Self-calibration method for non-orthogonal error of dual-axis frame system frame and accelerometer error

Abstract

A self-calibration method for frame non-orthogonality error and accelerometer error in a dual-axis frame inertial system is proposed. Under static base conditions, the platform is locked at 10 frame angular positions, accelerometer measurements are collected, and the specific force measurement of the inertial system in the platform coordinate system at each locked position is calculated. The attitude matrix of the inertial system from the platform coordinate system to the local horizontal coordinate system at each locked position is also calculated, yielding the acceleration of the inertial system in the local horizontal coordinate system at each locked position, which is used as the error observation. The residuals of the error coefficients are calculated using a total least squares algorithm, and the estimated values ​​of the measured parameters are corrected. Iterative calculations are performed until the iterative convergence criterion is met, obtaining the self-calibration results for each error coefficient. Through the self-calibration and compensation of the error coefficients, the accuracy of attitude measurement of the dual-axis frame inertial system carrier or base affected by the non-orthogonality error of the axis system can be improved.

Description

Technical Field

[0001] This invention relates to a self-calibration method for the non-orthogonality error of the frame and the accelerometer error of a dual-axis frame inertial system, belonging to the field of inertial navigation technology. Background Technology

[0002] Inertial systems utilize accelerometers and gyroscopes to measure the angular and linear motion parameters of a vehicle, and calculate information such as the vehicle's velocity, position, and attitude through navigation. Based on the method of establishing the inertial measurement reference, inertial systems can be divided into two categories: platform-type inertial systems and strapdown inertial systems.

[0003] A platform-type inertial system (also known as an inertial platform) mounts inertial measurement elements (mainly including gyroscopes and accelerometers) on the same inertial measurement assembly (hereinafter referred to as the platform). The gyroscopes are used to sense the angular motion of the platform, and the rotating frame positioning mechanism controls the platform to track the navigation coordinate system and isolates the angular motion of the carrier. Then, the accelerometers are used to measure the acceleration information (specific force) of the platform in the navigation coordinate system, and the navigation computer performs integration calculations to obtain information such as the velocity and position of the platform.

[0004] Strapdown inertial systems do not have a rotation control mechanism that tracks the navigation coordinate system during navigation. They only use gyroscopes to sense the angular motion of the platform, and then the navigation computer calculates the attitude angles of the platform to determine the relative angular position relationship (attitude matrix) between the current platform coordinate system and the navigation coordinate system. Then, accelerometers are used to measure the specific force in the platform coordinate system. The attitude matrix obtained from the attitude calculation is used for coordinate transformation to obtain the acceleration information in the navigation coordinate system. Finally, integration is performed to obtain information such as the velocity and position of the platform.

[0005] In inertial system applications, it is necessary to compensate for the errors of inertial instruments to improve navigation accuracy. These errors include zero bias and scaling factor errors of gyroscopes and accelerometers, as well as installation errors. Calibration is typically required before the inertial system begins navigation. The attitude angles and angular motion information of the carrier are calculated from the attitude angle output values ​​of the platform and the measurements from the rotation mechanism frame angle sensors. Therefore, it is also necessary to compensate for the non-orthogonality errors of the rotation frame and the errors of the frame angle sensors. Summary of the Invention

[0006] The technical problem to be solved by the present invention is to overcome the shortcomings of the prior art and provide a self-calibration method for the non-orthogonal error of the frame and the accelerometer error of a dual-axis frame inertial system, thereby solving the problem of self-calibration of the non-orthogonal error of the frame and the accelerometer error of a dual-axis frame inertial system.

[0007] The objective of this invention is achieved through the following technical solutions: A self-calibration method for frame non-orthogonality error and accelerometer error in a dual-axis frame system includes: 1) Place the biaxial frame inertial system under test on a stable foundation with vibration isolation function to achieve a horizontal attitude angle of less than 3° for the inertial system base; 2) Control the frame shifting mechanism of the inertial system to lock the stage at 10 different frame angular positions and collect accelerometer measurements; 3) Calculate the error coefficient observation matrix for each calibration locking frame angular position, and form the overall error coefficient observation matrix; 4) Calculate the specific force of the inertial system in the table coordinate system at each locked position using accelerometer measurements; 5) Calculate the attitude matrix of the inertial system from the platform coordinate system to the local horizontal coordinate system at each locked position; 6) Calculate the acceleration of the inertial system in the local horizontal coordinate system at each locked position, as an error observation; 7) Use the overall least squares algorithm to obtain the estimated values ​​of the error coefficients; 8) Use the estimated values ​​of the error coefficients to correct the estimated values ​​of the calibrated parameters and the base attitude angle; 9) Use the corrected estimate to perform iterative calculations, repeating steps 4) to 8) until the correction amount in the estimated error coefficient satisfies the iterative convergence criterion, thus completing the error self-calibration method; In step 3), the method for determining the overall observation matrix of error coefficients is as follows: Let the expression for the direction cosine matrix from the table coordinate system to the inertial system base coordinate system under ideal conditions be:

