Single-axis frame inertial navigation system error calibration and compensation method

Abstract

The application discloses a single-shaft frame type inertial navigation system error calibration and compensation method. Under the condition of a static base, a single-shaft turntable is used to lock the table body at eight different angle positions, acceleration measurement values are collected, specific force measurement values of the inertial navigation system under the table body coordinate system at each locking position are calculated, attitude matrices of the inertial navigation system table body coordinate system to the local horizontal coordinate system at each locking position are calculated, accelerations of the inertial navigation system under the local horizontal coordinate system at each locking position are obtained, and the accelerations are taken as error observation values. A total least square algorithm is used to obtain residual errors of error coefficients, to correct measured parameter estimation values, to perform iterative calculation until an iterative convergence criterion is met, to obtain calibration results of each error coefficient, to estimate attitude angles of the single-shaft turntable base and installation angles of the inertial navigation system on the single-shaft turntable, and to improve the inertial navigation system carrier or base attitude measurement precision influenced by shaft system non-orthogonal errors through error coefficient calibration and compensation.

Description

TECHNICAL FIELD

[0001] The application relates to a single-axis frame type inertial navigation system error calibration and compensation method and belongs to the technical field of inertial navigation. BACKGROUND

[0002] An inertial navigation system measures carrier angular motion and linear motion parameters by using an accelerometer and a gyroscope, and obtains information such as velocity, position and attitude of the carrier through navigation calculation. According to the establishment mode of the inertial measurement reference, the inertial navigation system can be divided into two types: a platform type inertial navigation system and a strapdown type inertial navigation system.

[0003] The platform type inertial navigation system (also known as an inertial platform) installs inertial measurement elements (mainly including a gyroscope and an accelerometer) on the same inertial measurement assembly (hereinafter referred to as a platform body), uses the gyroscope to sense the angular motion of the platform body, controls the platform body to track a navigation coordinate system through a rotating frame indexing mechanism, and isolates the angular motion of the carrier; and then uses the accelerometer to measure the acceleration information (specific force) of the platform body in the navigation coordinate system, and obtains the velocity and position information of the platform body through integral operation of a navigation computer.

[0004] The strapdown type inertial navigation system does not have a rotating control mechanism for tracking the navigation coordinate system in the navigation process, only uses the gyroscope to sense the angular motion of the platform body, and then calculates the attitude angle of the platform body through a navigation computer to determine the relative angular position relationship (attitude matrix) between the platform body coordinate system and the navigation coordinate system, uses the accelerometer to measure the specific force in the platform body coordinate system, performs coordinate transformation through the attitude matrix obtained through attitude calculation to obtain the acceleration information in the navigation coordinate system, and then performs integral operation to obtain the velocity and position information of the platform body.

[0005] In order to suppress the long-time accumulation of errors such as instrument zero offset of the inertial navigation system, the inertial navigation system introduces a rotation modulation technology, controls the rotation of the platform body through a rotating frame indexing mechanism, and uses the integral link of inertial navigation calculation to eliminate the navigation errors caused by the errors such as instrument zero offset of the inertial instrument. Common rotary inertial navigation systems have single-axis, double-axis and other forms. The single-axis rotary inertial navigation system usually adopts a modulation scheme of rotating around the vertical axis, and some products adopt a continuous rotation or whole-circle alternate rotation scheme. The rotating mechanism usually needs to be installed with a conductive slip ring for power supply. Another part of the products adopts a four-position indexing scheme, and the maximum angular distance from the zero position of the rotating shaft is 270°. This type of single-axis rotary inertial navigation system can be powered through wires without the need to install a conductive slip ring, and has higher inherent reliability.

