A dual-axis frame inertial navigation system error self-calibration and compensation method

Abstract

A kind of double-axis frame inertial navigation system error self-calibration and compensation method, under static base condition, in 8 frame angle position locking platform, acquisition accelerometer measurement value, calculate the specific force measurement value of inertial navigation system in each locking position platform coordinate system, and calculate the attitude matrix of inertial navigation system in each locking position platform coordinate system to local horizontal coordinate system, obtain the acceleration of inertial navigation system in each locking position local horizontal coordinate system, as error observation quantity.Using total least squares algorithm to obtain the residual of error coefficient, correct the estimated value of measured parameter, carry out iterative calculation until meeting iteration convergence criterion, obtain the self-calibration result of each error coefficient;Through the self-calibration and compensation of error coefficient, the influence of shaft system non-orthogonal error on the attitude measurement precision of double-axis frame inertial navigation system carrier or base can be improved.

Description

TECHNICAL FIELD

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

[0002] An inertial navigation system measures the angular motion and linear motion parameters of a carrier by using an accelerometer and a gyroscope, and obtains the speed, 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 a platform type inertial navigation system and a strapdown type inertial navigation system.

[0003] The platform type inertial navigation system (also referred to 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 rotating 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 speed and position 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 the attitude calculation, obtains the acceleration information in the navigation coordinate system, and then performs integral operation to obtain the speed and position of the platform body.

[0005] In the application of the inertial navigation system, the errors of the inertial instruments need to be compensated to improve the navigation precision. The errors that need to be compensated include the zero bias, scale factor error and installation error of the gyroscope and the accelerometer, and the like. The calibration is usually performed before the navigation of the inertial navigation system. The attitude angle and other angular motion information of the carrier need to be calculated from the output value of the attitude angle of the platform body and the measurement value of the frame angle sensor of the rotating mechanism, so the non-orthogonal error of the rotating frame and the error of the frame angle sensor also need to be compensated. SUMMARY

[0006] The technical problem to be solved by the application is to overcome the shortcomings of the prior art and solve the self-calibration and compensation problem of the errors of the two-axis frame type inertial navigation system.

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

[0008] The technical problem to be solved by the application is to overcome the shortcomings of the prior art and solve the self-calibration and compensation problem of the errors of the two-axis frame type inertial navigation system.

[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 vibration isolation, such as a marble slab or 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 made as follows: Figure 1 As shown. Press Figure 1 The diagram shows the definition of the polarity of the accelerometer's X, Y, and Z channels relative to the input axis: X p Z p The axes are perpendicular to each other in an approximately horizontal position, Y p The axis is perpendicular to X. p OZ p Plane, X p Y p Z p An orthogonal coordinate system is formed using the right-hand rule, pointing in the front, top, and right directions of the platform coordinate system, respectively. The zero-point of the frame angle sensor is defined as follows: when the outputs of all frame angle sensors in the inertial navigation system are zero, the base coordinate system and the platform coordinate system approximately coincide, have the same polarity, and X... p Y p Z p Pointing to the front, top, and right directions of the base coordinate system respectively, X p Z p respectively with X F Z F Parallel and with the same polarity. Assume the range of the frame angle sensor measurement value is [0, 360°].

[0010] (2) Control the frame rotation mechanism of the inertial navigation system to lock the platform at the frame angular positions shown in Table 1 below. After the platform is locked and 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 for data acquisition in Table 1 is not required.

[0011] Table 1. Inertial Navigation System Self-Calibration Locking Frame Angular Position

[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 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 platform coordinate system to the inertial navigation system base coordinate system be:

[0014]

[0015] In the formula, c ijThe elements of the cosine matrix in this direction Let H be the angle values ​​of the outer ring, middle ring, and inner ring frames in the k-th row of Table 1, respectively. Then, the error coefficient observation matrix H of the k-th self-calibration locking position is... (k) The calculation method is as follows

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

[0017] In the formula, the expression for each submatrix is:

[0018]

[0019] In the formula, 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:

[0020]

[0021] (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:

[0022]

[0023] 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.

[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] In the formula, k = 1, 2, ... 8; These are the measured values ​​of the outer and inner ring frame angle sensors for the k-th self-calibrated locking frame angle position, respectively, in rad. is the inner ring frame angle, unit: rad; γ ij is the frame non-orthogonal error angle, unit: rad, i,j=x,y,z.

