Error calibration and compensation method for single-axis frame type inertial navigation system

Abstract

An error calibration and compensation method for a single-axis frame type inertial navigation system comprises the following steps: under the condition of a static base, locking a table body at eight different angular positions by using a single-axis rotary table, collecting measured values of an accelerometer, calculating specific force measured values of the inertial navigation system under a table body coordinate system at each locking position, and calculating the error of the inertial navigation system; and calculating an attitude matrix from the table body coordinate system of the inertial navigation system at each locking position to the local horizontal coordinate system 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, carrying out iterative calculation until the iterative convergence criterion is met, obtaining the calibration result of each error coefficient, estimating the attitude angle of the base of the single-axis turntable and the mounting angle of the inertial navigation system on the single-axis turntable, and calculating the mounting angle of the inertial navigation system on the single-axis turntable through the calibration and compensation of the error coefficients. The influence of the non-orthogonal error of the shaft system on the attitude measurement precision of the carrier or the base of the frame-type inertial navigation system can be improved.

Description

Technical Field

[0001] The invention relates to an error calibration and compensation method for a single-axis frame type inertial navigation system, 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 order to suppress the long-term accumulation of errors such as zero bias of inertial navigation system instruments, the inertial navigation system introduces rotation modulation technology, which controls the rotation of the console body by rotating the frame transfer mechanism, and uses the integral link of inertial navigation calculation to eliminate navigation errors caused by zero bias of inertial instruments. Common rotary inertial navigation systems are single-axis and dual-axis. Among them, the single-axis rotary inertial navigation system usually adopts a modulation scheme that rotates around the celestial axis. Some products adopt continuous rotation or full-circle alternating rotation schemes, and their rotating mechanisms usually need to be installed with conductive slip rings for power supply; while other products adopt a four-position transfer scheme, with a maximum angular distance of 270° from the zero position of the rotating axis. This type of single-axis rotary inertial navigation system can be powered by wires, without the need to install conductive slip rings, and has higher inherent reliability.

[0006] 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

[0007] The technical problem to be solved by the present invention is to overcome the deficiencies of the prior art and solve the error calibration and compensation problems of a single-axis frame-type inertial navigation system.

[0008] The purpose of the present invention is achieved through the following technical solutions:

[0009] A single-axis frame inertial navigation system error calibration and compensation method, comprising:

[0010] (1) The single-axis frame-type inertial navigation system to be tested is installed on a single-axis turntable with a stable foundation, 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 inertial navigation system frame orientation is adjusted as follows: Figure 3 shown. Figure 3 Middle Y F The inertial navigation system rotation frame axis; Z t For a single-axis turntable, the axis should be approximately parallel to the local horizontal plane (the angle is less than 3°). Figure 3 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. F Parallel to Y p , polarity and Y p Same. Press Figure 3 Define the zero position of the inertial navigation system frame angle sensor and the zero position of the single-axis turntable axis: F When the axis frame angle sensor output is zero, the base coordinate system and the stage coordinate system are approximately coincident, with the same polarity, and the X p , Y p , Z p The Z axis points to the front, top, and right directions of the inertial navigation system base.p With Z t Same direction, polarity as Z t Same; when Z t When the output of the axis angle sensor is zero, the Y F With Y p Vertically upward, X p With Z p It is approximately in a horizontal position. Assume that the measurement value of the inertial navigation system and the rotation angle sensor of the single-axis turntable ranges from [0,360°].

[0011] (2) Control the frame rotation mechanism of the inertial navigation system and the single-axis turntable, lock the table body at the frame angle position shown in Table 1 below, and after the lock 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.

[0012] Table 1 Angular positions of the self-calibrated locking frame of the inertial navigation system

[0013] Position number Inertial navigation system rotation frame angular position (°) Single axis turntable shaft angle position (°) 1 0 270 2 0 180 3 0 90 4 0 0 5 90 or 270 0 6 90 or 270 90 7 90 or 270 180 8 90 or 270 270

[0014] (3) Calculate the error coefficient measurement matrix of each calibration locking frame angular position and form the overall error coefficient measurement matrix. Suppose the direction cosine matrix expression from the stage coordinate system to the single-axis turntable base coordinate system in the ideal case is:

[0015]