[0008] Among them, c ij The elements of the cosine matrix in this direction, φ 1(k) , φ 2(k) Let H be the outer ring frame angle measurement value and the inner ring frame angle measurement value at the k-th locking position, respectively. Then, the error coefficient observation matrix H at the k-th locking position is... (k) The calculation method is as follows:

[0009] The expressions for each submatrix are as follows:

[0010] in, For the sub-array , the component vectors; They are respectively:

[0011]

[0012]

[0013]

[0014] Among them, H 1(k) c ij Taking the calculation result of the k-th locked position, the expression for the overall observation matrix of the error coefficient is: .

[0015] Preferably, the range of the measured value of the frame angle sensor is [0, 360°].

[0016] Preferably, in step 2), after the lock is stabilized, accelerometer measurements are collected at a frequency of 10 Hz or higher for at least 3 minutes.

[0017] Preferably, in step 2), the 10 different corner positions of the locking platform are as follows: The outer ring frame corner position is 270°, and the inner ring frame corner position is 0°. The outer ring frame corner position is 180°, and the inner ring frame corner position is 0°; The outer ring frame corner position is 90°, and the inner ring frame corner position is 0°; The outer ring frame angle is 0°, and the inner ring frame angle is 0°. The outer ring frame angle position is α1, and the inner ring frame angle position is 0°. The outer ring frame angle is 270° or 90°, and the inner ring frame angle is α2; The outer ring frame corner position is 0°, and the inner ring frame corner position is 270° or 90°; The outer ring frame corner position is 90°, and the inner ring frame corner position is 270° or 90°; The outer ring frame corner position is 180°, and the inner ring frame corner position is 270° or 90°; The outer ring frame corner position is 270°, and the inner ring frame corner position is 270° or 90°; The values ​​of α1 and α2 are in the range of [10°, 80°] or [100°, 170°] or [190°, 260°] or [280°, 350°].

[0018] Preferably, in step 4), the expression for the force measurement value at the k-th locking position is:

[0019] Where k = 1, 2, … 10; K 0j The j-axis accelerometer has zero bias; K 1j This is the accelerometer scale factor; E ij The installation error angle represents the effect of the i-direction specific force on the j-direction accelerometer measurement. Δ nj The asymmetric scaling error coefficient of the j-axis accelerometer; K 2j For the j-axis accelerometer quadratic term; The j-axis accelerometer outputs pulses in the k-th locked position under stable locking conditions, which is the total number of output pulses in the stable locking state divided by the locking time. i, j = x, y, z; Calibration parameter K 0j E ij , Δ nj , K 2j The initial value of K is 0. 1j The initial value is taken from the instrument's factory nominal value.

[0020] Preferably, in step 5), the attitude matrix of the inertial system from the platform coordinate system to the local horizontal coordinate system at each locked position is:

[0021] Where k = 1, 2, … 10; The subscript m indicates the base coordinate system; m1 is the outer ring coordinate system; m2 is the inner ring coordinate system; The direction cosine matrix from the outer ring coordinate system to the base coordinate system; This is the direction cosine matrix from the inner ring coordinate system to the outer ring coordinate system; Let be the direction cosine matrix from the table coordinate system to the inner ring coordinate system; φ 1(k) , φ 2(k) These are the measured angle values ​​of the outer ring and inner ring frames at the kth locking position, respectively, with Δφ2 being the zero offset of the inner ring frame angle. γ ij Let i, j = x, y, z, be the non-orthogonal error angles of the frame.

[0022] Preferably, in step 6), the acceleration of the inertial system in the local horizontal coordinate system at each locked position is:

[0023] Where k = 1, 2, … 10; α j Let j be the base attitude angle, j = x, z; This refers to the gravitational acceleration in the local horizontal coordinate system. Let be the acceleration error observation at the k-th locked position.