[0006] In inertial navigation system application, the error of inertial instrument needs to be compensated to improve navigation accuracy. The error to be compensated includes the zero offset of gyroscope and accelerometer, scale factor error, and installation error, etc. Calibration is usually needed before navigation of inertial navigation system. The angular motion information such as attitude angle of carrier needs to be calculated from the output value of attitude angle of platform and the measured value of frame angle sensor of rotating mechanism, so the non-orthogonal error of rotating frame and the error of frame angle sensor also need to be compensated. SUMMARY

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

[0008] The object of the present application is achieved by the following technical solutions:

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

[0010] (1) The measured single-axis frame type inertial navigation system is installed on a single-axis turntable with a stable foundation, so that the horizontal attitude angle of the base of the inertial navigation system is less than 3°. The base attitude angle of the inertial navigation system is adjusted, and the frame positioning mechanism is controlled, so that the orientation of the inertial navigation system frame is as shown in Figure 3 . Figure 3 Y F is the rotating frame axis of the inertial navigation system; Z t is the rotating shaft of the single-axis turntable, which should be approximately parallel to the local horizontal plane (the included angle is less than 3°). The polarity of the X, Y, Z channels of the accelerometer and the input shaft is defined as shown in Figure 3 . p , Z p axes are perpendicular to each other in the approximate horizontal position, Y p axis is perpendicular to the X p OZ p plane, X p , Y p , Z p form an orthogonal coordinate system according to the right-hand rule, respectively pointing to the front, up, and right directions of the platform coordinate system. The rotating shaft Y F of the inertial navigation system is parallel to Y p , and the polarity is the same as Y p . The zero position of the inertial navigation system frame angle sensor and the zero position of the single-axis turntable rotating shaft are defined as shown in Figure 3 . When the Y F axis frame angle sensor output is zero, the base coordinate system and the platform coordinate system are approximately coincident, and the polarity is the same, X p , Y p , Z p axes point to the front, up, and right directions of the base of the inertial navigation system, respectively.p With Z t Same direction, polarity same as Z t Same; when Z t When the axis angle sensor output is zero, Y F With Y p Vertically upward, X p With Z p It is approximately in a horizontal position. Assume that the range of the measured values ​​of the inertial navigation system and the rotation axis angle sensor of the single-axis turntable is [0, 360°].

[0011] (2) Control the frame indexing mechanism of the inertial navigation system and the single-axis turntable, lock the stage at the frame angular positions shown in Table 1 below, and after the locking is stable, 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 in Table 1 for data acquisition is not required.

[0012] Table 1. Inertial Navigation System Self-Calibration Locking Frame Angular Position

[0013] Position Number Inertial navigation system turntable frame angle position (°) Single axis turntable rotation axis 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 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 single-axis turntable base coordinate system be:

[0015]

[0016] In the formula, c ij The elements of the cosine matrix in this direction Let Ф be the rotation angle value of the inertial navigation system in the k-th row of Table 1. 1(k) Let H be the single-axis rotary table rotation angle value in the k-th row of Table 1. Then, the error coefficient observation matrix H for the k-th self-calibration locking position is... (k) The calculation method is as follows

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

[0018] In the formula, the expression for each submatrix is:

[0019]

[0020]

[0021] H 1(k) c ij The result calculated at position k should be taken. The expression for the overall observation matrix of the error coefficients is as follows:

[0022]

[0023] (4) Calculate the specific force measurement value of the inertial navigation system in the platform coordinate system at each locked position using accelerometer measurements. The expression for the specific force measurement value at the k-th position is:

[0024]

[0025] In the formula, k = 1, 2, ... 8; K 0j The j-axis accelerometer has zero bias, unit: pulses / s; K 1j E is the accelerometer scaling factor, in units of pulses per (s·g0). ij The installation error angle represents the effect of the i-direction specific force on the j-direction accelerometer measurement, in rad; Δ nj The asymmetric scaling error coefficient for the j-axis accelerometer is given in units of 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 taken from the instrument's factory nominal value.

[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] In the formula, k = 1, 2, ... 8; γ represents the measured value of the rotation frame angle sensor in a single-axis inertial navigation system, in rad; ij The non-orthogonal error angle of the frame is expressed in 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] In the formula, k = 1, 2, ... 8; α j The base attitude angle (j = x, z) is expressed in rad. This represents the gravitational acceleration in the local horizontal coordinate system, in units of g0. Since the actual acceleration of the inertial navigation system is 0, That is, the acceleration error observation at the k-th locking position. θx , θ y are the installation angles of the inertial navigation system along the x-axis and y-axis on the single-axis turntable, respectively.