[0016] In the formula, c ij For the elements of this direction cosine matrix, is the rotation frame angle value of the inertial navigation system in the kth row in Table 1, Ф 1(k) is the single-axis turntable rotation angle value of the kth row in Table 1. Then the error coefficient observation matrix H of the kth self-calibrated locking position is (k) The calculation method is

[0017] H (k) =[H 1(k) H 2(k) H 3(k) H 4(k) ]

[0018] In the formula, the expression of each sub-matrix is

[0019]

[0020]

[0021] 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

[0022]

[0023] (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:

[0024]

[0025] Where, k = 1, 2, ... 8; K 0j is the zero bias of the accelerometer in the j direction, unit: pulse number / s; K 1j E is the accelerometer scale factor, unit: pulse number / (s·g0); 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.

[0026] (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:

[0027]

[0028] Where k = 1, 2, ... 8; is the measurement value of the rotation frame angle sensor of the single-axis inertial navigation system, unit: rad; γ ij is the frame non-orthogonality error angle, unit: rad,i,j=x,y,z.

[0029] (6) Calculate the acceleration of the inertial navigation system in the local horizontal coordinate system g at each locked position:

[0030]

[0031] 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.x ,θ y are the installation angles of the inertial navigation system on the single-axis turntable along the x-axis and y-axis respectively.

[0032] (7) Use the total least squares algorithm to obtain the estimated value of the error coefficient:

[0033] X=(H T H) -1 H T Z=[X1 X2 … X 18 ] T

[0034] Where X is the error coefficient vector, X j is its j-th dimension component (j=1,2,...,18); H is the error coefficient overall observation matrix; Z is The total observation quantity composed of

[0035]

[0036] In the formula, is the specific force measurement value of the kth self-calibrated locking frame angular position, k = 1, 2, ... 8.

[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) +X1

[0040] K 0y | (n+1) =K 0y | (n) +X2

[0041] K 0z | (n+1) =K 0z | (n) +X3

[0042] Accelerometer scale factor:

[0043] K 1x | (n+1) =K 1x | (n) / (1-X4)

[0044] K 1y | (n+1) =K 1y | (n) / (1-X5)

[0045] K 1z | (n+1) =K 1z | (n) / (1-X6)

[0046] Accelerometer installation error:

[0047] E xy | (n+1) =E xy | (n) +X7

[0048] E xz | (n+1) =E xz | (n) +X8

[0049] E yz | (n+1) =E yz | (n) +X9

[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 yz | (n+1) =γ yz | (n) +X 15

[0059] γ yx | (n+1) =γ yx | (n) +X 16

[0060] Installation angle of inertial navigation system on single-axis turntable:

[0061] θ x | (n+1) =θ x | (n) +X 17

[0062] θ y | (n+1) =θ y | (n) +X 18

[0063] 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.

[0064] (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 j 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. (j=1,2,…,18) In engineering applications, the number of iterations N can generally be directly set to 5 to 10 times.

[0065] Compared with the prior art, the present invention has the following beneficial effects:

[0066] The present invention realizes the calibration of the frame non-orthogonal error coefficients for the single-axis frame inertial navigation system, and can calibrate all significant error coefficients of the commonly used accelerometer error model under the 1g gravity field, including zero bias, scale factor, installation error, and asymmetric scale error, and can calibrate the installation angle of the inertial navigation system on the single-axis turntable. The calibration process requires the frame angle rotation range of the inertial navigation system to not exceed ±90°, so it is suitable for a single-axis rotary inertial navigation system powered by a wire. The method only needs to lock the frame angle position of the inertial navigation system and the single-axis turntable, and does not need to track the navigation coordinate system such as the inertial coordinate system. The rotation control mechanism of the inertial navigation system and the single-axis turntable is relatively easy to implement.

[0067] By calibrating and compensating the error coefficient, the measurement accuracy of the inertial navigation system carrier or base attitude can be improved, and a high-precision table attitude measurement reference benchmark can be provided for the inertial navigation system under static base conditions and single-axis turntable test conditions, thereby improving the performance of inertial navigation system self-calibration, initial alignment, inertial navigation and other application solutions related to the table attitude accuracy. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 It is a schematic diagram of the process of the present invention.

[0069] Figure 2 This is the frame orientation of the frame-type inertial navigation system of the present invention.

[0070] Figure 3 It is the frame orientation after the frame-type inertial navigation system of the present invention is installed on the single-axis turntable. DETAILED DESCRIPTION

[0071] 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.

