Three-axis frame type inertial navigation system error self-calibration and compensation method

Abstract

The invention relates to an error self-calibration and compensation method for a three-axis frame type inertial navigation system, which realizes complete shaft system non-orthogonal error coefficient self-calibration, including frame non-orthogonal error and frame angle zero offset, and can calibrate all error coefficients of a common accelerometer error model. Through self-calibration and compensation of the error coefficient, the carrier or base attitude measurement precision of the frame-type inertial navigation system can be improved, and a high-precision table attitude measurement reference can be provided for the inertial navigation system under the static base condition; and thus, the performance of application schemes such as self-calibration, initial alignment and inertial navigation of the inertial navigation system related to the table body attitude precision is improved.

Description

Technical Field

[0001] The invention relates to a three-axis frame type inertial navigation system error self-calibration and compensation method, belonging to the technical field of inertial navigation. Background Art

[0002] The inertial navigation system uses accelerometers and gyroscopes to measure the angular and linear motion parameters of the carrier, and obtains the carrier's speed, position, attitude and other information through navigation calculations. According to the way the inertial measurement reference is established, the inertial navigation system can be divided into two categories: platform-based inertial navigation systems and strapdown inertial navigation systems.

[0003] The platform-type inertial navigation system (also known as inertial platform) installs inertial measurement elements (mainly including gyroscopes and accelerometers) on the same inertial measurement assembly (hereinafter referred to as the platform), uses the gyroscope to sense the angular motion of the platform, controls the platform to track the navigation coordinate system through a rotating frame transfer mechanism, and isolates the angular motion of the carrier; then uses an accelerometer to measure the acceleration information (specific force) of the platform in the navigation coordinate system, and uses the navigation computer to perform integral operations to obtain information such as the speed and position of the platform's movement.

[0004] The strapdown inertial navigation system does not have a rotation control mechanism to track the navigation coordinate system during navigation. It only uses the gyroscope to sense the angular motion of the platform, and then calculates the platform attitude angle through the navigation computer to determine the relative angular position relationship between the current platform coordinate system and the navigation coordinate system (attitude matrix). The accelerometer is then used to measure the specific force in the platform coordinate system, and the attitude matrix obtained through attitude calculation is used to perform coordinate transformation to obtain the acceleration information in the navigation coordinate system. Then, an integral operation is performed to obtain information such as the speed and position of the platform movement.

[0005] In the application of inertial navigation system, the error of inertial instrument needs to be compensated to improve navigation accuracy. The errors that need to be compensated include zero bias, scale factor error, and installation error of gyroscope and accelerometer, which usually need to be calibrated before the navigation of inertial navigation system. The angular motion information such as attitude angle of the carrier needs to be calculated by the attitude angle output value of the platform and the measurement value of the frame angle sensor of the rotating mechanism, so the non-orthogonal error of the rotating frame and the frame angle sensor error also need to be compensated. Summary of the invention

[0006] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and solve the error self-calibration and compensation problem of a three-axis frame type inertial navigation system.

[0007] The purpose of the present invention is achieved through the following technical solutions:

[0008] A method for self-calibration and compensation of errors of a three-axis frame inertial navigation system is proposed. Under the condition of a static base, the platform is locked at 9 frame angle positions, and accelerometer measurements are collected. The specific force measurement values ​​of the inertial navigation system in the platform coordinate system of each locked position are calculated by using the accelerometer measurements, and the attitude matrix of the inertial navigation system from the platform coordinate system to the local horizontal coordinate system at each locked position is calculated, and the acceleration of the inertial navigation system in the local horizontal coordinate system at each locked position is obtained as the error observation. The residual of the error coefficient is obtained by the total least squares algorithm, and the estimated value of the measured parameter is corrected. The corrected error coefficient estimate is used for iterative calculation until the iterative convergence criterion is met to obtain the self-calibration results of each error coefficient. The method can calibrate 20 error coefficients such as accelerometer zero bias, scale factor error, installation error, asymmetric scale error, frame non-orthogonality error, and frame angle sensor zero bias. Through self-calibration and compensation of error coefficients, the measurement accuracy of the attitude of the carrier or base of the frame-type inertial navigation system affected by the non-orthogonal error of the axis system can be improved, and a high-precision reference benchmark for the attitude measurement of the platform can be provided for the inertial navigation system under static base conditions, thereby improving the performance of application solutions such as self-calibration, initial alignment and inertial navigation of the inertial navigation system related to the accuracy of the platform attitude.