[0024] Preferably, in step 7), the estimated values ​​of the error coefficients are obtained using the overall least squares algorithm:

[0025] Where X is the vector of estimated error coefficients; X i Let be the i-th component of the error coefficient estimate vector, i=1, 2, ..., 21; Z is The overall observations are expressed as follows: .

[0026] Preferably, in step 8), the estimated values ​​of the calibrated parameters and the base attitude angle are corrected using the least squares estimation results. The calculation method is as follows: Accelerometer zero bias:

[0027] Accelerometer scale factor:

[0028] Accelerometer installation error:

[0029] Accelerometer asymmetric scaling error:

[0030] Accelerometer quadratic error:

[0031] Base attitude angle:

[0032] Frame non-orthogonality error:

[0033] Zero bias of frame angle sensor:

[0034] Where n is the number of iterations, representing the result of the nth error separation, n=0, 1, 2, …; n=0 represents the initial value of the error coefficient.

[0035] Compared with the prior art, the present invention has the following advantages: This invention enables complete self-calibration of the axis non-orthogonal error coefficients for a dual-axis frame inertial system, including frame non-orthogonal error and frame angle zero bias. It can also calibrate all significant error coefficients of commonly used accelerometer error models under a 1g gravitational field, including zero bias, scaling factor, installation error, asymmetric scaling error, and quadratic term error coefficients.

[0036] This invention improves the attitude measurement accuracy of a dual-axis frame-type inertial system carrier or base by self-calibrating and compensating for the error coefficient, and provides a high-precision reference for the attitude measurement of the inertial system under static base conditions, thereby improving the performance of inertial system self-calibration, initial alignment and inertial navigation applications related to the attitude accuracy of the inertial system.

[0037] The method of the present invention only requires locking the frame angular position of the inertial system and the single-axis turntable, without needing to track navigation coordinate systems such as the inertial coordinate system. The rotation control mechanism of the inertial system and the single-axis turntable is relatively easy to implement. Attached Figure Description

[0038] Figure 1 This is a frame orientation diagram of the biaxial frame inertial system of the present invention.

[0039] Figure 2 This is a flowchart illustrating the method of the present invention. Detailed Implementation

[0040] To make the objectives, technical solutions, and advantages of the present invention clearer, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0041] This invention discloses a self-calibration method for non-orthogonal errors of a dual-axis frame-type inertial system and accelerometer errors. Under static base conditions, the platform is locked at 10 frame angular positions, and accelerometer measurements are collected. The specific force of the inertial system in the platform coordinate system at each locked position is calculated using these accelerometer measurements. The attitude matrix of the inertial system from the platform coordinate system to the local horizontal coordinate system at each locked position is also calculated, yielding the acceleration of the inertial system in the local horizontal coordinate system at each locked position, which is used as the error observation. The residuals of the error coefficients are calculated using the overall least squares algorithm, and the estimated values ​​of the measured parameters are corrected. Iterative calculations are then performed using the corrected error coefficient estimates until the iterative convergence criterion is met, resulting in the self-calibration results for each error coefficient. Figure 2As shown, it can calibrate 21 error coefficients, including accelerometer zero bias, scale factor error, installation error, asymmetric scale error, frame non-orthogonality error, frame angle sensor zero bias, and quadratic term error coefficients. Through self-calibration and compensation of error coefficients, it can improve the attitude measurement accuracy of the dual-axis frame inertial system carrier or base affected by axis non-orthogonality error, and provide a high-precision table attitude measurement reference for inertial systems under static base conditions, thereby improving the performance of inertial system self-calibration, initial alignment, and inertial navigation applications related to table attitude accuracy.

[0042] A self-calibration method for frame non-orthogonality error and accelerometer error of a dual-axis frame inertial system, specifically including: (1) The biaxial frame inertial system to be tested (hereinafter referred to as the inertial system) is placed on a stable foundation with vibration isolation, such as a marble slab or turntable, so that the horizontal attitude angle of the inertial system base is less than 3°. By adjusting the attitude angle of the inertial system base and controlling the frame rotation mechanism, the orientation of the inertial system frame is made as follows: Figure 1 As shown. Press Figure 1 The diagram shows the definition of the polarity of the accelerometer's X, Y, and Z channels relative to the input axis: X p Z p The axes are perpendicular to each other in an approximately horizontal position, Y p The axis is perpendicular to X. p OZ p Plane, X p Y p Z p An orthogonal coordinate system is formed using the right-hand rule, pointing in the front, top, and right directions of the stage coordinate system, respectively. The zero-point of the frame angle sensor is defined as follows: when the outputs of all frame angle sensors in the inertial system are zero, the base coordinate system and the stage coordinate system approximately coincide, have the same polarity, and X... p Y p Z p Pointing to the front, top, and right directions of the base coordinate system respectively, X p Z p respectively with X F Z F Parallel and with the same polarity. Assume the range of the frame angle sensor measurement values ​​is [0, 360°].