[0032] (7) The estimated value of the error coefficient is obtained by using the total least squares algorithm:

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

[0034] In the formula, X is the error coefficient vector, X j is the jth component (j = 1, 2, …, 18) thereof; H is the error coefficient total observation matrix; Z is the total observation quantity composed of , whose expression is

[0035]

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

[0037] (8) The estimated value of the calibrated parameter and the base attitude angle is corrected by using the least squares estimation result, and the calculation method is as follows:

[0038] Accelerometer zero offset:

[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 misalignment 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 asymmetry scale 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 misalignment 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 the inertial navigation system on a 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 iterations, representing the result of the nth error separation, where n = 0, 1, 2, ... and n = 0 represents the initial value of the error coefficient.

[0064] (9) Iterative calculations are performed using the corrected error coefficient estimates, i.e., steps (4) to (8) are repeated until each component X of the correction amount X (least squares estimation result) is obtained. j All satisfy the iterative convergence criterion: ( If the convergence criterion value is the j-th dimension component, then the estimated values ​​of each error coefficient after the correction of the current least squares estimation result are the self-calibration results of each error coefficient. (j=1,2,…,18) In engineering applications, the iteration number N can generally be directly taken as 5 to 10 times.

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

[0066] The present application realizes the frame non-orthogonal error coefficient calibration for a single-axis frame inertial navigation system, and can calibrate all error coefficients of a common accelerometer error model under a 1g gravity field, including zero offset, scale factor, installation error, and asymmetric scale error, and can calibrate the installation angle of the inertial navigation system on a single-axis turntable. The calibration process requires that the inertial navigation system frame angle rotation range is not more than ±90°, and thus is suitable for a single-axis rotating inertial navigation system using a wire power supply. The present method only needs to lock the frame angle positions of the inertial navigation system and the single-axis turntable, and does not need to track the inertial coordinate system or other navigation coordinate systems, and is relatively easy to realize for the rotation control mechanism of the inertial navigation system and the single-axis turntable.

[0067] Through the error coefficient calibration and compensation, the carrier or base attitude measurement accuracy of the inertial navigation system can be improved, and a high-precision table body attitude measurement reference datum can be provided for the inertial navigation system under static base conditions and single-axis turntable test conditions, and thus the performance of the inertial navigation system self-calibration, initial alignment and inertial navigation related to the table body attitude accuracy can be improved. BRIEF DESCRIPTION OF DRAWINGS

[0068] Figure 1 The figure is a flowchart of the method of the present application.

[0069] Figure 2 The figure is the frame orientation of the frame inertial navigation system of the present application.

[0070] Figure 3 The figure is the frame orientation of the frame inertial navigation system of the present application after being installed on a single-axis turntable. DETAILED DESCRIPTION

[0071] In order to make the purpose, technical scheme and advantages of the present application more clear, the embodiments of the present application will be further described in detail below with reference to the drawings.

[0072] A single-axis frame inertial navigation system error calibration and compensation method, under static base conditions, uses a single-axis turntable to assist in locking the table body at 8 different angle positions, collects the accelerometer measurement values, calculates the specific force measurement values of the inertial navigation system under the table body coordinate system at each locking position by using the accelerometer measurement values, calculates the attitude matrix of the inertial navigation system table body coordinate system to the local horizontal coordinate system at each locking position, obtains the acceleration of the inertial navigation system under the local horizontal coordinate system at each locking position as the error observation, uses the total least squares algorithm to obtain the residual error of the error coefficient, corrects the measured parameter estimation value, and iteratively calculates using the corrected error parameter estimation value until the iteration convergence criterion is met, and the calibration results of each error coefficient are obtained, such as Figure 1The 14 error coefficients of accelerometer zero offset, scale factor error, installation error, asymmetric scale error, and frame non-orthogonal error, etc. can be calibrated, and the attitude angle of the single-axis turntable base and the installation angle of the inertial navigation system on the single-axis turntable can be estimated. Through the calibration and compensation of the error coefficients, the influence of the shaft system non-orthogonal error on the frame inertial navigation system carrier or base attitude measurement precision can be improved, and a high-precision table body attitude measurement reference datum can be provided for the inertial navigation system under the static base condition and the single-axis turntable test condition, so as to improve the performance of the inertial navigation system self-calibration, initial alignment and inertial navigation related to the table body attitude precision.