[0009] More specific:

[0010] A three-axis frame inertial navigation system error self-calibration and compensation method, such as Figure 2 As shown, the following steps are included:

[0011] (1) The three-axis frame-type inertial navigation system to be tested is placed on a stable foundation with seismic isolation, such as a marble slab or a turntable, so that the horizontal attitude angle of the inertial navigation system base is less than 3°. By adjusting the attitude angle of the inertial navigation system base and controlling the frame transfer mechanism, the inertial navigation system frame orientation is adjusted as follows: Figure 1 Press Figure 1 The following table shows the definition of the polarity of the accelerometer's X, Y, and Z channels and input axes: p , Z p The axes are perpendicular to each other in a nearly horizontal position, Y p Axis perpendicular to X p OZ p Plane, X p , Y p , Z p According to the right-hand rule, an orthogonal coordinate system is formed, pointing to the front, top, and right directions of the platform coordinate system. The zero position of the frame angle sensor is defined as: when the output of the frame angle sensor of the inertial navigation system is zero, the base coordinate system and the platform coordinate system are approximately coincident, with the same polarity, and X p , Y p , Z pThey point to the front, top and right directions of the base coordinate system respectively. Assume that the range of the frame angle sensor measurement value is [0,360°].

[0012] (2) Control the rotating frame of the inertial navigation system and lock the platform at the frame angle position shown in Table 1. After the locking is stable, collect accelerometer measurement values ​​for no less than 3 minutes at a frequency of more than 10 Hz and calculate the average value. Where W p j is the average value of the j-axis accelerometer measurement, in pulses / s. There is no requirement for the order of the frame angle positions locked by data acquisition in Table 1.

[0013] Table 1 Angular positions of the self-calibrated locking frame of the inertial navigation system

[0014] Position number Outer ring frame angle (°) Center frame angle (°) Inner ring frame angle (°) 1 0 0 0 2 90 0 0 3 90 <![CDATA[α 1 ]]> 0 4 90 <![CDATA[α 2 ]]> 0 5 180 0 0 6 270 0 0 7 0 0 90 8 0 0 180 9 0 0 270

[0015] Among them, α 1 ,α 2 The value can be in the range of [10°, 170°] and [190°, 350°], usually |α 1 -α 2 |≥10°.

[0016] (3) Calculate the error coefficient observation matrix of each calibrated locking position and form the overall error coefficient observation matrix.

[0017]

[0018] In the formula, c ij For the elements of this direction cosine matrix, are the outer ring, middle ring, and inner ring frame angle values ​​of the kth row in Table 1, respectively. Then the error coefficient observation matrix H of the kth self-calibration locking position is (k) The calculation method is

[0019] H (k) =[H 1(k) H 2(k) H 3(k) H 4(k) ]

[0020] In the formula, the expression of each sub-matrix is

[0021]

[0022] In the formula, H 1(k) Medium ij The calculation result of the kth position should be taken. The expression of the error coefficient overall observation matrix is

[0023]

[0024] (4) Use the accelerometer measurement value to calculate the specific force measurement value of the inertial navigation system in the platform coordinate system at each locked position. The expression of the specific force measurement value at the kth position is:

[0025]

[0026] Where, k = 1, 2, ... 9; K 0j is the zero bias of the accelerometer in the j direction, unit: pulse number / s; K 1j is the accelerometer scale factor, unit: pulse number / (s·g 0 );E ij is the installation error angle, which indicates the influence of the i-direction specific force on the j-direction accelerometer measurement value, unit: rad; Δ nj is the asymmetric scale error coefficient of the accelerometer in the j direction, unit: 1. (i, j = x, y, z.) Calibration parameter K 0j ,E ij ,Δ nj The initial value of K is 0. 1j The initial value is the factory nominal value of the instrument.

[0027] (5) Calculate the attitude matrix (direction cosine matrix) of the inertial navigation system from the platform coordinate system to the local horizontal coordinate system at each locked position:

[0028]

[0029] Where k = 1, 2, ... 9; They are the measured values ​​of the outer ring, middle ring, and inner ring frame angle sensors, in rad; are the measured values ​​of the outer ring, middle ring, and inner ring frame angle sensors of the kth self-calibrated locking frame angle position, in rad; is the corresponding frame angle zero bias, unit: rad, j = 1, 2, 3; γ ij is the frame non-orthogonal error angle, unit: rad,i,j=x,y,z.

