roll angle.

Compared with the prior art, the invention has the advantages that:

(1) the method breaks through the constraint that the SINS needs to be rotated by 180 degrees or 90 degrees around the Z axis through an indexing mechanism in the traditional fixed two-position initial attitude calculation, but does not need to be rotated to any position around any axis through the indexing mechanism, and is a spatial three-dimensional arbitrary two-position initial attitude calculation method. The reduction of the calculation precision of the initial posture of the two fixed positions caused by low precision of the indexing mechanism is avoided, namely, the calculation precision of the initial posture is improved. In addition, the SINS can be rotated to any position around any axis, and the application in practical engineering is greatly facilitated.

(2) The invention utilizes the data output by the gyroscope and the accelerometer on two positions to improve the observability of the SINS system, improve the filtering effect of the Kalman filter, better estimate the misalignment angle, the constant drift of the gyroscope and the constant offset of the accelerometer, and correct the attitude matrix by utilizing the estimated misalignment angle to obtain more accurate course angle, pitch angle and roll angle.

(3) The invention can complete the tasks of drift measurement and calibration while calculating the initial attitude, not only improves the calculation precision of the initial attitude of the system, but also improves the calibration precision, and can effectively improve the navigation positioning precision by compensating in the SINS navigation state.

Drawings

FIG. 1 is a flow chart of an initial pose determination method of the present invention;

FIG. 2 is a schematic view of heading angle *, pitch angle θ and roll angle γ, where Ox_ny_nz_nFor navigation, i.e. the northeast geographic coordinate system, Ox_by_bz_bIs a carrier coordinate system. Wherein fig. 2a shows a secondary navigation coordinate system Ox_ny_nz_nRotates counterclockwise * around zn axis and the carrier coordinate system Ox_by_bz_bSuperposition, * is the course angle; fig. 2b shows a slave navigation coordinate system Ox_ny_nz_nAround x_nAxis anticlockwise rotation theta and carrier coordinate system Ox_by_bz_bSuperposing, wherein theta is a pitch angle; fig. 2c shows a navigation coordinate system Ox_ny_nz_nAround y_nAxle anticlockwise rotation gamma and carrier coordinate system Ox_by_bz_bAnd (5) overlapping, wherein gamma is the roll angle.

Detailed Description

As shown in fig. 1, the specific implementation method of the present invention is as follows:

1. preparation of strapdown inertial navigation system

After the SINS is started, entering a preparation state.

2. First position data acquisition

After the SINS is prepared, the SINS is kept still at an initial position (called a first position), 5 minutes of gyroscope output and accelerometer output are collected, and if the SINS is low in precision, the collecting time can be properly prolonged.

3. First position attitude calculation

The navigation coordinate system is taken as the northeast geographic coordinate system, the first position heading angle *₁Angle of pitch theta₁And roll angle γ₁As shown in fig. 2a, 2b and 2 c.

The accelerometer output has the following relationship with the gravitational acceleration and the gyroscope output with the earth rotation angular rate:

[\begin{matrix} f_{x 1} \\ f_{y 1} \\ f_{z 1} \end{matrix}] = C_{n b}^{} [\begin{matrix} 0 \\ 0 \\ g \end{matrix}] . . . (6)

in the formula (f)_x1、f_y1And f_z1And ω_x1、ω_y1And ω_z1The specific force and the angular rate of the X-axis output, the Y-axis output and the Z-axis output of the SINS at the first position are respectively; g is the acceleration of gravity; omega_ieThe angular velocity of the earth rotation is the projection of the angular velocity of the earth in the east, north and sky directions, which is omega-0 omega_iecosL ω_iesinL]L represents the local latitude; c_n ^bFor navigation of the transformation matrix tied to the carrier system, we can write:

C_{n}^{b} = {(C_{b}^{n})}^{T} = [\begin{matrix} C_{11} & C_{13} & C_{13} \\ C_{21} & C_{12} & C_{23} \\ C_{31} & C_{32} & C_{33} \end{matrix}] .

the formula (6) and (7) can be used for obtaining:

C_{13} = \frac{f_{x 1}}{g}

C_{23} = \frac{f_{y 1}}{g}

C_{33} = \frac{f_{z 1}}{g}

C₁₁＝C₂₂C₃₃-C₂₃C₃₂

C₂₁＝-C₁₂C₃₃+C₁₃C₃₂

C₃₁＝C₁₂C₂₃-C₁₃C₂₂

θ_{1 main}＝arcsin(C₂₃) (9)

θ₁＝θ_{1 main} (10)

* determined by formula (10)₁、θ₁And gamma₁Namely the heading angle, the pitch angle and the roll angle of the SINS at the first position.

4. Second position data acquisition

Rotating the SINS from an initial position to any position (called a second position) around a space three-dimensional arbitrary axis by an arbitrary method, keeping the SINS still at the second position, and acquiring 5-minute gyroscope output and accelerometer output.