[0072] A single-axis frame inertial navigation system error calibration and compensation method, under the condition of a static base, with the assistance of a single-axis turntable, the platform is locked at 8 different angular positions, and the accelerometer measurement values ​​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 measurement values, and the attitude matrix from the platform coordinate system of the inertial navigation 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 parameter estimate is used for iterative calculation until the iterative convergence criterion is met, and the calibration results of each error coefficient are obtained, such as Figure 1As shown. It can calibrate 14 error coefficients such as accelerometer zero bias, scale factor error, installation error, asymmetric scale error, and frame non-orthogonality error, and estimate the attitude angle of the single-axis turntable base and the installation angle of the inertial navigation system on the single-axis turntable. Through the calibration and compensation of the error coefficients, the measurement accuracy of the carrier or base attitude of the frame-type inertial navigation system affected by the axis non-orthogonality error can be improved, and a high-precision table attitude measurement reference can be provided for the inertial navigation system under static base conditions and single-axis turntable test conditions, thereby improving the performance of the inertial navigation system self-calibration, initial alignment, inertial navigation and other application solutions related to the table attitude accuracy.

[0073] A single-axis frame inertial navigation system error calibration and compensation method, specifically:

[0074] (1) The single-axis frame-type inertial navigation system to be tested is installed on a single-axis turntable with a stable foundation, 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 inertial navigation system frame orientation is adjusted as follows: Figure 3 shown. Figure 3 Middle Y F The inertial navigation system rotation frame axis; Z t For a single-axis turntable, the axis should be approximately parallel to the local horizontal plane (the angle is less than 3°). Figure 3 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. F Parallel to Y p , polarity and Y p Same. Press Figure 3 Define the zero position of the inertial navigation system frame angle sensor and the zero position of the single-axis turntable axis: F When the axis frame angle sensor output is zero, the base coordinate system and the stage coordinate system are approximately coincident, with the same polarity, and the X p , Y p , Z p The Z axis points to the front, top, and right directions of the inertial navigation system base. p With Z t The direction is the same. , the polarity is the same as Z t Same; when Z t When the output of the axis angle sensor is zero, the Y FWith Y p Vertically upward, X p With Z p It is approximately in a horizontal position. Assume that the measurement value of the inertial navigation system and the rotation angle sensor of the single-axis turntable ranges from [0,360°].

[0075] (2) Control the frame rotation mechanism of the inertial navigation system and the single-axis turntable, lock the table body at the frame angle position shown in Table 1 below, and after the lock 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.

[0076] Table 1 Angular positions of the self-calibrated locking frame of the inertial navigation system

[0077] Position number Inertial navigation system rotation frame angular position (°) Single axis turntable shaft angle position (°) 1 0 270 2 0 180 3 0 90 4 0 0 5 90 or 270 0 6 90 or 270 90 7 90 or 270 180 8 90 or 270 270

[0078] (3) Calculate the error coefficient measurement matrix of each calibration locking frame angular position and form the overall error coefficient measurement matrix. Suppose the direction cosine matrix expression from the stage coordinate system to the single-axis turntable base coordinate system in the ideal case is:

[0079]

[0080] In the formula, c ij For the elements of this direction cosine matrix, is the rotation frame angle value of the inertial navigation system in the kth row in Table 1, Ф 1(k) is the single-axis turntable rotation angle value of the kth row in Table 1. Then the error coefficient observation matrix H of the kth self-calibrated locking position is (k) The calculation method is

[0081] H (k) =[H 1(k) H 2(k) H 3(k) H 4(k) ]

[0082] In the formula, the expression of each sub-matrix is

[0083]

[0084]

[0085] 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

[0086]

[0087] (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:

[0088]

[0089] Where, k = 1, 2, ... 8; K 0j is the zero bias of the accelerometer in the j direction, unit: pulse number / s; K 1j E is the accelerometer scale factor, unit: pulse number / (s·g0); 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.

[0090] (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:

[0091]

[0092] Where k = 1, 2, ... 8; is the measurement value of the rotating frame angle sensor of the single-axis inertial navigation system, unit: rad; γ ij is the frame non-orthogonality error angle, unit: rad,i,j=x,y,z.

[0093] (6) Calculate the acceleration of the inertial navigation system in the local horizontal coordinate system g at each locked position:

[0094]

[0095] 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. x ,θ y are the installation angles of the inertial navigation system on the single-axis turntable along the x-axis and y-axis respectively.