[0043] (2) Control the frame rotation mechanism of the inertial system, lock the platform at the frame angular position shown in Table 1 below, and after locking and stabilizing, collect accelerometer measurements at a frequency of 10Hz or higher for no less than 3 minutes, and calculate the average value. In the formula, W p j The average value of the j-axis accelerometer measurements is expressed in pulses per second. The order of the frame angle positions locked for data acquisition in Table 1 is not required.

[0044] Table 1. Inertial System Self-Calibration Locking Frame Angular Position

[0045] Among them, α1 and α2 can take values ​​in the range of [10°, 80°], [100°, 170°], [190°, 260°], and [280°, 350°].

[0046] (3) Calculate the error coefficient observation matrix for each calibration locking frame angular position, and form the overall error coefficient observation matrix. Let the expression for the direction cosine matrix from the ideal table coordinate system to the inertial system base coordinate system be:

[0047] Among them, c ij The elements of the cosine matrix in this direction, φ 1(k) , φ 2(k) Let H be the measured angles of the outer and inner ring frames at the k-th locking position, respectively. Then, the error coefficient observation matrix H at the k-th locking position is... (k) The calculation method is as follows

[0048] The expression for each submatrix is ​​as follows:

[0049]

[0050]

[0051]

[0052]

[0053] Among them, H 1(k) c ij The calculation result for the k-th locked position should be taken. The expression for the overall observation matrix of the error coefficients is as follows:

[0054] (4) Calculate the specific force measurement value of the inertial system in the table coordinate system at each locked position using accelerometer measurements. The expression for the specific force measurement value at the k-th locked position is:

[0055] Where k = 1, 2, … 10; K 0j The j-axis accelerometer has zero bias, unit: pulses / s; K 1j Accelerometer scaling factor, unit: pulses / (s) g0); E ij The installation error angle represents the effect of the i-direction specific force on the j-direction accelerometer measurement, in rad; Δ nj K represents the asymmetric scaling error coefficient of the j-axis accelerometer, in units of 1. 2j For the j-axis accelerometer quadratic term, the unit is 1 / g0; The j-axis accelerometer outputs pulses over time at the k-th locked position in a stable state, which is the total number of pulses output in the stable state divided by the locking time. Unit: pulses / s; i, j = x, y, z. Calibration parameter K. 0j E ij , Δ nj , K 2j The initial value of K is 0. 1j The initial value is taken from the instrument's factory nominal value.

[0056] (5) Calculate the attitude matrix (direction cosine matrix) of the inertial system from the platform coordinate system to the local horizontal coordinate system at each locked position:

[0057] Where k = 1, 2, … 10; φ 1(k) , φ 2(k) Δφ2 represents the measured angles of the outer and inner ring frames at the k-th locking position, in rad; Δφ2 is the zero offset of the inner ring frame angle, in rad, j=1, 2; γ ij The non-orthogonal error angle of the frame is expressed in rad, where i, j = x, y, z. (6) Calculate the acceleration of the inertial system in the local horizontal coordinate system at each locked position:

[0058] Where k = 1, 2, … 10; α j The base attitude angle (j=x, z.) is expressed in rad. Let g be the gravitational acceleration in the local horizontal coordinate system, in g0. Since the actual acceleration of the inertial system is 0, That is, the acceleration error observation at the k-th locked position.

[0059] (7) The estimated values ​​of the error coefficients are obtained using the overall least squares algorithm:

[0060] Where Z is The overall observations are expressed as follows:

[0061] (8) The estimated values ​​of the calibrated parameters and the base attitude angle are corrected using the least squares estimation results. The calculation method is as follows: Accelerometer zero bias:

[0062] Accelerometer scale factor:

[0063] Accelerometer installation error:

[0064] Accelerometer asymmetric scaling error:

[0065] Accelerometer quadratic error:

[0066] Base attitude angle:

[0067] Frame non-orthogonality error:

[0068] Zero bias of frame angle sensor:

[0069] In the above, n represents the number of iterations, indicating the result of the nth error separation, where n = 0, 1, 2, … and n = 0 represents the initial value of the error coefficient.