[0030] (6) Calculate the acceleration of the inertial navigation system in the local horizontal coordinate system g at each locked position:

[0031]

[0032] Where k = 1, 2, ... 9; α j is the base attitude angle (j = x, z.), unit: rad; is the gravitational acceleration in the local horizontal coordinate system, unit: g 0 .Since the actual acceleration of the inertial navigation system is 0, That is, the acceleration error observation at the kth locking position.

[0033] (7) Use the total least squares algorithm to obtain the estimated value of the error coefficient:

[0034] X=(H T H) -1 H T Z=[X 1 X 2 … X 20 ] T

[0035] In the formula, Z is The total observation quantity composed of

[0036]

[0037] (8) Use the least squares estimation result to correct the estimated value of the calibrated parameter and the base attitude angle. The calculation method is as follows:

[0038] Accelerometer bias:

[0039] K 0x | (n+1) =K 0x | (n) +X 1

[0040] K 0y | (n+1) =K 0y | (n) +X 2

[0041] K 0z | (n+1) =K 0z | (n) +X 3

[0042] Accelerometer scale factor:

[0043] K 1x | (n+1) =K 1x | (n) / (1-X 4 )

[0044] K 1y | (n+1) =K 1y | (n) / (1-X 5 )

[0045] K 1z | (n+1) =K 1z | (n) / (1-X 6 )

[0046] Accelerometer installation error:

[0047] E xy | (n+1) =E xy | (n) +X 7

[0048] E xz | (n+1) =E xz | (n) +X 8

[0049] E yz | (n+1) =E yz | (n) +X 9

[0050] Accelerometer asymmetric scaling error:

[0051] Δ nx | (n+1) =Δ nx | (n) +X 10

[0052] Δ ny | (n+1) =Δ ny | (n) +X 11

[0053] Δ nz | (n+1) =Δ nz | (n) +X 12

[0054] Base attitude angle:

[0055] α x | (n+1) =α x | (n) +X 13

[0056] α z | (n+1) =α z | (n) +X 14

[0057] Frame non-orthogonality error:

[0058] γ xy | (n+1) =γ xy |(n) +X 15

[0059] γ yz | (n+1) =γ yz | (n) +X 16

[0060] γ zx | (n+1) =γ zx | (n) +X 17

[0061] γ zy | (n+1) =γ zy | (n) +X 18

[0062] Frame angle sensor zero bias:

[0063]

[0064] In the above formulas, n is the number of iterative calculations, representing the result of the nth error separation, n = 0, 1, 2, ... wherein n = 0 represents the initial value of the error coefficient.

[0065] (9) Perform iterative calculation using the corrected error coefficient estimate, i.e. repeat steps (4) to (8) until each component X of the correction value X (least squares estimation result) is i All satisfy the iterative convergence criterion: ( is the convergence criterion value of the j-th dimension component), then the estimated values ​​of the error coefficients after the current least squares estimation result is corrected are the self-calibration results of the error coefficients. (i=1,2,…,20.) In engineering applications, the number of iterations N can generally be directly set to 5 to 10 times.

[0066] Furthermore, for an inertial navigation system having three accelerometers with orthogonally mounted input axes configured on the platform and three rotating frame axes, the error parameters shown in Table 2 below can be calibrated.

[0067] Table 2 Calibration parameters of this method

[0068] Error coefficient quantity Accelerometer bias 3 Accelerometer scale error 3 Accelerometer Asymmetric Scaling Error Factor 3 Accelerometer installation error 3 Inner ring frame non-orthogonal error angle 2 Non-orthogonal error angle of the middle ring frame 1 Outer ring frame non-orthogonal error angle 1 Inner ring shaft frame angle zero offset 1 Center ring axis frame angle zero offset 1

[0069] By compensating for the above error coefficients, the force measurement accuracy of the inertial navigation system and the base attitude angle measurement accuracy can be improved, thereby improving the inertial navigation accuracy and the carrier attitude measurement accuracy. The compensation method is as follows:

[0070] For an inertial navigation system with three accelerometers installed orthogonally on the platform, the accelerometer measurement value of the compensation error coefficient in the 1g gravity field environment of the static base self-calibration is expressed as follows:

[0071]

[0072] In the formula, f p is the specific force measurement output by the accelerometer combination, in g 0 ; K 0j is the zero bias of the accelerometer in the j direction, in pulses / s; K 1j is the scale factor error of the j-axis accelerometer, in pulses / s / g 0 ; E ij is the i-axis accelerometer around O j Installation error angle of the positive axis, in rad; W j p is the output value of the accelerometer in the j direction, in pulses / s; Δ nj It is the asymmetric scale factor error of the j-axis accelerometer, reflecting the difference between the positive and negative scale factors measured by the j-axis accelerometer, and its unit is 1. Where i, j = x, y, z.

[0073] For an inertial navigation system with three rotating frame axes, ideally, when the frame angle is at zero, the table coordinate system should be parallel to the base coordinate system, and each frame rotation axis should be parallel to each axis of the table coordinate system. However, due to factors such as part tolerance and reference deviation during the processing and assembly of the single inertial navigation system, processing and assembly errors are generally introduced, mainly in the form of inertial instrument installation errors and non-orthogonal errors of the frame axis system.

[0074] Assume that the frame orientation of the three-axis frame inertial navigation system is X, Y, and Z from outside to inside. When each rotating frame is at zero position, the rotation axes of each frame are orthogonal to each other, and the input axis of each axial accelerometer is approximately parallel to the direction of the corresponding frame rotation axis. Figure 1 shown.

[0075] Figure 1 In the equation, the subscript p represents the table coordinate system, and the subscript m represents the base coordinate system. The mathematical model of the axis non-orthogonality error of this three-axis frame inertial navigation system can be expressed by the direction cosine matrix from the table coordinate system to the base coordinate system:

[0076]

[0077] In the formula, m 3 is the inner ring frame coordinate system, m 2 is the middle ring frame coordinate system, m 1 is the outer ring frame coordinate system. The expressions of each matrix factor are as follows:

[0078] (1) The direction cosine matrix from the platform coordinate system to the inner ring frame coordinate system is:

[0079]

[0080] In the formula, γ zx ,γ zy is the non-orthogonal error angle of the inner ring frame.

[0081] (2) The direction cosine matrix from the inner ring frame coordinate system to the middle ring frame coordinate system is:

[0082]

[0083] In the formula, γ yz is the non-orthogonal error angle of the middle ring frame, is the measurement value of the inner ring frame angle sensor, It is the zero bias of the inner ring frame angle sensor.

[0084] (3) The direction cosine matrix from the middle ring frame coordinate system to the outer ring frame coordinate system is

[0085]

[0086] In the formula, γ xy is the non-orthogonal error angle of the table axis, is the measurement value of the middle ring frame angle sensor, It is the zero bias of the center ring frame angle sensor.

[0087] (4) The direction cosine matrix from the outer ring frame coordinate system to the base coordinate system is:

[0088]

[0089] In the formula, Measured value of the outer ring frame angle sensor.

[0090] Compared with the prior art, the present invention has the following beneficial effects:

[0091] The present invention realizes complete self-calibration of axis non-orthogonality error coefficients for the frame-type inertial navigation system, including frame non-orthogonality error and frame angle zero bias, and can calibrate all error coefficients of commonly used accelerometer error models. Through self-calibration and compensation of error coefficients, the measurement accuracy of the carrier or base attitude of the frame-type inertial navigation system can be improved, and a high-precision reference benchmark for the table attitude measurement can be provided for the inertial navigation system under static base conditions, thereby improving the performance of application solutions such as self-calibration, initial alignment and inertial navigation of the inertial navigation system related to the accuracy of the table attitude. BRIEF DESCRIPTION OF THE DRAWINGS

[0092] Figure 1 This is the frame orientation of the frame-type inertial navigation system of the present invention.

[0093] Figure 2 It is a schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0094] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be further described in detail below with reference to the accompanying drawings.