5. Filtering the data at two positions

* will be mixed₁、θ₁And gamma₁As initial parameters, processing data output by the gyroscope and the accelerometer at two positions by using a Kalman filtering technology to accurately estimate a misalignment angle phi_x、φ_yAnd phi_z(the northeast geographyPhi in the coordinate system_E、φ_NAnd phi_U) And gyroscope constant drift and accelerometer constant bias.

(1) Establishment of SINS initial attitude determination error model

The navigation coordinate system is taken as a northeast geographical coordinate system, errors of position and vertical speed are omitted, errors of an accelerometer and a gyroscope are taken as a random bias whitening noise process, and an error model of the SINS is as follows:

in the formula, subscripts E, N, U represent east, north, and day, respectively. Angular rate of rotation omega of the earth_ieIn east and northAnd the projection in the vertical direction is [0 ω ═ 0 ω_iecosL ω_iesinL]＝[0 Ω_N Ω_U]L represents the local latitude; subscripts x, y and z are carrier coordinate systems; t is_ij(i-1, 2, 3; j-1, 2, 3) is an attitude matrix C_b ⁿThe elements (A) and (B) in (B),

C_{b}^{n} {= {T_{ij}}}_{i = 1,2,3; j = 1,2,3} .

(2) establishment of SINS initial attitude determination Kalman filtering model

For a strapdown inertial navigation system, equation (11) is modified to the form:

wherein W (t) is white Gaussian noise of N (O, Q); state variable X_a＝[δV_E δV_N φ_E φ_N φ_U]^T，X_b＝[▽_x▽_yε_xε_yε_z]^T(ii) a Random noise state vector

Wherein, δ V_E、δV_NEast and north velocity errors, phi, respectively_E、φ_NIs a horizontal misalignment angle; phi is a_UIs the azimuth misalignment angle; ▽_x、▽_yFor random constant bias of accelerometers, epsilon_x、ε_y、ε_zIs the gyroscope random constant drift; 0_5×5And 0_5×1All are zero matrices of specified dimensions; f and T_iContent of the representativeThe following were used:

T_{i} = [\begin{matrix} T_{11} & T_{12} & 0 & 0 & 0 \\ T_{21} & T_{22} & 0 & 0 & 0 \\ 0 & 0 & T_{11} & T_{12} & T_{13} \\ 0 & 0 & T_{21} & T_{22} & T_{23} \\ 0 & 0 & T_{31} & T_{32} & T_{33} \end{matrix}],

(12) the formula is a system equation for determining a Kalman filtering model for the initial attitude of the strapdown inertial navigation system. In order to apply the kalman filter to perform the optimal estimation of the state vector, a system observation equation needs to be established. Two horizontal velocity errors are selected as observed quantities, and a system observation equation is established

Wherein η (t) is the system observation noise vector, which is the gaussian white noise process of N (O, R).

(3) Establishment of discrete Kalman filtering model

From the system equation and the observation equation, a discrete kalman filter equation can be established as follows.

The filter equation:

gain equation:

K_{k} = P_{k, k - 1} H_{k}^{T} {[H_{k} P_{k, k - 1} H_{k}^{T} + R_{k}]}^{- 1} . . . (15)

prediction error variance equation:

filter error variance equation:

P_k＝[I-K_kH_k]P_k，k-1 (17)

in the formula phi_k，k-1For the discretized state transition matrix (system matrix), Q, R are covariance matrices of the system noise and the observed noise, respectively.

(4) Initial condition of filtering

X(0)＝0_10×1；

The values of the medium-precision SINS corresponding to P (0), Q and R are as follows:

P(0)＝diag{(0.3m/s)²，(0.3m/s)²，(30′)²，(10″)²，(10″)²，

(100μg)²，(100μg)²，(0.1°)²，(0.1°)²，(0.1°)²}；

Q＝diag{(100μg)²，(100μg)²，(0.1°)²，(0.1°)²，(0.1°)²，0，0，0，0，0}；

R＝diag{(0.1m/s)²，(0.1m/s)²}。

6. calculating gyroscope random constant drift and accelerometer random constant bias

▽ estimated by the filter_x、▽_yI.e. the accelerometer is biased at a random constant, epsilon_x、ε_y、ε_zBeing gyroscopesA random constant drift.

7. Conversion matrix C between the calculation of the carrier coordinate system b and the calculation of the geographical coordinate system n_b ^n′

C can be calculated by utilizing angular increment or angular speed information output by a gyroscope and adopting a quaternion method_b ^n′The calculation steps are as follows:

(1) using heading angle *₁Angle of pitch theta₁And roll angle γ₁Initializing the attitude at the first position, and calculating an initial transformation matrix C_b ^n′And a quaternion q, the calculation formula is as follows:

order to

Then there are:

<math> <mrow> <msub> <mi>q</mi> <mn>0</mn> </msub> <mo>=</mo> <mo>&PlusMinus;</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msqrt> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mn>11</mn> </msub> <mo>+</mo> <msub> <mi>T</mi> <mn>22</mn> </msub> <mo>-</mo> <msub> <mi>T</mi> <mn>33</mn> </msub> </msqrt> </mrow> </math>