[0070] (9) Iterative calculation is performed using the corrected error coefficient estimates, i.e., steps (4) to (8) are repeated until all components Xi of the correction amount X (least squares estimation result) satisfy the iterative convergence criterion: ( If is the convergence criterion value of the j-th dimension component, then the estimated values ​​of each error coefficient after correction of the current least squares estimation result are the self-calibration results of each error coefficient. (i=1, 2, …, 21.) In engineering applications, the number of iterations N can generally be directly taken as 5~10 times.

[0071] Furthermore, for an inertial system with three orthogonally mounted accelerometers on the platform and two rotating frame axes, the present invention can calibrate the error parameters shown in Table 2 below.

[0072] Table 2. Parameters that can be calibrated using this method

[0073] By compensating for the above error coefficients, the accuracy of the specific force measurement and the base attitude angle measurement of the inertial system can be improved, thereby improving the accuracy of inertial navigation and the vehicle attitude measurement. The compensation method is as follows: For an inertial system with three orthogonally mounted accelerometers on a platform, under a 1g gravitational field environment during static base self-calibration, the expression for the accelerometer measurement value with compensation error coefficient is:

[0074] Among them, f p (k) The specific force measurement value output by the accelerometer assembly is in g0; K 0j K represents the zero bias of the j-axis accelerometer, measured in pulses per second. 1j E represents the scale factor error of the j-axis accelerometer, expressed in pulses per second (g0). ij For i-axis accelerometer around O j Installation error angle in the positive direction of the axis, in rad; K 2j The term is the quadratic term of the j-axis accelerometer, with units of 1 / g0; W j p The output value of the j-axis accelerometer is expressed in pulses per second; Δ nj The error is the asymmetric scaling factor error of the j-axis accelerometer, reflecting the difference between the positive and negative scaling factors of the j-axis accelerometer measurement, with a unit of 1. Where i, j = x, y, z.

[0075] For an inertial system with two rotating frame axes, ideally, when the frame angle is at zero, the platform coordinate system should be parallel to the base coordinate system, and each frame rotation axis should be parallel to each axis of the platform coordinate system. However, due to factors such as part tolerances and datum deviations during the machining and assembly of the inertial system, machining and assembly errors are generally introduced. These errors mainly manifest as inertial instrument installation errors and non-orthogonal errors of the frame axis system.

[0076] Assume the frame orientation of the dual-axis frame inertial system is Z-axis from the outside in, then Y-axis. When each rotating frame is at zero position, the rotation axes of each frame are orthogonal to each other, and the input axes of each axial accelerometer are approximately parallel to the corresponding frame rotation axis. For example... Figure 1 As shown.

[0077] Figure 1 In the table, subscript p denotes the table coordinate system and subscript m denotes the base coordinate system. The mathematical model for the non-orthogonality error of the axis systems in this biaxial frame inertial system can be expressed by the direction cosine matrix from the table coordinate system to the base coordinate system as follows:

[0078] Where m2 represents the inner ring frame coordinate system, and m1 represents the outer ring frame coordinate system. The expressions for each matrix factor are as follows: (1) The direction cosine matrix from the platform coordinate system to the inner ring frame coordinate system is:

[0079] Where, γ yz , γ yx The non-orthogonal error angle of the inner ring frame.

[0080] (2) The direction cosine matrix from the inner ring frame coordinate system to the outer ring frame coordinate system is:

[0081] Where, γ zy φ2 is the non-orthogonal error angle of the outer ring frame, φ2 is the measured value of the inner ring frame angle sensor, and Δφ2 is the zero bias of the inner ring frame angle sensor.

[0082] (3) The direction cosine matrix from the outer ring frame coordinate system to the base coordinate system is:

[0083] Wherein, φ1 is the measurement value of the outer ring frame angle sensor.

