Error self-calibration and compensation method for double-shaft frame type inertial navigation system

Abstract

A double-shaft frame type inertial navigation system error self-calibration and compensation method comprises the following steps: under the condition of a static base, locking a table body at eight frame angular positions, collecting measured values of an accelerometer, calculating specific force measured values of an inertial navigation system under a table body coordinate system at each locking position, and calculating the error of the inertial navigation system according to the specific force measured values; and calculating an attitude matrix of the inertial navigation system from the table body coordinate system to the local horizontal coordinate system at each locking position to obtain the acceleration of the inertial navigation system under the local horizontal coordinate system at each locking position, and taking the acceleration as an error observed quantity. Solving the residual error of the error coefficient by adopting a total least square algorithm, correcting the estimated value of the measured parameter, and carrying out iterative calculation until an iterative convergence criterion is met, so as to obtain the self-calibration result of each error coefficient; through self-calibration and compensation of the error coefficient, the influence of the non-orthogonal error of the shaft system on the attitude measurement precision of the carrier or the base of the double-shaft frame type inertial navigation system can be improved.

Description

Technical Field

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

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

[0003] A platform-based inertial navigation system (also known as an inertial platform) installs inertial measurement elements (mainly gyroscopes and accelerometers) on the same inertial measurement unit (hereinafter referred to as the platform). The gyroscope senses the angular motion of the platform, and the rotating frame indexing mechanism controls the platform to track the navigation coordinate system and isolate the angular motion of the carrier. The accelerometer then measures the acceleration information (specific force) of the platform in the navigation coordinate system, and the navigation computer performs integral calculations to obtain information such as the speed and position of the platform.

[0004] During the navigation process, the strapdown inertial navigation system does not have a rotation control mechanism to track the navigation coordinate system. 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. The attitude matrix obtained by attitude calculation is used to perform coordinate transformation to obtain the acceleration information in the navigation coordinate system, and then an integral operation is performed to obtain information such as the speed and position of the platform movement.

[0005] Inertial navigation system applications require compensation for inertial instrument errors to improve navigation accuracy. Errors requiring compensation include gyroscope and accelerometer bias, scale factor error, and installation errors. Calibration is typically required before the inertial navigation system begins operating. Angular motion information, such as the carrier's attitude angle, is calculated from the platform's attitude angle output and the measurements of the rotation mechanism's frame angle sensor. Therefore, compensation for the non-orthogonality error of the rotating frame and the frame angle sensor error is also necessary. 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 problems of a dual-axis frame type inertial navigation system.

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

[0008] A dual-axis frame type inertial navigation system error self-calibration and compensation method, comprising:

[0009] (1) The dual-axis frame-type inertial navigation system (hereinafter referred to as the inertial navigation system) to be tested is placed on a stable foundation with seismic isolation such as a marble plate 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 rotation mechanism, the orientation of the inertial navigation system frame is adjusted as follows: Figure 1 Press Figure 1 The following table defines 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 an approximately 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 inertial navigation system frame angle sensor is zero, the base coordinate system and the platform coordinate system are approximately coincident, with the same polarity, and X p 、Y p 、Z p Point to the front, top, and right directions of the base coordinate system respectively, X p 、Z p Respectively with X F 、Z F Parallel, with the same polarity. Assume that the range of the frame angle sensor measurement value is [0,360°].

[0010] (2) Control the frame indexing mechanism 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 10 Hz or more 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 angular positions locked for data acquisition in Table 1.

[0011] Table 1 Angular positions of the self-calibrated locking frame of the inertial navigation system

[0012] Position number Inner ring frame angle (°) Outer ring frame angle (°) 1 0 270 2 0 180 3 0 90 4 0 0 5 270 or 90 0 6 270 or 90 90 7 270 or 90 180 8 270 or 90 270

[0013] (3) Calculate the error coefficient measurement matrix of each calibration locking frame angular position and form the overall error coefficient measurement matrix. Assume that the direction cosine matrix expression from the platform coordinate system to the inertial navigation system base coordinate system in the ideal case is

[0014]

[0015] Where c ijFor the elements of this direction cosine matrix, are the outer ring, middle ring, and inner ring frame angle values ​​in the kth row of Table 1, respectively. Then the error coefficient observation matrix H of the kth self-calibration locking position is (k) The calculation method is

[0016] H (k) =[H 1(k) H 2(k) H 3(k) H 4(k) ]

[0017] In the formula, the expression of each sub-matrix is

[0018]

[0019] Where H 1(k) Middle C ij The calculation result of the kth position should be taken. The expression of the error coefficient overall observation matrix is

[0020]

[0021] (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:

[0022]

[0023] Where, k = 1, 2, ... 8; 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: number of pulses / (s·g0); E ij is the installation error angle, which represents 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 j-axis accelerometer, unit: 1. (i, j = x, y, z.) Calibration parameter K 0j ,E ij ,Δ nj The initial value is 0, K 1j The initial value is the factory nominal value of the instrument.