<math> <mrow> <msub> <mi>q</mi> <mn>1</mn> </msub> <mo>=</mo> <mo>&PlusMinus;</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msqrt> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mn>11</mn> </msub> <mo>+</mo> <msub> <mi>T</mi> <mn>22</mn> </msub> <mo>-</mo> <msub> <mi>T</mi> <mn>33</mn> </msub> </msqrt> </mrow> </math>

<math> <mrow> <msub> <mi>q</mi> <mn>2</mn> </msub> <mo>=</mo> <mo>&PlusMinus;</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msqrt> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mn>11</mn> </msub> <mo>+</mo> <msub> <mi>T</mi> <mn>22</mn> </msub> <mo>-</mo> <msub> <mi>T</mi> <mn>33</mn> </msub> </msqrt> </mrow> </math>

<math> <mrow> <msub> <mi>q</mi> <mn>3</mn> </msub> <mo>=</mo> <mo>&PlusMinus;</mo> <mfrac> <mn>1</mn> <mn>2</mn> </mfrac> <msqrt> <mn>1</mn> <mo>+</mo> <msub> <mi>T</mi> <mn>11</mn> </msub> <mo>+</mo> <msub> <mi>T</mi> <mn>22</mn> </msub> <mo>-</mo> <msub> <mi>T</mi> <mn>33</mn> </msub> </msqrt> </mrow> </math>

(2) updating quaternion q₀、q₁、q₂、q₃And a conversion matrix C_b ^n′

Wherein,

conversion matrix C_b ^n′The update formula of (2) is as follows:

8. calculate heading angle *₂Angle of pitch theta₂And roll angle γ₂

Phi estimated using Kalman filtering_E、φ_N、φ_UCalculating a transformation matrix C between a real geographic coordinate system n and a calculated geographic coordinate system n_n′ ⁿ. According to C_n′ ⁿC calculated by the formula (20)_b ^n′Calculating a transformation matrix C between the carrier coordinate system b and the real geographic coordinate system n_b ⁿThen from C_b ⁿCalculating a heading angle * for the second location₂Angle of pitch theta₂And roll angle γ₂This is taken as the initial attitude of the SINS. The specific calculation steps are as follows:

(1) calculating a transformation matrix C between a real geographic coordinate system n and a calculated geographic coordinate system n_n ^n′

(2) Calculating a transformation matrix C between the carrier coordinate system b and the real geographic coordinate system n_b ⁿ

(3) Calculate heading angle *₂Angle of pitch theta₂And roll angle γ₂

Heading angle *₂Angle of pitch theta₂And roll angleγ₂As shown in fig. 2a, 2b and 2 c.

C calculated from the formula (22)_b ⁿIs marked as

C_{b}^{n} = [\begin{matrix} T_{11} & T_{12} & T_{13} \\ T_{21} & T_{22} & T_{23} \\ T_{31} & T_{32} & T_{33} \end{matrix}] . . . (23)

And because of

Thus, from equations (23) and (24), heading angle * may be determined₂Angle of pitch theta₂And roll angle γ₂Principal value of, i.e.

If the heading angle *₂Angle of pitch theta₂And roll angle γ₂Are respectively defined as [0, 2 pi ]]、

[-π，+π]. Then *₂、θ₂And gamma₂The true value of (c) can be determined by:

θ₂＝θ_{2 main} (26)

* determined by formula (26)₂、θ₂And gamma₂Namely the course angle, the pitch angle and the roll angle of the SINS at the second position, and the course angle, the pitch angle and the roll angle are used as the initial attitude of the SINS entering the navigation working state.

Claims

1. A strap-down inertial navigation system initial attitude determination method is characterized by comprising the following steps:

(1) after the SINS preheating preparation is finished, keeping the SINS at an initial position, namely a first position, standing still, and collecting gyroscope output and accelerometer output;

(2) calculating a heading angle * for the first location based on the relationship of the accelerometer output to gravitational acceleration and the relationship of the gyroscope output to the angular rate of rotation of the earth₁Angle of pitch theta₁And roll angle γ₁；

(3) Rotating the SINS from a first position to any position around a spatial three-dimensional arbitrary axis, wherein the position is called a second position, keeping the SINS still at the second position, and collecting gyroscope output and accelerometer output;

(4) using kalman filtering technique, *₁、θ₁And gamma₁Processing data output by the gyroscope and the accelerometer on two positions as initial parameters, and calculating an error angle between a geographic coordinate system n' and a real geographic coordinate system n when estimating a second position, which is referred to as a misalignment angle phi for short_x、φ_yAnd phi_zGyroscope constant drift and accelerometer constant bias;

(5) phi estimated using Kalman filtering_x、φ_yAnd phi z calculating a transformation matrix C between the real geographic coordinate system n and the calculated geographic coordinate system n_n＇ ⁿAccording to the angular increment or angular speed information output by the gyroscope, a quaternion method is adopted to calculate a conversion matrix C between a carrier coordinate system b and a geographical coordinate system n_b ^n′Then from C_b ⁿCalculating a heading angle * for the second location₂Angle of pitch theta₂And roll angle γ₂This is taken as the initial attitude of the SINS.