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

[0028]

[0029] In the formula, k=1,2,…8; α j is the base attitude angle (j=x,z.), unit: rad; is the gravity acceleration under the local horizontal coordinate system, unit: g0. Since the actual acceleration of the inertial navigation system is 0, that is, the acceleration error observation of the kth locking position.

[0030] (7) The estimated value of the error coefficient is obtained by using the total least squares algorithm:

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

[0032] In the formula, Z is the total observation composed of X1,X2,…,Xn, and its expression is

[0033]

[0034] (8) The estimated value of the calibrated parameters and the base attitude angle is corrected by using the least squares estimation result, and the calculation method is as follows:

[0035] Accelerometer zero offset:

[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 mounting 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 asymmetrical scale 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-orthogonal 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 offset:

[0059]

[0060] In the above formulas, n is the number of iteration calculations, represents the result of the n-th error separation, n=0, 1, 2, …, wherein n=0 represents the initial value of the error coefficient.

[0061] (9) using the modified error coefficient estimate to perform iterative calculation, i.e. repeating steps (4)-(8) until each component Xi of the correction amount X (least square estimation result) meets the iterative convergence criterion: ( is the convergence criterion value of the j-th dimensional component), then the modified error coefficient estimate of the current least square estimation result is the self-calibration result of each error coefficient. (i=1, 2, …, 18.) In engineering applications, the iteration number N can be directly taken as 5-10 times.

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

[0063] The application realizes complete shaft non-orthogonal error coefficient self-calibration for a dual-axis frame inertial navigation system, including frame non-orthogonal error and frame angle zero offset, 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. Through self-calibration and compensation of error coefficients, the carrier or base attitude measurement precision of the dual-axis frame inertial navigation system can be improved, and a high-precision table attitude measurement reference datum can be provided for the inertial navigation system under a static base condition, thereby improving the performance of inertial navigation system self-calibration, initial alignment and inertial navigation related to table attitude precision. The 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, and is relatively easy to realize for the rotation control mechanism of the inertial navigation system and the single-axis turntable. BRIEF DESCRIPTION OF DRAWINGS

[0064] Figure 1 A dual-axis frame inertial navigation system frame orientation diagram.

[0065] Figure 2 A flowchart of the method of the application. DETAILED DESCRIPTION

[0066] To make the objectives, technical solutions and advantages of the application clearer, the embodiments of the application will be further described in detail below with reference to the drawings.

[0067] A dual-axis frame inertial navigation system error self-calibration and compensation method, under a static base condition, locks the table at eight frame angle positions, collects accelerometer measurement values, calculates the specific force measurement values of the inertial navigation system under the table coordinate system at each locked position by using the accelerometer measurement values, calculates the attitude matrix of the inertial navigation system from the table coordinate system to the local horizontal coordinate system at each locked position, obtains the acceleration of the inertial navigation system under the local horizontal coordinate system at each locked position, and uses the acceleration as an error observation. The total least squares algorithm is used to obtain the residual error of the error coefficients, correct the estimated value of the measured parameters, and perform iterative calculation with the corrected error coefficient estimated value until the iterative convergence criterion is met, to obtain the self-calibration results of each error coefficient, as shown in FIG. 2. Eighteen error coefficients, including accelerometer zero offset, scale factor error, installation error, asymmetric scale error, frame non-orthogonal error, and frame angle sensor zero offset, can be calibrated. Through self-calibration and compensation of error coefficients, the influence of shaft non-orthogonal error on the dual-axis frame inertial navigation system carrier or base attitude measurement precision can be improved, and a high-precision table attitude measurement reference datum can be provided for the inertial navigation system under a static base condition, thereby improving the performance of inertial navigation system self-calibration, initial alignment and inertial navigation related to table attitude precision. Figure 2

[0068] ​A two-axis frame type inertial navigation system error self-calibration and compensation method, specifically comprises:

[0069] (1) The measured two-axis frame type inertial navigation system (hereinafter referred to as inertial navigation system) is placed on a marble platform or a turntable with shock isolation effect, so that the inertial navigation system base horizontal attitude angle is less than 3°. By adjusting the inertial navigation system base attitude angle, and controlling the frame positioning mechanism, the inertial navigation system frame orientation is as shown in Figure 1 Figure 1 The X, Y, Z channels of the accelerometer and the polarity of the input shaft are defined as shown in p p The X, Y, Z 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, X p , Y p , Z p According to the right-hand rule, they form an orthogonal coordinate system, pointing to the front, up, and right directions of the platform coordinate system, respectively. The zero position of the frame angle sensor is defined as: when the outputs of the inertial navigation system frame angle sensor are all zero, the base coordinate system and the platform coordinate system are approximately coincident, and the polarities are the same, X p , Y p , Z p Point to the front, up, and right directions of the base coordinate system, respectively, and X p , Z p are parallel to X F , Z F , respectively, and the polarities are the same. The measurement range of the frame angle sensor is set to [0, 360°].

[0070] (2) Control the frame positioning mechanism of the inertial navigation system, lock the platform at the frame angle positions shown in Table 1 below, and collect accelerometer measurement values for not less than 3 minutes at a frequency of 10 Hz or more after locking, and calculate the average value Where W p j is the average value of the j-axis accelerometer measurement, with the unit of pulse number / s. The sequence of the frame angle positions for data collection locking in Table 1 has no requirement.

[0071] Table 1 Self-calibration locking frame angle position of 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 observation matrix of each self-calibration locking frame angle position, and form the total error coefficient observation matrix. The directional cosine matrix expression from the platform coordinate system to the inertial navigation system base coordinate system under ideal conditions is

[0074] ​​

[0075] In the formula, c ij The elements of the cosine matrix in this direction Let H be the angle values ​​of the outer ring, middle ring, and inner ring frames in the k-th row of Table 1, respectively. Then, the error coefficient observation matrix H of the k-th self-calibration locking position is... (k) The calculation method is as follows

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

[0077] In the formula, the expression for each submatrix is:

[0078]

[0079] In the formula, 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:

[0080]

[0081] (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:

[0082]

[0083] 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.

[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] In the formula, k = 1, 2, ... 8; are the measured values of the outer ring and inner ring frame angle sensors, respectively, in radian; are the inner ring frame angle zero offsets, in radian, j = 1, 2; ij are the frame non-orthogonal error angles, in radian, i, j = x, y, z.

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

[0088]

[0089] where k = 1, 2, …, 8; a j are the base attitude angles (j = x, z.), in radian; is the gravitational acceleration in the local horizontal coordinate system, in g0. Since the actual acceleration of the inertial navigation system is 0, is the acceleration error observation of the kth locking position.

[0090] (7) Use the total least squares algorithm to obtain 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 total observation composed of

[0093]

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

[0095] Accelerometer zero offset:

[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 mounting 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 asymmetry scale 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) = a x | (n) + X 13

[0113] a z | (n+1) = a z | (n) + X 14

[0114] Frame non-orthogonal error:

[0115] g zy | (n+1) = g zy | (n) + X 15

[0116] g yz | (n+1) = g yz | (n) + X 16

[0117] g yx | (n+1) = g yx | (n) + X 17

[0118] Frame angle sensor zero offset:

[0119]

[0120] In the above formulas, n is the number of iteration calculations, represents the result of the n-th error separation, n = 0, 1, 2, …, wherein n = 0 represents the initial value of the error coefficient.

[0121] (9) Using the corrected error coefficient estimate to perform iterative calculation, that is, repeating steps (4)-(8) until each component Xi of the correction amount X (least square estimation result) meets the iterative convergence criterion: ( is the convergence criterion value of the j-th dimension component), then the corrected error coefficient estimate of the current least square estimation result is the self-calibration result of each error coefficient. (i = 1, 2, …, 18.) In engineering applications, the iteration number N can be directly taken as 5-10 times.

[0122] Further, for an inertial navigation system with three input shaft orthogonal installation accelerometers and two rotating frame shafts, the present application can calibrate the error parameters shown in Table 2.