[0024] (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:

[0025]

[0026] Where k = 1, 2, ... 8; are the measurement values ​​of the outer ring and inner ring frame angle sensors of the kth self-calibrated locking frame angle position, respectively, in rad; is the inner ring frame angular zero bias, unit: rad; γ ij is the frame non-orthogonality error angle, unit: rad,i,j=x,y,z.

[0027] (6) Calculate the acceleration of the inertial navigation system in the local horizontal coordinate system g at each locked position:

[0028]

[0029] Where k = 1, 2, ... 8; α j is the base attitude angle (j = x, z.), unit: rad; is the gravitational acceleration in the local horizontal coordinate system, unit: g0. Since the actual acceleration of the inertial navigation system is 0, That is, the acceleration error observation at the kth locking position.

[0030] (7) Use the total least squares algorithm to find the estimated value of the error coefficient:

[0031] X=(H T H) -1 H T Z=[X1 X2 … X 18 ] T

[0032] Where Z is The overall observation quantity composed of

[0033]

[0034] (8) Use the least squares estimation result to correct the estimated values ​​of the calibrated parameters and the base attitude angle. The calculation method is as follows:

[0035] Accelerometer bias:

[0036] K 0x | (n+1) =K 0x | (n) +X1

[0037] K 0y | (n+1) =K 0y | (n) +X2

[0038] K 0z | (n+1) =K 0z | (n) +X3

[0039] Accelerometer scale factor:

[0040] K1x | (n+1) =K 1x | (n) / (1-X4)

[0041] K 1y | (n+1) =K 1y | (n) / (1-X5)

[0042] K 1z | (n+1) =K 1z | (n) / (1-X6)

[0043] Accelerometer installation error:

[0044] E xy | (n+1) =E xy | (n) +X7

[0045] E xz | (n+1) =E xz | (n) +X8

[0046] E yz | (n+1) =E yz | (n) +X9

[0047] Accelerometer asymmetric scaling error:

[0048] Δ nx | (n+1) =Δ nx | (n) +X 10

[0049] Δ ny | (n+1) =Δ ny | (n) +X 11

[0050] Δ nz | (n+1) =Δ nz | (n) +X 12

[0051] Base attitude angle:

[0052] α x | (n+1) =α x | (n) +X 13

[0053] α z | (n+1) =α z | (n) +X 14

[0054] Frame non-orthogonality error:

[0055] γ zy | (n+1) =γ zy | (n) +X 15

[0056] γ yz | (n+1) =γ yz | (n) +X 16

[0057] γ yx | (n+1) =γ yx | (n) +X 17

[0058] Frame angle sensor zero bias:

[0059]

[0060] In the above formulas, n is the number of iterative calculations, representing the result of the nth error separation, n = 0, 1, 2, ..., where n = 0 represents the initial value of the error coefficient.

[0061] (9) Perform iterative calculations using the corrected error coefficient estimates, i.e., repeat steps (4) to (8) until all components Xi of the correction value X (least squares estimation result) meet the iterative convergence criterion: ( is the convergence criterion value for the j-th dimension component), then the estimated error coefficients after the current least squares estimate is corrected are the self-calibration results for each error coefficient. (i = 1, 2, …, 18.) In engineering applications, the number of iterations N can generally be set to 5 to 10.

[0062] Compared with the prior art, the present invention has the following beneficial effects:

[0063] The present invention realizes complete self-calibration of axis non-orthogonality error coefficients for a dual-axis frame inertial navigation system, including frame non-orthogonality error and frame angular zero bias, and can simultaneously calibrate all significant error coefficients of a commonly used accelerometer error model under a 1g gravity field, including zero bias, scaling factor, installation error, and asymmetric scaling error. Through self-calibration and compensation of error coefficients, the attitude measurement accuracy of the carrier or base of the dual-axis frame inertial navigation system can be improved, and a high-precision platform attitude measurement reference datum 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 platform attitude accuracy. This method only requires locking the frame angular position of the inertial navigation system and the single-axis turntable, without the need to track navigation coordinate systems such as the inertial coordinate system, and is relatively easy to implement for the rotation control mechanism of the inertial navigation system and the single-axis turntable. BRIEF DESCRIPTION OF THE DRAWINGS

[0064] Figure 1 This is the frame orientation diagram of the dual-axis frame inertial navigation system of the present invention.