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

[0074] (1) The measured single-axis frame inertial navigation system is installed on a single-axis turntable with a stable foundation, so that the inertial navigation system base horizontal attitude angle is less than 3°. By adjusting the base attitude angle of the inertial navigation system and controlling the frame positioning mechanism, the inertial navigation system frame orientation is as shown in Figure 3 . Figure 3 Y F is the rotation frame axis of the inertial navigation system; Z t is the single-axis turntable rotation axis, which should be approximately parallel to the local horizontal plane (the included angle is less than 3°). The polarity of the X, Y, Z channels of the accelerometer and the input shaft is defined as shown in Figure 3 . p , Z p axes are perpendicular to each other in the approximate horizontal position, and the Y p axis is perpendicular to the X p OZ p plane, and the X p , Y p , Z p axes form an orthogonal coordinate system according to the right-hand rule, respectively pointing to the front, up, and right directions of the table body coordinate system. The inertial navigation system rotation axis Y F is parallel to Y p , and the polarity is the same as Y p . The zero positions of the inertial navigation system frame angle sensor and the single-axis turntable rotation axis are defined as shown in Figure 3 . F When the Y p axis frame angle sensor output is zero, the base coordinate system and the table body coordinate system are approximately coincident, and the polarity is the same, the X p , Y p , Z p axes point to the front, up, and right directions of the inertial navigation system base, respectively, and Z t is the same as Z t direction, and the polarity is the same as Z t . When the Z FWith Y p Vertical upward, X p With Z p Approximately in the horizontal position. Set the inertial navigation system and single-axis turntable shaft angle sensor measurement value range [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 collect accelerometer measurement values for not less than 3 min at a frequency of 10 Hz or more after locking and stabilizing In the formula, W p j is the average value of the j-axis accelerometer measurement, with units of: pulse number / s. There is no requirement for the sequence of the frame angle positions in Table 1 for data acquisition locking.

[0076] Table 1 Inertial navigation system self-calibration locking frame angle position

[0077] Position Number Inertial navigation system turntable frame angle position (°) Single axis turntable rotation axis 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 observation matrix of each self-calibration locking frame angle position, and form the overall error coefficient observation matrix. Set the direction cosine matrix expression of the table body coordinate system to the single-axis turntable base coordinate system in the ideal case as

[0079]

[0080] In the formula, c ij is the element of this direction cosine matrix, is the inertial navigation system rotation frame angle value in the kth row of Table 1, Ф 1(k) is the single-axis turntable shaft angle value in the kth row of Table 1. The calculation method of the error coefficient observation matrix H (k) of the kth self-calibration locking position 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) c ij in the kth position should take the calculation result. The expression of the overall error coefficient observation matrix is

[0086]

[0087] (4) The specific force measurements of the inertial navigation system in the platform coordinate system at each locking position are calculated using the accelerometer measurements, and the expression of the specific force measurement at the kth position is

[0088]

[0089] where k = 1, 2, …, 8; K 0j is the zero bias of the jth accelerometer, and the unit is pulse number / s; K 1j is the scale factor of the accelerometer, and the unit is pulse number / (s·g0); E ij is the installation error angle, which represents the influence of the ith specific force on the jth accelerometer measurement, and the unit is rad; Δ nj is the asymmetric scale error coefficient of the jth accelerometer, and the unit is 1. (i, j = x, y, z.) The initial values of the calibration parameters K 0j , E ij , Δ nj are 0, and the initial values of the calibration parameters K 1j are the factory nominal values of the instruments.

[0090] (5) The attitude matrix (direction cosine matrix) of the inertial navigation system from the platform coordinate system to the local horizontal coordinate system at each locking position is calculated as follows:

[0091]

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

[0093] (6) The acceleration of the inertial navigation system in the local horizontal coordinate system g at each locking position is calculated as follows:

[0094]

[0095] where k = 1, 2, …, 8; α j is the base attitude angle (j = x, z.), and the unit is rad; is the gravitational acceleration in the local horizontal coordinate system, and the unit is g0, and since the actual acceleration of the inertial navigation system is 0, that is, the acceleration error observation at the kth locking position. θ x , θ y are the installation angles of the inertial navigation system along the x-axis and the y-axis on the single-axis turntable, respectively.