[0123] Table 2 Parameters that can be calibrated by the present method

[0124] Error Coefficient Number Accelerometer Bias 3 Accelerometer Scale Error 3 Accelerometer Asymmetry Scale Error Factor 3 Accelerometer Misalignment Error 3 Inner Ring Frame Misalignment Error Angle 2 Outer Ring Frame Misalignment Error Angle 1 Inner Ring Shaft Frame Angle Bias 1

[0125] 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 the inertial navigation accuracy and the carrier attitude measurement accuracy can be improved. The compensation method is as follows:

[0126] For the inertial navigation system with three input axis orthogonal installed accelerometers on the platform, in the 1g gravity field environment of static base self-calibration, the accelerometer measurement value expression of the compensation error coefficient is

[0127]

[0128] In the formula, f p is the specific force measurement value of the accelerometer combination output, the unit is g0; K 0j is the zero offset of the j direction accelerometer, the unit is pulse number / s; K 1j is the scale factor error of the j direction accelerometer, the unit is pulse number / s / g0; E ij is the installation error angle of the i direction accelerometer around the O j axis positive direction, the unit is rad; W j p is the output value of the j direction accelerometer, the unit is pulse number / s; Δ nj is the non-symmetrical scale factor error of the j direction accelerometer, reflecting the difference between the positive and negative scale factors of the j direction accelerometer, the unit is 1. Wherein i, j = x, y, z.

[0129] For the inertial navigation system with two rotating frame axes on 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 each frame rotating shaft should be parallel to the corresponding axis direction of the platform coordinate system. However, due to the factors such as part tolerance and reference deviation in the machining and assembly process of the inertial navigation system single machine, machining and assembly errors are generally introduced, mainly in the form of inertial instrument installation error and non-orthogonal error of frame axis system.

[0130] Suppose the frame orientation of the two-axis frame type inertial navigation system is Z direction, Y direction from outside to inside, when each rotating frame is at zero position, each frame rotating shaft is orthogonal to each other, and the input axis of each axis direction accelerometer is approximately parallel to the corresponding frame rotating shaft direction. As Figure 1 shown.

[0131] Figure 1 In the formula, subscript p represents the platform coordinate system, and subscript m represents the base coordinate system. The mathematical model of the non-orthogonal error of the axis system of the two-axis frame type inertial navigation system can be expressed as the direction cosine matrix from the platform coordinate system to the base coordinate system as

[0132]

[0133] wherein m2 is the inner gimbal frame coordinate system, and m1 is the outer gimbal frame coordinate system. Expressions of each matrix factor are as follows:

[0134] (1) The direction cosine matrix from the table coordinate system to the inner gimbal frame coordinate system is

[0135]

[0136] wherein γ yz , γ yx is the inner gimbal frame non-orthogonal error angle.

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

[0138]

[0139] wherein γ zy is the outer gimbal frame non-orthogonal error angle, is the inner gimbal frame angle sensor measurement value, is the inner gimbal frame angle sensor zero offset.

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

[0141]

[0142] wherein is the outer gimbal frame angle sensor measurement value.

[0143] Embodiment:

[0144] A specific embodiment and application effect of the present application are given based on a simulation test. It is assumed that the frame orientation of the inertial navigation system is as shown in Figure 1 Table 2. It is assumed that each error coefficient of the inertial navigation system is a normal distribution random constant: the accelerometer equivalent value range is 5000±50 pulses / (s·g0), the accelerometer zero offset value range is [-0.25, 0.25] pulses / s, the accelerometer non-symmetrical scale error value range is [-5e-6, 5e-6], the frame installation error value range is [-180, 180] angular seconds, the frame non-orthogonal error angle value range is [-180, 180] angular seconds, the frame angle sensor zero offset value range is [-180, 180] angular seconds, the inertial navigation system base horizontal attitude angle value range is [-3°, 3°], and the base azimuth angle is uniformly distributed within the range of [0°, 360°).

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

[0146] The actual attitude matrix of the platform is calculated according to the mathematical model of the non-orthogonal error of the shaft system of the two-axis frame inertial navigation system, 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 values at each calibration position are calculated according to the accelerometer specific force output error model, the data sampling frequency is 100Hz, and the data acquisition time at each position is 3min.

[0147] The simulation generated accelerometer measurement values are processed by using the calculation method of steps (2)-(9) of the present application, the iteration number N=10 is taken, and the self-calibration results obtained are shown in Table 3.

[0148] Table 3 Self-calibration simulation test results

[0149]

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

[0151] The contents not described in detail in the specification of the present application are the known technology of those skilled in the art.