[0065] Figure 2 Schematic diagram of the process of the present invention. DETAILED DESCRIPTION

[0066] To make the objectives, technical solutions and advantages of the present invention more clear, the embodiments of the present invention will be described in further detail below with reference to the accompanying drawings.

[0067] A dual-axis frame-type inertial navigation system error self-calibration and compensation method, under static base conditions, locks the platform at 8 frame angle positions, collects accelerometer measurements, and uses the accelerometer measurements to calculate the specific force measurement value of the inertial navigation system in the platform coordinate system at each locked position. 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 total least squares algorithm is used to calculate the residual of the error coefficient, 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, and the self-calibration results of each error coefficient are obtained, such as Figure 2 As shown in the figure, 18 error coefficients can be calibrated, including accelerometer bias, scale factor error, installation error, asymmetric scale error, frame non-orthogonality error, and frame angle sensor bias. Through self-calibration and compensation of error coefficients, the attitude measurement accuracy of the carrier or base of a dual-axis frame-based inertial navigation system affected by axis non-orthogonality error can be improved. It also provides a high-precision reference for platform attitude measurement for inertial navigation systems operating on a static base, thereby improving the performance of inertial navigation system self-calibration, initial alignment, and inertial navigation applications related to platform attitude accuracy.

[0068] A dual-axis frame inertial navigation system error self-calibration and compensation method, specifically comprising:

[0069] (1) The dual-axis frame-type inertial navigation system (hereinafter referred to as the inertial navigation system) to be tested is placed on a stable foundation with seismic isolation such as a marble plate 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 rotation mechanism, the orientation of the inertial navigation system frame is adjusted as follows: Figure 1 Press Figure 1 The following table defines 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 an approximately 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 inertial navigation system frame angle sensor is zero, the base coordinate system and the platform coordinate system are approximately coincident, with the same polarity, and X p 、Y p 、Z p Point to the front, top, and right directions of the base coordinate system respectively, X p 、Z p Respectively with X F 、Z F Parallel, with the same polarity. Assume that the range of the frame angle sensor measurement value is [0,360°].

[0070] (2) Control the frame indexing mechanism 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 10 Hz or more 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 angular positions locked for data acquisition in Table 1.

[0071] Table 1 Angular positions of the self-calibrated locking frame of the inertial navigation system

[0072] Position number Inner ring frame angle (°) Outer ring frame angle (°) 1 0 270 2 0 180 3 0 90 4 0 0 5 270 or 90 0 6 270 or 90 90 7 270 or 90 180 8 270 or 90 270

[0073] (3) Calculate the error coefficient measurement matrix of each calibration locking frame angular position and form the overall error coefficient measurement matrix. Assume that the direction cosine matrix expression from the platform coordinate system to the inertial navigation system base coordinate system in the ideal case is

[0074]

[0075] Where c ij For the elements of this direction cosine matrix, are the outer ring, middle ring, and inner ring frame angle values ​​in the kth row of Table 1, respectively. Then the error coefficient observation matrix H of the kth self-calibration locking position is (k) The calculation method is

[0076] H (k) =[H 1(k) H 2(k) H 3(k) H 4(k) ]

[0077] In the formula, the expression of each sub-matrix is

[0078]

[0079] Where H 1(k) Middle C ij The calculation result of the kth position should be taken. The expression of the error coefficient overall observation matrix is

[0080]

[0081] (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:

[0082]

[0083] Where, k = 1, 2, ... 8; 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: number of pulses / (s·g0); E ij is the installation error angle, which represents 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 j-axis accelerometer, unit: 1. (i, j = x, y, z.) Calibration parameter K 0j ,E ij ,Δ nj The initial value is 0, K 1j The initial value is the factory nominal value of the instrument.

[0084] (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:

[0085]

[0086] Where k = 1, 2, ... 8; are the measurement values ​​of the outer ring and inner ring frame angle sensors of the kth self-calibrated locking frame angle position, respectively, in rad; is the inner ring frame angular zero bias, unit: rad, j = 1, 2; γ ij is the frame non-orthogonality error angle, unit: rad,i,j=x,y,z.

[0087] (6) Calculate the acceleration of the inertial navigation system in the local horizontal coordinate system g at each locked position:

[0088]

[0089] Where k = 1, 2, ... 8; α j is the base attitude angle (j = x, z.), unit: rad; is the gravitational acceleration in the local horizontal coordinate system, unit: g0. Since the actual acceleration of the inertial navigation system is 0, That is, the acceleration error observation at the kth locking position.