[0096] (7) The estimated value of error coefficient is calculated by using the total least square algorithm:

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

[0098] In the formula, X is the error coefficient vector, X j is the j-th dimensional component (j = 1, 2, …, 18) thereof; H is the error coefficient total observation matrix; Z is the total observation quantity composed of , whose expression is

[0099]

[0100] In the formula, is the k-th self-calibration lock frame angular position of specific force measurement value, k = 1, 2, … 8.

[0101] (8) The estimated value of calibrated parameters and base attitude angle is corrected by using the least square estimation result, and the calculation method is as follows:

[0102] Accelerometer zero offset:

[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 scale 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 misalignment error:

[0122] γ yz | (n+1) = γ yz | (n) + X 15

[0123] γ yx | (n+1) = γ yx | (n) + X 16

[0124] The installation angle of the inertial navigation system in the 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 formula, n is the iteration calculation times, represents the result of the n-th error separation, n = 0, 1, 2, …, wherein n = 0 represents the initial value of the error coefficient.

[0128] (9) using the modified error coefficient estimate to perform iterative calculation, that is, repeating steps (4)-(8) until each component X of the correction amount X (the least square estimation result) satisfies the iterative convergence criterion: j each component X of the correction amount X (the least square estimation result) satisfies the iterative convergence criterion: ( is the convergence criterion value of the j-th dimension component), then the modified error coefficient estimate of the current least square estimation result is the self-calibration result of each error coefficient. (j = 1, 2, …, 18) In engineering applications, the iteration times N can be directly taken as 5-10 times.

[0129] Further, the method of the present application uses a single-axis turntable or other rotating mechanism for assistance, and for the inertial navigation system with three input shaft orthogonal installation accelerometers and one rotating frame shaft, the error parameters shown in Table 2 can be calibrated.

[0130] Table 2 Parameters that can be calibrated by the method

[0131] Error Coefficient Number Accelerometer bias 3 Accelerometer scale factor error 3 Accelerometer non-symmetrical scale factor error factor 3 Accelerometer installation error 3 Rotating frame non-orthogonality error angle 2

[0132] By compensating the above error coefficients, the specific force measurement accuracy and the base attitude angle measurement accuracy of the inertial navigation system can be improved, and further the inertial navigation accuracy and the carrier attitude measurement accuracy can be improved. The compensation method is as follows:

[0133] For the inertial navigation system with three input shaft orthogonal installation accelerometers in the inertial navigation system, in the 1g gravity field environment of the static base self-calibration, the accelerometer measurement value expression for compensating the error coefficient is

[0134]

[0135] where f p is the specific force measurement output of the accelerometer combination, in g0; K 0j is the bias of the j-axis accelerometer, in pulses / s; K 1j is the scale factor error of the j-axis accelerometer, in pulses / s / g0; E ij is the installation error angle of the i-axis accelerometer around the positive direction of O j axis, in rad; W j p is the output value of the j-axis accelerometer, in pulses / s; Δ nj is the non-symmetrical scale factor error of the j-axis accelerometer, reflecting the difference between the positive and negative scale factors of the j-axis accelerometer, in 1. Where i, j = x, y, z.

[0136] For an inertial navigation system with one rotating frame axis of the platform, in the ideal case, when the frame angle is at zero position, the platform coordinate system should be parallel to the base coordinate system, and the frame rotation axis should be parallel to the corresponding axis of the platform coordinate system. However, due to factors such as part tolerance and reference deviation in the process of machining and assembling of the inertial navigation system, machining and assembling errors are generally introduced, mainly in the form of inertial instrument installation error and non-orthogonal error of the frame axis system.

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

[0138] Figure 2 where the subscript p represents the platform coordinate system, and the subscript m represents the base coordinate system. The mathematical model of the non-orthogonal error of the axis system of this single-axis frame type inertial navigation system can be represented by the direction cosine matrix from the platform coordinate system to the base coordinate system as

[0139]

[0140] where m2 is the inner ring frame coordinate system, and m1 is the outer ring frame coordinate system. The expressions of the matrix factors are as follows:

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

[0142]

[0143] where 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 base coordinate system of the inertial navigation system is

[0145]

[0146] wherein, is a measurement value of the outer ring frame angle sensor.