[0152] Although the present application has been disclosed with the above preferred embodiments, 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, which does not depart from the technical solutions of the present application, belongs to the protection scope of the technical solutions of the present application.

Claims

1. A method for error self-calibration and compensation of a dual-axis frame-based inertial navigation system, characterized in that, The method comprises the following steps: (1) placing the measured dual-axis frame inertial navigation system on a stable base with shock isolation, so that the horizontal attitude angle of the base of the inertial navigation system is less than 3°; (2) controlling the frame rotating mechanism of the inertial navigation system to lock the table body at 8 frame angle positions, collecting the acceleration sensor measurement values after locking and stabilizing; (3) calculating the error coefficient observation matrix of each calibration and locking 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 table body coordinate system at each locking position by using the acceleration sensor measurement values; (5) calculating the attitude matrix of the inertial navigation system from the table body coordinate system at each locking position to the local horizontal coordinate system; (6) calculating the acceleration of the inertial navigation system in the local horizontal coordinate system at each locking position as the error observation value; (7) using the total least square algorithm to obtain the estimated value of the error coefficient; (8) using the estimated value of the error coefficient to correct the estimated value of the calibrated parameters and the base attitude angle; (9) using the corrected estimated value to perform iterative calculation, and repeating steps (4)-(8) until the correction amount in the estimated value of the error coefficient meets the iterative convergence criterion.

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

3. The dual-axis frame-based INS error self-calibration and compensation method according to claim 1, wherein, In step (2), the acceleration sensor measurement values are collected at a frequency of more than 10 Hz for not less than 3 min after locking and stabilizing.

4. The dual-axis frame-based INS error self-calibration and compensation method according to claim 1, wherein, In step (2), the self-calibration locking frame angle positions of the inertial navigation system are as shown in the following table: The sequence of the frame angle positions in the table has no requirement.

5. The dual-axis frame-based INS error self-calibration and compensation method according to claim 1, wherein, In step (3), the directional cosine matrix expression of the table body coordinate system to the base coordinate system of the inertial navigation system in an ideal case is: In the formula, c ij The element of the direction cosine matrix is The error coefficient observation matrix H (k) of the kth position is calculated as follows: 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) 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 dual-axle frame-based inertial navigation system error self-calibration and compensation method according to claim 5, characterized in that, In step (4), the expression of the specific force measurement value at the k position is: 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 asymmetric scale error coefficient of the j-direction accelerometer; i, j = x, y, z; calibration parameter K 0j , E ij , Δ nj is initialized to 0, K 1j is initialized to the instrument factory nominal value.

7. The dual-axle frame-based inertial navigation system error self-calibration and compensation method according to claim 6, characterized in that, In step (5), the attitude matrix of the inertial navigation system from the table body coordinate system at each locking position to the local horizontal coordinate system is: wherein is the inner ring frame angle zero offset; γ ij is the frame non-orthogonality error angle, i,j = x,y,z.

8. The dual-axis frame-based INS error self-calibration and compensation method according to claim 7, wherein, 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; a j is the base attitude angle, j = x, z; is the gravity acceleration in the local horizontal coordinate system.

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

10. The dual-axle frame-based inertial navigation system error self-calibration and compensation method according to claim 9, characterized in that, In step (8), the estimated 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: Accelerometer zero offset: 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) K 1y | (n+1) = K 1y | (n) (1 - X5) K 1z | (n+1) = K 1z | (n) (1 - X6) Accelerometer installation error: E xy | (n+1) = E xy | (n) + X7 E xz | (n+1) = E xz | (n) + X8 E yz | (n+1) = E yz | (n) + X9 Accelerometer asymmetric scale 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 Base attitude angle: α x | (n+1) ＝α x | (n) +X 13 α z | (n+1) ＝α z | (n) +X 14 Frame non-orthogonal error: gamma zy | (n+1) = gamma zy | (n) + X 15 gamma yz | (n+1) = gamma yz | (n) + X 16 gamma yx | (n+1) = gamma yx | (n) + X 17 Frame angle sensor zero offset: In the above formulas, n is the number of iterative calculations, indicating the result of the n-th error separation, n = 0, 1, 2, …, wherein n = 0 represents the initial value of the error coefficient.

Images