[0096] (7) Use the total least squares algorithm to obtain the estimated value of the error coefficient:

[0097] X=(H T H) -1 H T Z=[X1 X2 … X 18 ] T

[0098] Where X is the error coefficient vector, X j is its j-th dimension component (j=1,2,...,18); H is the error coefficient overall observation matrix; Z is The total observation quantity composed of

[0099]

[0100] In the formula, is the specific force measurement value of the kth self-calibrated locking frame angular position, k = 1, 2, ... 8.

[0101] (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:

[0102] Accelerometer bias:

[0103] K 0x | (n+1) =K 0x | (n) +X1

[0104] K 0y | (n+1) =K 0y | (n) +X2

[0105] K 0z | (n+1) =K 0z | (n) +X3

[0106] Accelerometer scale factor:

[0107] K 1x | (n+1) =K 1x | (n) / (1-X4)

[0108] K 1y | (n+1) =K 1y | (n) / (1-X5)

[0109] K 1z | (n+1) =K 1z |(n) / (1-X6)

[0110] Accelerometer installation error:

[0111] E xy | (n+1) =E xy | (n) +X7

[0112] E xz | (n+1) =E xz | (n) +X8

[0113] E yz | (n+1) =E yz | (n) +X9

[0114] Accelerometer asymmetric scaling error:

[0115] Δ nx | (n+1) =Δ nx | (n) +X 10

[0116] Δ ny | (n+1) =Δ ny | (n) +X 11

[0117] Δ nz | (n+1) =Δ nz | (n) +X 12

[0118] Base attitude angle:

[0119] α x | (n+1) =α x | (n) +X 13

[0120] α z | (n+1) =α z | (n) +X 14

[0121] Frame non-orthogonality error:

[0122] γ yz | (n+1) =γ yz | (n) +X 15

[0123] γ yx | (n+1) =γ yx | (n) +X 16

[0124] Installation angle of inertial navigation system on single-axis turntable:

[0125] θ x | (n+1) =θ x | (n) +X 17

[0126] θ y | (n+1) =θ y | (n) +X 18

[0127] 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.

[0128] (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 j 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. (j=1,2,…,18) In engineering applications, the number of iterations N can generally be directly set to 5 to 10 times.

[0129] Furthermore, the method of the present invention utilizes a single-axis turntable or other rotating mechanism as an aid, configures the table with three accelerometers with orthogonally mounted input axes, and has an inertial navigation system with one rotating frame axis, and can calibrate the error parameters shown in Table 2 below.

[0130] Table 2 Calibration parameters of this method

[0131] Error coefficient quantity Accelerometer bias 3 Accelerometer scale error 3 Accelerometer Asymmetric Scaling Error Factor 3 Accelerometer installation error 3 Non-orthogonal error angle of rotating frame 2

[0132] 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:

[0133] 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:

[0134]

[0135] In the formula, 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, in pulses / s / g0; 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.

[0136] For an inertial navigation system with a rotating frame axis, ideally, when the frame angle is at zero, the coordinate system of the platform should be parallel to the coordinate system of the base, and the frame rotation axis should be parallel to the axis corresponding to the coordinate system of the platform. However, due to factors such as part tolerance and reference deviation in the processing and assembly of the inertial navigation system, processing and assembly errors are generally introduced, which are mainly manifested in the installation error of the inertial instrument and the non-orthogonal error of the frame axis system.

[0137] Assume that the frame rotation axis of the single-axis frame inertial navigation system is along the Y-axis direction and is approximately parallel to the input axis of the Y-axis accelerometer. Figure 2 shown.

[0138] Figure 2 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 single-axis frame inertial navigation system can be expressed by the direction cosine matrix from the table coordinate system to the base coordinate system:

[0139]

[0140] 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:

[0141] (1) The direction cosine matrix from the table coordinate system to the rotating frame coordinate system is:

[0142]

[0143] In the formula, γ yz ,γ yx is the non-orthogonal error angle of the inner ring frame.

[0144] (2) The direction cosine matrix from the rotating frame coordinate system to the inertial navigation system base coordinate system is:

[0145]

[0146] In the formula, Measured value of the outer ring frame angle sensor.