[0147] Embodiment:

[0148] The specific implementation and application effects of the present application are given based on simulation tests. It is assumed that the frame orientation of the inertial navigation system is as shown in Figure 2 Table 2. It is assumed that each error coefficient of the inertial navigation system shown in Table 2 is a normal distribution random constant: the accelerometer scale factor is in the range of 5000±50 pulses / (s·g0), the accelerometer zero offset is in the range of [-0.25, 0.25] pulses / s, the accelerometer asymmetric scale error is in the range of [-5e-6, 5e-6], the accelerometer installation error is in the range of [-180, 180] angle seconds, the frame non-orthogonal error angle is in the range of [-180, 180] angle seconds, the installation angle of the inertial navigation system on the single-axis turntable is in the range of [-300, 300] angle seconds, the horizontal attitude angle of the single-axis turntable base is in the range of [-3°, 3°], and the azimuth angle is in the range of [0°, 360°) and is subject to uniform distribution.

[0149] The self-calibration lock frame angle position used for self-calibration is shown in Table 3.

[0150] Table 3: Self-calibration lock frame angle position of the inertial navigation system

[0151] Position Number Inertial navigation system turntable frame angle position (°) Single axis turntable rotation axis 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 non-orthogonal error model of the shaft system of the single-axis frame type inertial navigation system and the installation angle model of the single-axis turntable, the actual attitude matrix of the table body is calculated, the gravitational acceleration is projected into the table body coordinate system, the actual sensitive specific force of the accelerometer combination is obtained, the accelerometer specific force measurement value at 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 at each position is 3 min.

[0153] The accelerometer measurement value generated by simulation is processed by using the calculation method of steps (2)-(9) of the present application, the iteration number N is taken as 10, and the self-calibration result obtained is shown in Table 4.

[0154] Table 4: Self-calibration simulation test result

[0155]

[0156]

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

[0158] The contents not described in detail in the specification of the present application are the known technology of the skilled in the art.

[0159] Although the present application has been disclosed with the preferred embodiments as above, it is not intended to limit the present application, and any person skilled in the art can make possible changes and modifications to the technical solutions of the present application by using the disclosed methods and technical contents without departing from the spirit and scope of the present application. Therefore, any simple modification, equivalent change and modification made to the above embodiments according to the technical essence of the present application without departing from the technical solutions of the present application shall fall within the protection scope of the technical solutions of the present application.

Claims

1. A method for error calibration and compensation of a single-axis frame-based inertial navigation system, characterized in that, The method comprises the following steps: (1) mounting the single-axis frame inertial navigation system to be measured on a single-axis turntable with a stable base, so that the base attitude angle of the inertial navigation system is less than 3°; (2) controlling the frame rotating mechanism of the inertial navigation system and the single-axis turntable to lock the turntable body at 8 different angle positions, and collecting the accelerometer measurement values; (3) calculating the error coefficient observation matrix of each calibration-locked frame angle position, and forming the total error coefficient observation matrix; (4) calculating the specific force measurement values of the inertial navigation system in the turntable body coordinate system at each locked position by using the accelerometer measurement values; (5) calculating the attitude matrix of the inertial navigation system from the turntable body coordinate system to the local horizontal coordinate system at each locked position; (6) calculating the acceleration of the inertial navigation system in the local horizontal coordinate system at each locked position as the error observation value; (7) obtaining the estimation value of the error coefficient by using the total least square algorithm; (8) correcting the estimation value of the calibrated parameters and the base attitude angle by using the estimation value of the error coefficient; (9) performing iterative calculation by using the corrected estimation value, and repeating steps (4) to (8) until the correction amount in the estimation value of the error coefficient meets the iterative convergence criterion.

2. The single-axis gimbaled inertial navigation system error calibration and compensation method of claim 1, wherein, The measurement value range of the rotation shaft angle sensor of the inertial navigation system and the single-axis turntable is [0, 360°].

3. The single-axis gimbaled inertial navigation system error calibration and compensation method of claim 1, wherein, In step (2), the accelerometer measurement values are collected at a frequency of more than 10 Hz for not less than 3 min after the turntable body is locked.