[0084] Example: The specific implementation methods and application effects of this invention are presented based on simulation experiments. Assume the frame orientation of the inertial system is as follows... Figure 1 As shown in Table 2, all error coefficients of the inertial system are assumed to be normally distributed random constants: the accelerometer equivalent ranges from 5000 ± 50 pulses / (s). The accelerometer zero bias range is [-0.25, 0.25] pulses / s, the accelerometer asymmetric scaling error range is [-5e-6, 5e-6], the accelerometer quadratic term error range is [-5e-5, 5e-5](1 / g0), the accelerometer installation error range is [-180, 180] arcseconds, the frame non-orthogonal error angle range is [-180, 180] arcseconds, the frame angle sensor zero bias range is [-180, 180] arcseconds, the inertial system base horizontal attitude angle range is [-3°, 3°], and the base azimuth angle follows a uniform distribution within the range of [0°, 360°).

[0085] The self-calibration locking frame corner positions used for self-calibration are shown in Table 3.

[0086] Table 3. Locking frame angular positions used in inertial system self-calibration examples

[0087] The actual attitude matrix of the platform is calculated using the mathematical model of the non-orthogonal error of the axis system of the dual-axis frame inertial system. The gravitational acceleration is projected onto the platform coordinate system to obtain the actual sensitive specific force of the accelerometer assembly. The specific force measurement value of the accelerometer at each calibration position is calculated according to the accelerometer specific force output error model. The data sampling frequency is 100Hz and the data acquisition time at each position is 3min.

[0088] The calculation method of steps (2) to (9) of this invention is used to process the simulated accelerometer measurement values. The number of iterations N=10, and the self-calibration results are shown in Table 4 below.

[0089] Table 4 Results of self-calibration simulation test

[0090] Simulation results verified the effectiveness of the method of the present invention.

[0091] The contents not described in detail in this specification are common knowledge to those skilled in the art.

[0092] Although the present invention has been disclosed above with reference to preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art can make possible changes and modifications to the technical solutions of the present invention by utilizing the methods and techniques disclosed above without departing from the spirit and scope of the present invention. Therefore, any simple modifications, equivalent changes and alterations made to the above embodiments based on the technical essence of the present invention without departing from the content of the technical solutions of the present invention shall fall within the protection scope of the technical solutions of the present invention.

Claims

1. A self-calibration method for frame non-orthogonality error and accelerometer error in a dual-axis frame system, characterized in that, include: 1) Place the biaxial frame inertial system under test on a stable foundation with vibration isolation function to achieve a horizontal attitude angle of less than 3° for the inertial system base; 2) Control the frame shifting mechanism of the inertial system to lock the stage at 10 different frame angular positions and collect accelerometer measurements; 3) Calculate the error coefficient observation matrix for each calibration locking frame angular position, and form the overall error coefficient observation matrix; 4) Calculate the specific force of the inertial system in the table coordinate system at each locked position using accelerometer measurements; 5) Calculate the attitude matrix of the inertial system from the platform coordinate system to the local horizontal coordinate system at each locked position; 6) Calculate the acceleration of the inertial system in the local horizontal coordinate system at each locked position, as an error observation; 7) Use the overall least squares algorithm to obtain the estimated values ​​of the error coefficients; 8) Use the estimated values ​​of the error coefficients to correct the estimated values ​​of the calibrated parameters and the base attitude angle; 9) Use the corrected estimate to perform iterative calculations, repeating steps 4) to 8) until the correction amount in the estimated error coefficient satisfies the iterative convergence criterion, thus completing the error self-calibration method; In step 3), the method for determining the overall observation matrix of error coefficients is as follows: Let the expression for the direction cosine matrix from the table coordinate system to the inertial system base coordinate system under ideal conditions be: Among them, c ij The elements of the cosine matrix in this direction, φ 1(k) , φ 2(k) Let H be the measurement values ​​of the outer ring frame angle sensor and the inner ring frame angle sensor at the k-th locking position, respectively. Then, the error coefficient observation matrix H at the k-th locking position is... (k) The calculation method is as follows: The expressions for each submatrix are as follows: in, For the sub-array , the component vectors; They are respectively: Among them, H 1(k) c ij Taking the calculation result of the k-th locked position, the expression for the overall observation matrix of the error coefficient is: 。 2. The self-calibration method for frame non-orthogonality error and accelerometer error of a dual-axis frame system according to claim 1, characterized in that, Assume the range of the frame angle sensor measurement value is [0, 360°].

3. The self-calibration method for frame non-orthogonality error and accelerometer error of a dual-axis frame system according to claim 1, characterized in that, In step 2), after the system is locked and stabilized, accelerometer measurements are collected at a frequency of 10 Hz or higher for at least 3 minutes.