[0147] Example:

[0148] 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 2 As shown. Assume that the error coefficients of the inertial navigation system shown in Table 2 are all normally distributed random constants: the accelerometer scale factor ranges from 5000±50 pulses / (s·g0), the accelerometer zero bias ranges from [-0.25, 0.25] pulses / s, the accelerometer asymmetric scale error ranges from [-5e-6, 5e-6], the accelerometer installation error ranges from [-180, 180] arc seconds, the frame non-orthogonal error angle ranges from [-180, 180] arc seconds, the inertial navigation system installation angle ranges from [-300, 300] arc seconds, the horizontal attitude angle of the single-axis turntable base ranges from [-3°, 3°], and the azimuth angle is uniformly distributed in the range of [0°, 360°).

[0149] The self-calibration locking frame angular positions used for self-calibration are shown in Table 3 below.

[0150] Table 3 Angular position of the self-calibrated locking frame of the inertial navigation system

[0151] Position number Inertial navigation system rotation frame angular position (°) Single axis turntable shaft angle position (°) 1 0 270 2 0 180 3 0 90 4 0 0 5 270 0 6 270 90 7 270 180 8 270 270

[0152] According to the axis non-orthogonal error model of the single-axis frame inertial navigation system and the single-axis turntable installation angle model, the actual attitude matrix of the platform is calculated, 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.

[0153] 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.

[0154] Table 4 Self-calibration simulation test results

[0155]

[0156]

[0157] The simulation test results verify the effectiveness of the method of the present invention.

[0158] The contents not described in detail in the specification of the present invention belong to the common knowledge of those skilled in the art.

[0159] 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 single-axis frame inertial navigation system error calibration and compensation method, characterized in that: include: (1) The single-axis frame-type inertial navigation system to be tested is installed on a single-axis turntable with a stable foundation, so that the horizontal attitude angle of the inertial navigation system base is less than 3°; (2) Control the inertial navigation system and the frame indexing mechanism of the single-axis turntable, lock the table at eight different angular positions, and collect accelerometer measurements; (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 single-axis frame inertial navigation system error calibration and compensation method according to claim 1, characterized in that: Assume that the measurement value range of the inertial navigation system and the rotation angle sensor of the single-axis turntable is [0,360°].

3. The single-axis frame inertial navigation system error calibration and compensation method according to claim 1, characterized in that: In step (2), after the platform is locked and stabilized, the accelerometer measurement values ​​are collected for no less than 3 minutes at a frequency of more than 10 Hz.

4. The single-axis frame inertial navigation system error calibration and compensation method according to claim 1, characterized in that: In step (2), the 8 inertial navigation systems self-calibrate and lock the frame angle positions as shown in the following table: There is no requirement for the order of the frame angle positions.

5. The single-axis frame inertial navigation system error calibration and compensation method according to claim 1, characterized in that: In step (3), the direction cosine matrix expression from the platform coordinate system to the single-axis turntable base coordinate system under ideal conditions is assumed to be: In the formula, c ij For the elements of this direction cosine matrix, is the rotation frame angle value of the inertial navigation system in the kth row in Table 1, Ф 1(k) is the single-axis turntable shaft angle value in the kth row in Table 1; then the error coefficient observation matrix H of the kth self-calibration locking position (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 single-axis frame inertial navigation system error 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, ... 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, 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 single-axis frame inertial navigation system error 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, ... 8; is the measurement value of the rotation frame angle sensor of the single-axis inertial navigation system; γ ij is the frame non-orthogonal error angle, i,j=x,y,z.

8. The single-axis frame inertial navigation system error 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, ... 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 of the kth locking position; θ x ,θ y are the installation angles of the inertial navigation system on the single-axis turntable along the x-axis and y-axis, respectively.

9. The single-axis frame inertial navigation system error 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 18 ] T Where X is the error coefficient vector, X j is its j-th dimension component (j=1,2,...,18); H is the error coefficient overall observation matrix; Z is The total observation quantity composed of is expressed as: In the formula, is the specific force measurement value of the kth self-calibrated locking frame angular position, k = 1, 2, ...

8.

10. The single-axis frame inertial navigation system error 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 yz | (n+1) =c yz | (n) +X 15 c yx | (n+1) =c yx | (n) +X 16 Installation angle of inertial navigation system on single-axis turntable: i x | (n+1) =θ x | (n) +X 17 i y | (n+1) =θ y | (n) +X 18 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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