4. The single-axis gimbaled inertial navigation system error calibration and compensation method of claim 1, wherein, In step (2), the 8 inertial navigation system self-calibration-locked frame angle positions are as follows: In step (3), the expression of the direction cosine matrix from the turntable body coordinate system to the base coordinate system of the single-axis turntable in an ideal case is as follows:

5. The single-axis gimbaled inertial navigation system error calibration and compensation method of claim 1, wherein, In step (4), the expression of the specific force measurement value at the k position is as follows: where c ij is the element of the direction cosine matrix, is the inertial navigation system rotation frame angle measurement value at the kth position, Ф 1(k) is the single-axis turntable rotation axis angle measurement value at the kth position; then the error coefficient observation matrix H (k) at the kth position is calculated as follows: H (k) = [H 1(k) H 2(k) H 3(k) H 4(k) ] In step (5), the attitude matrix of the inertial navigation system from the turntable body coordinate system to the local horizontal coordinate system at each locked position is as follows: In the formula, H 1(k) The middle c ij According to the calculation result of the kth position, the expression of the error coefficient overall observation matrix is:

6. The single-axis gimbaled inertial navigation system error calibration and compensation method according to claim 5, wherein, In step (6), the acceleration of the inertial navigation system in the local horizontal coordinate system g at each locked position is as follows: where k = 1, 2,... 8; K 0j is the accelerometer zero offset; K 1j is the accelerometer scale factor; E ij is the installation error angle, representing the effect of the i- directional specific force on the j-direction accelerometer measurement; Δ nj is the non-symmetrical scale error coefficient of the j-direction accelerometer, i, j = x, y, z, calibrated parameter K 0j , E ij , Δ nj is initialized to 0, K 1j is initialized to the factory nominal value of the instrument.

7. The single-axis gimbaled inertial navigation system error calibration and compensation method according to claim 6, wherein, In step (7), the estimation value of the error coefficient is obtained by using the total least square algorithm: where k = 1, 2,... 8; is the inertial navigation system rotation frame angle measurement for the kth position; γ ij is the frame non-orthogonality error angle, i, j = x, y, z.

8. The single-axis gimbaled inertial navigation system error calibration and compensation method according to claim 7, wherein, In step (8), the estimation value of the calibrated parameters and the base attitude angle is corrected by using the least square estimation result, and the calculation method is as follows: wherein k = 1, 2,... 8; a j is the base attitude angle, j = x, z; is the gravity acceleration in the local horizontal coordinate system, Ф 1(k) is the kth position single-axis turntable rotation axis angle measurement value; θ x , θ y are the installation angles of the inertial navigation system along the x-axis and y-axis on the single-axis turntable, respectively.

9. The single-axis gimbaled inertial navigation system error calibration and compensation method of claim 8, wherein, Accelerometer zero offset: X = (H T H) -1 H T Z = [X1 X2... X 18 ] T where X is a 18x1 vector of the 18th dimension components of X j is the jth dimension component of X, j = 1, 2,..., 18; H is the error coefficient total observation matrix; Z is the total observation quantity composed of the 18th dimension components of X, whose expression is:

10. The single-axis gimbaled inertial navigation system error calibration and compensation method of claim 9, wherein, Accelerometer scale factor: Accelerometer installation error: 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 asymmetric scale error: K 1x | (n+1) = K 1x | (n) (1 - X4) K 1y | (n+1) = K 1y | (n) (1 - X5) K 1z | (n+1) = K 1z | (n) (1 - X6) Base attitude angle: E xy | (n+1) = E xy | (n) + X7 E xz | (n+1) = E xz | (n) + X8 E yz | (n+1) = E yz | (n) + X9 Frame non-orthogonal error: Δ nx | (n+1) = Δ nx | (n) + X 10 Δ ny | (n+1) = Δ ny | (n) + X 11 Δ nz | (n+1) = Δ nz | (n) + X 12 Installation angle of the inertial navigation system on the single-axis turntable: α x | (n+1) ＝α x | (n) +X 13 α z | (n+1) ＝α z | (n) +X 14 In the above formulas, n is the number of iterative calculations, n=0, 1, 2, …, wherein n=0 represents the initial value of the error coefficient. gamma yz | (n+1) = gamma yz | (n) + X 15 gamma yx | (n+1) = gamma yx | (n) + X 16 ​ θ x | (n+1) = θ x | (n) + X 17 θ y | (n+1) = θ y | (n) + X 18 ​

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