[0095] Based on simulation experiments, the specific implementation methods and application effects of the present invention are given. Assume that the frame orientation of the inertial navigation system is as follows: Figure 1 Assume that the error coefficients of the inertial navigation system shown in Table 2 are all normal distribution random constants: the accelerometer equivalent value range is 5000±50 pulses / (s·g 0 ), the accelerometer zero bias range is [-0.25, 0.25] pulse number / s, the accelerometer asymmetric scale error range is [-5e-6, 5e-6], the accelerometer installation error range is [-180, 180] arc seconds, the frame non-orthogonality error angle range is [-180, 180] arc seconds, the frame angle sensor zero bias range is [-180, 180] arc seconds, the inertial navigation system base horizontal attitude angle range is [-3°, 3°], and the base azimuth angle is uniformly distributed in the range of [0°, 360°).

[0096] The self-calibration locking frame angular positions used for self-calibration are shown in Table 3 below.

[0097] Table 3 Lock frame angular positions used in the inertial navigation system self-calibration example

[0098] Position number Outer ring frame angle (°) Center frame angle (°) Inner ring frame angle (°) 1 0 0 0 2 90 0 0 3 90 30 0 4 90 330 0 5 180 0 0 6 270 0 0 7 0 0 90 8 0 0 180 9 0 0 270

[0099] The actual attitude matrix of the platform is calculated according to the mathematical model of the non-orthogonal error of the axis system of the three-axis frame inertial navigation system, and the gravity acceleration is projected into the platform coordinate system to obtain the actual sensitive specific force of the accelerometer combination. The accelerometer specific force measurement value of each calibration position is calculated according to the accelerometer specific force output error model. The data sampling frequency is 100 Hz, and the data collection time for each position is 3 minutes.

[0100] The calculation method of steps (2) to (9) of the present invention is applied to process the simulated accelerometer measurement values, and the number of iterations N=10 is taken. The self-calibration results obtained are shown in Table 4 below.

[0101] Table 4 Self-calibration simulation test results

[0102]

[0103] The simulation test results verify the effectiveness of the method of the present invention.

[0104] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

[0105] Although the present invention has been disclosed as above in the form of a preferred embodiment, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solution of the present invention by using the methods and technical contents disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and modifications made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solution of the present invention shall fall within the protection scope of the technical solution of the present invention.

Claims

1. A three-axis frame inertial navigation system error self-calibration and compensation method, characterized in that: include: (1) The three-axis frame-type inertial navigation system to be tested is placed on a stable foundation with seismic isolation, so that the horizontal attitude angle of the inertial navigation system base is less than 3°; (2) Control the rotating frame of the inertial navigation system, lock the platform at nine frame angle positions, and collect accelerometer measurements after the lock is stable; (3) Calculate the error coefficient observation matrix of each calibrated locking position and form the overall error coefficient observation matrix; (4) using the accelerometer measurements to calculate the specific force measurements of the inertial navigation system in the body coordinate system at each locked position; (5) Calculate the attitude matrix of the inertial navigation system from the platform coordinate system to the local horizontal coordinate system at each locked position; (6) Calculate the acceleration of the inertial navigation system in the local horizontal coordinate system at each locked position of the inertial navigation system; (7) Use the total least squares algorithm to obtain an estimate of the error coefficient; (8) Using the least squares estimation results to correct the estimated values ​​of the calibrated parameters and the base attitude angle; (9) Perform iterative calculation using the corrected estimated value, and repeat steps (4) to (8) until the correction amount in the estimated value of the error coefficient meets the iterative convergence criterion.

2. The three-axis frame inertial navigation system error self-calibration and compensation method according to claim 1, characterized in that: Assume that the frame angle sensor measurement value range is [0,360°].

3. The three-axis frame inertial navigation system error self-calibration and compensation method according to claim 2, characterized in that: In step (2), after the lock is stable, collect accelerometer measurement values ​​for no less than 3 minutes at a frequency of more than 10 Hz.

4. The three-axis frame inertial navigation system error self-calibration and compensation method according to claim 3 is characterized in that: In step (2), the inertial navigation system self-calibrates the locked frame angle position as shown in the following table: There is no requirement for the order of the frame angle positions locked for data acquisition in the table.

5. The three-axis frame inertial navigation system error self-calibration and compensation method according to claim 4, characterized in that: In step (3), the overall observation matrix of error coefficients is: Among them, the error coefficient observation matrix H of the kth self-calibration locking position is (k) The calculation method is: H (k) =[H 1(k) H 2(k) H 3(k) H 4(k) ] In the formula, H 1(k) Medium ij The calculation result of the kth position should be taken; c ij For the elements of this direction cosine matrix, They are the outer ring, middle ring, and inner ring frame angle values ​​in the kth row of Table 1, respectively.