[0090] (7) Use the total least squares algorithm to find the estimated value of the error coefficient:

[0091] X=(H T H) -1 H T Z=[X1 X2 … X 18 ] T

[0092] Where Z is The overall observation quantity composed of

[0093]

[0094] (8) Use the least squares estimation result to correct the estimated values ​​of the calibrated parameters and the base attitude angle. The calculation method is as follows:

[0095] Accelerometer bias:

[0096] K 0x | (n+1) =K 0x | (n) +X1

[0097] K 0y | (n+1) =K 0y | (n) +X2

[0098] K 0z | (n+1) =K 0z | (n) +X3

[0099] Accelerometer scale factor:

[0100] K 1x | (n+1) =K 1x | (n) / (1-X4)

[0101] K 1y | (n+1) =K 1y | (n) / (1-X5)

[0102] K 1z | (n+1) =K 1z | (n) / (1-X6)

[0103] Accelerometer installation error:

[0104] E xy | (n+1) =E xy | (n) +X7

[0105] E xz | (n+1) =E xz | (n) +X8

[0106] E yz | (n+1) =E yz | (n) +X9

[0107] Accelerometer asymmetric scaling error:

[0108] Δ nx | (n+1) =Δ nx | (n) +X 10

[0109] Δ ny | (n+1) =Δ ny | (n) +X 11

[0110] Δ nz | (n+1) =Δ nz | (n) +X 12

[0111] Base attitude angle:

[0112] α x |(n+1) =α x | (n) +X 13

[0113] α z | (n+1) =α z | (n) +X 14

[0114] Frame non-orthogonality error:

[0115] γ zy | (n+1) =γ zy | (n) +X 15

[0116] γ yz | (n+1) =γ yz | (n) +X 16

[0117] γ yx | (n+1) =γ yx | (n) +X 17

[0118] Frame angle sensor zero bias:

[0119]

[0120] In the above formulas, n is the number of iterative calculations, representing the result of the nth error separation, n = 0, 1, 2, ..., where n = 0 represents the initial value of the error coefficient.

[0121] (9) Perform iterative calculations using the corrected error coefficient estimates, i.e., repeat steps (4) to (8) until all components Xi of the correction value X (least squares estimation result) meet the iterative convergence criterion: ( is the convergence criterion value for the j-th dimension component), then the estimated error coefficients after the current least squares estimate is corrected are the self-calibration results for each error coefficient. (i = 1, 2, …, 18.) In engineering applications, the number of iterations N can generally be set to 5 to 10.

[0122] Furthermore, for an inertial navigation system configured with three accelerometers with orthogonally mounted input axes on a platform and having two rotation frame axes, the present invention can calibrate the error parameters shown in Table 2 below.

[0123] Table 2 Calibration parameters of this method

[0124] 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 Outer ring frame non-orthogonal error angle 1 Inner ring shaft frame angle zero offset 1

[0125] 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:

[0126] For an inertial navigation system with three accelerometers mounted orthogonally on the platform, the accelerometer measurement value of the compensation error coefficient is expressed as follows in the 1g gravity field environment of the static base self-calibration:

[0127]

[0128] Where, f p is the specific force measurement value output by the accelerometer combination, in g0; 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, the unit is pulse number / s / g0; E ij is the i-axis accelerometer around O j The installation error angle of the positive axis, in rad; W j p is the output value of the j-axis accelerometer, in pulses / s; Δ nj 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, with the unit of 1. Where i, j = x, y, z.

[0129] For an inertial navigation system with a platform having 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 component tolerances and datum deviations during the machining and assembly of a single inertial navigation system, machining and assembly errors are generally introduced. These errors primarily manifest as inertial instrument installation errors and non-orthogonality errors in the frame axis system.

[0130] Assume that the frame orientation of the dual-axis frame inertial navigation system is Z-direction and Y-direction 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.

[0131] Figure 1 In the equation, the subscript p represents the platform coordinate system, and the subscript m represents the base coordinate system. The mathematical model of the axis non-orthogonality error of this dual-axis frame inertial navigation system can be expressed by the direction cosine matrix from the platform coordinate system to the base coordinate system:

[0132]

[0133] Where m2 is the inner ring frame coordinate system, and m1 is the outer ring frame coordinate system. The expressions of each matrix factor are as follows:

[0134] (1) The direction cosine matrix from the platform coordinate system to the inner ring frame coordinate system is:

[0135]

[0136] Where, γ yz ,γ yx is the non-orthogonal error angle of the inner ring frame.

[0137] (2) The direction cosine matrix from the inner ring frame coordinate system to the outer ring frame coordinate system is

[0138]

[0139] Where, γ zy is the non-orthogonal error angle of the outer 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.