4. The self-calibration method for frame non-orthogonality error and accelerometer error of a dual-axis frame system according to claim 3, characterized in that, In step 2), the 10 different corner positions of the locking platform are as follows: The outer ring frame corner position is 270°, and the inner ring frame corner position is 0°. The outer ring frame corner position is 180°, and the inner ring frame corner position is 0°; The outer ring frame corner position is 90°, and the inner ring frame corner position is 0°; The outer ring frame angle is 0°, and the inner ring frame angle is 0°. The outer ring frame angle position is α1, and the inner ring frame angle position is 0°. The outer ring frame angle is 270° or 90°, and the inner ring frame angle is α2; The outer ring frame corner position is 0°, and the inner ring frame corner position is 270° or 90°; The outer ring frame corner position is 90°, and the inner ring frame corner position is 270° or 90°; The outer ring frame corner position is 180°, and the inner ring frame corner position is 270° or 90°; The outer ring frame corner position is 270°, and the inner ring frame corner position is 270° or 90°; The values ​​of α1 and α2 are in the range of [10°, 80°] or [100°, 170°] or [190°, 260°] or [280°, 350°].

5. The self-calibration method for frame non-orthogonality error and accelerometer error of a dual-axis frame system according to claim 4, characterized in that, In step 4), the expression for the force measurement value at the k-th locking position is: Where k = 1, 2, … 10; K 0j The j-axis accelerometer has zero bias; K 1j This is the accelerometer scale factor; E ij The installation error angle represents the effect of the i-direction specific force on the j-direction accelerometer measurement. Δ nj The asymmetric scaling error coefficient of the j-axis accelerometer; K 2j For the j-axis accelerometer quadratic term; The j-axis accelerometer outputs pulses in the k-th locked position under stable locking conditions, which is the total number of output pulses in the stable locking state divided by the locking time. i, j = x, y, z; Calibration parameter K 0j E ij , Δ nj , K 2j The initial value of K is 0. 1j The initial value is taken from the instrument's factory nominal value.

6. The self-calibration method for frame non-orthogonality error and accelerometer error of a dual-axis frame system according to claim 5, characterized in that, In step 5), the attitude matrix of the inertial system from the platform coordinate system to the local horizontal coordinate system at each locked position is: Where k = 1, 2, … 10; The subscript m indicates the base coordinate system; m1 is the outer ring coordinate system; m2 is the inner ring coordinate system; The direction cosine matrix from the outer ring coordinate system to the base coordinate system; This is the direction cosine matrix from the inner ring coordinate system to the outer ring coordinate system; Let be the direction cosine matrix from the table coordinate system to the inner ring coordinate system; φ 1(k) , φ 2(k) These are the measured angle values ​​of the outer ring and inner ring frames at the kth locking position, respectively, with Δφ2 being the zero offset of the inner ring frame angle. γ ij Let i, j = x, y, z, be the non-orthogonal error angles of the frame.

7. The self-calibration method for frame non-orthogonality error and accelerometer error of a dual-axis frame system according to claim 6, characterized in that, In step 6), the acceleration of the inertial system in the local horizontal coordinate system at each locked position is: Where k = 1, 2, … 10; α j Let j be the base attitude angle, j = x, z; This refers to the gravitational acceleration in the local horizontal coordinate system. Let be the acceleration error observation at the k-th locked position.

8. The self-calibration method for frame non-orthogonality error and accelerometer error of a dual-axis frame system according to claim 7, characterized in that, In step 7), the estimated values ​​of the error coefficients are obtained using the overall least squares algorithm: Where X is the vector of estimated error coefficients; X i Let be the i-th component of the error coefficient estimate vector, i=1, 2, ..., 21; Z is The overall observations are expressed as follows: 。 9. The self-calibration method for frame non-orthogonality error and accelerometer error of a dual-axis frame system according to claim 8, characterized in that, In step 8), the estimated values ​​of the calibrated parameters and the base attitude angle are corrected using the least squares estimation results. The calculation method is as follows: Accelerometer zero bias: Accelerometer scale factor: Accelerometer installation error: Accelerometer asymmetric scaling error: Accelerometer quadratic error: Base attitude angle: Frame non-orthogonality error: Zero bias of frame angle sensor: Where n is the number of iterations, representing the result of the nth error separation, n=0, 1, 2, …; n=0 represents the initial value of the error coefficient.

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