6. The three-axis frame inertial navigation system error self-calibration and compensation method according to claim 5, characterized in that: In step (4), the expression of the k-th position specific force measurement value is: Where, k = 1, 2, ... 9; K 0j is the zero bias of the accelerometer in the j direction; K 1j is the accelerometer scale factor; E ij is the installation error angle, which indicates the influence of the i-direction specific force on the j-direction accelerometer measurement value; Δ nj is the asymmetric scale error coefficient of the accelerometer in the j direction, i,j = x, y, z, and the calibration parameter K 0j ,E ij ,Δ nj The initial value of K is 0. 1j The initial value is the factory nominal value of the instrument.

7. The three-axis frame inertial navigation system error self-calibration and compensation method according to claim 6, characterized in that: In step (5), the attitude matrix of the inertial navigation system from the platform coordinate system to the local horizontal coordinate system at each locked position is: Where k = 1, 2, ... 9; They are the measured values ​​of the outer ring, middle ring, and inner ring frame angle sensors respectively; are the measured values ​​of the outer ring, middle ring and inner ring frame angle sensors of the kth self-calibrated locking frame angle position, respectively; is the corresponding frame angle zero bias, j = 1, 2, 3; γ ij is the frame non-orthogonal error angle, i, j = x, y, z.

8. The three-axis frame inertial navigation system error self-calibration and compensation method according to claim 7, characterized in that: In step (6), the acceleration of the inertial navigation system in the local horizontal coordinate system g at each locking position is: Where, k = 1, 2, ... 9; α j is the base attitude angle, j = x, z; is the gravitational acceleration in the local horizontal coordinate system. Since the actual acceleration of the inertial navigation system is 0, That is, the acceleration error observation at the kth locking position.

9. The three-axis frame inertial navigation system error self-calibration and compensation method according to claim 8, characterized in that: In step (7), the total least squares algorithm is used to find the estimated value of the error coefficient: X =(H T H) -1 H T Z=[X1 X2 … X 20 ] T In the formula, Z is The total observation quantity composed of 10. The three-axis frame inertial navigation system error self-calibration and compensation method according to claim 9, characterized in that: In step (8), the least squares estimation result is used to correct the estimated value of the calibrated parameter and the base attitude angle. The calculation method is as follows: Accelerometer bias: K 0x | (n+1) =K 0x | (n) +X1 K 0y | (n+1) =K 0y | (n) +X2 K 0z | (n+1) =K 0z | (n) +X3 Accelerometer scale factor: K 1x | (n+1) =K 1x | (n) / (1-X4) <h2 style=";text-align:left;direction:ltr">K<h2 style=";text-align:left;direction:ltr"> 1y <h2 style=";text-align:left;direction:ltr"> |<h2 style=";text-align:left;direction:ltr"> (n+1) <h2 style=";text-align:left;direction:ltr"> =K<h2 style=";text-align:left;direction:ltr"> 1y <h2 style=";text-align:left;direction:ltr"> |<h2 style=";text-align:left;direction:ltr"> (n) <h2 style=";text-align:left;direction:ltr"> / (1-X5) K 1z | (n+1) =K 1z | (n) / (1-X6) Accelerometer installation error: TO xy | (n+1) =E xy | (n) +X7 AND xz | (n+1) =And xz | (n) +X8 E yz | (n+1) =E yz | (n) +X9 Accelerometer asymmetric scaling error: D nx | (n+1) =D nx | (n) +X 10 D ny | (n+1) =D ny | (n) +X 11 D nz | (n+1) =D nz | (n) +X 12 Base attitude angle: α x | (n+1) ＝α x | (n) +X 13 α z | (n+1) ＝α z | (n) +X 14 Frame non-orthogonality error: c xy | (n+1) =c xy | (n) +X 15 c yz | (n+1) =c yz | (n) +X 16 c zx | (n+1) =c zx | (n) +X 17 c zy | (n+1) =c zy | (n) +X 18 Frame angle sensor zero bias: In the above formulas, n is the number of iterative calculations, representing the result of the nth error separation, n = 0, 1, 2, ... wherein n = 0 represents the initial value of the error coefficient.

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