[0140] (3) The direction cosine matrix from the outer ring frame coordinate system to the base coordinate system is

[0141]

[0142] Where, Measured value of the outer ring frame angle sensor.

[0143] Example:

[0144] The specific implementation and application effects of the present invention are given based on simulation experiments. Assume that the frame orientation of the inertial navigation system is as follows: Figure 1 As shown in Table 2, it is assumed that the error coefficients of the inertial navigation system shown in Table 2 are all normally distributed random constants: the accelerometer equivalent value range is 5000±50 pulses / (s·g0), the accelerometer bias value range is [-0.25, 0.25] pulses / s, the accelerometer asymmetric scale error value range is [-5e-6, 5e-6], the accelerometer installation error value range is [-180, 180] arc seconds, the frame non-orthogonality error angle value range is [-180, 180] arc seconds, the frame angle sensor bias value range is [-180, 180] arc seconds, the inertial navigation system base horizontal attitude angle value range is [-3°, 3°], and the base azimuth angle obeys a uniform distribution in the range of [0°, 360°).

[0145] The self-calibration locking frame angle positions used for self-calibration are shown in Table 2. The inner ring shaft frame angle in positions 5 to 8 is 270°.

[0146] The actual attitude matrix of the platform is calculated according to the mathematical model of the axis non-orthogonality error of the dual-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 acquisition time for each position is 3 minutes.

[0147] 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 3 below.

[0148] Table 3 Self-calibration simulation test results

[0149]

[0150] The simulation test results verify the effectiveness of the method of the present invention.

[0151] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

[0152] Although the present invention has been disclosed above in terms of preferred embodiments, it is not intended to limit the present invention. Any person skilled in the art may make possible changes and modifications to the technical solutions 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 solutions of the present invention shall fall within the scope of protection of the technical solutions of the present invention.

Claims

1. A dual-axis frame inertial navigation system error self-calibration and compensation method, characterized in that: include: (1) The dual-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 frame transfer mechanism of the inertial navigation system, lock the platform at eight frame angle positions, and collect accelerometer measurement values ​​after the locking is stable; (3) Calculate the error coefficient measurement matrix of each calibration locking frame angular position and form the overall error coefficient measurement 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 as the error observation; (7) Use the total least squares algorithm to obtain an estimate of the error coefficient; (8) Correcting the estimated values ​​of the calibrated parameters and the base attitude angle using the estimated value of the error coefficient; (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 error self-calibration and compensation method of the dual-axis frame inertial navigation system according to claim 1 is characterized in that: Assume that the frame angle sensor measurement value range is [0,360°].

3. The error self-calibration and compensation method of the dual-axis frame inertial navigation system according to claim 1, 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 error self-calibration and compensation method of the dual-axis frame inertial navigation system according to claim 1, 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 error self-calibration and compensation method of the dual-axis frame inertial navigation system according to claim 1, characterized in that: In step (3), the direction cosine matrix expression from the platform coordinate system to the inertial navigation system base coordinate system under ideal conditions is assumed to be: 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: H (k) =[H 1(k) H 2(k) H 3(k) H 4(k) ] In the formula, the expression of each sub-matrix is: In the formula, H 1(k) Medium ij The calculation result of the kth position should be taken, and the expression of the overall observation matrix of the error coefficient is:

6. The error self-calibration and compensation method of the dual-axis frame inertial navigation system 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, ... 8; 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; 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 error self-calibration and compensation method of the dual-axis frame inertial navigation system 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, ... 8; are the measured values ​​of the outer ring and inner ring frame angle sensors of the kth self-calibrated locking frame angle position, respectively; is the inner ring frame angular zero deviation; γ ij is the frame non-orthogonal error angle, i, j = x, y, z.

8. The error self-calibration and compensation method of the dual-axis frame inertial navigation system 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, ... 8; α j is the base attitude angle, j = x, z; is the gravitational acceleration in the local horizontal coordinate system; is the observed acceleration error at the kth locking position.

9. The error self-calibration and compensation method of the dual-axis frame inertial navigation system according to claim 8, characterized in that: In step (7), the estimated value of the error coefficient is obtained by using the total least squares algorithm: X =(H T H) -1 H T Z=[X1 X2 … X 18 ] T In the formula, Z is The total observation quantity composed of is expressed as:

10. The error self-calibration and compensation method of the dual-axis frame inertial navigation system 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 zy | (n+1) =c zy | (n) +X 15 c yz | (n+1) =c yz | (n) +X 16 c yx | (n+1) =c yx | (n) +X 17 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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