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

Abstract

A three-axis frame inertial navigation system error self-calibration and compensation method realizes complete shaft non-orthogonal error coefficient self-calibration, including frame non-orthogonal error and frame angle zero offset, and can calibrate all error coefficients of a commonly used accelerometer error model. Through error coefficient self-calibration and compensation, the frame inertial navigation system carrier or base attitude measurement accuracy 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, thereby improving the performance of the inertial navigation system self-calibration, initial alignment and inertial navigation related to the table body attitude accuracy.

Description

TECHNICAL FIELD

[0001] The present application relates to a three-axis frame type inertial navigation system error self-calibration and compensation method, belonging to the technical field of inertial navigation. BACKGROUND

[0002] An inertial navigation system uses an accelerometer and a gyroscope to measure the angular motion and linear motion parameters of a carrier, 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 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 the navigation coordinate system through a rotating frame positioning mechanism, and isolates the angular motion of the carrier; then uses the accelerometer to measure the acceleration information (specific force) of the platform body in the navigation coordinate system, and performs integral operation through a navigation computer to obtain the speed and position of the platform body motion.

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

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

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

[0007] The object of the present application is achieved by the following technical solutions:

[0008] The application discloses a self-calibration and compensation method for errors of a three-axis frame type inertial navigation system.

[0009] More specifically,

[0010] A self-calibration and compensation method for errors of a three-axis frame type inertial navigation system comprises the following steps as shown in Figure 2

[0011] (1) Place the measured three-axis frame type inertial navigation system on a marble flat plate or a turntable having a shock isolation effect, so that the inertial navigation system base horizontal attitude angle is less than 3°. Adjust the inertial navigation system base attitude angle and control the frame rotating mechanism, so that the inertial navigation system frame orientation is as shown in Figure 1 (2) Define the polarity of the X, Y and Z channels of the accelerometer and the input shaft as shown in Figure 1 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 and Z p axes form an orthogonal coordinate system according to the right-hand rule and respectively point to the front, upper and right directions of the platform coordinate system. The zero position of the frame angle sensor is defined as follows: 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 have the same polarity, X p , Y p and Z p ​​Point to the front, upper, right direction of the base coordinate system respectively. Set the value range of the frame angle sensor measurement value as [0, 360°].

[0012] (2) Control the rotating frame of the inertial navigation system, lock the table body at the frame angle position shown in Table 1 below, and collect the accelerometer measurement value for not less than 3 min at a frequency of 10 Hz or more after locking and stabilizing, and calculate the average value In the formula, W p j is the average value of the measurement value of the j-axis accelerometer, and the unit is: pulse number / s. There is no requirement for the sequence of the frame angle position of the data collection locking in Table 1.

[0013] Table 1: Locking frame angle position of inertial navigation system self-calibration

[0014] Position number Outer ring frame angle (°) Middle ring frame angle (°) Inner ring frame angle (°) 1 0 0 0 2 90 0 0 3 90 [Alpha]1 0 4 90 [alpha]2 0 5 180 0 0 6 270 0 0 7 0 0 90 8 0 0 180 9 0 0 270

[0015] Wherein, α1, α2 can be taken in the range of [10°, 170°] and [190°, 350°], and usually |α1-α2|≥10°.

[0016] (3) Calculate the error coefficient observation matrix of each self-calibration locking position, and form the error coefficient overall observation matrix. Let

[0017]

[0018] In the formula, c ij is the element of the direction cosine matrix, are the outer ring, middle ring and inner ring frame angle values of the kth row in Table 1, then the calculation method of the error coefficient observation matrix H (k) of the kth self-calibration locking position is

[0019] H (k) = [H 1(k) H 2(k) H 3(k) H 4(k) ]

[0020] In the formula, the expression of each sub-matrix is

[0021]

[0022] In the formula, H 1(k) c ij of the kth position should be taken. The expression of the error coefficient overall observation matrix is

[0023]

[0024] (4) Calculate the specific force measurements of the inertial navigation system in the body coordinate system of each locking position using the accelerometer measurements. The expression of the specific force measurement of the kth position is

[0025]

[0026] where k = 1, 2, … 9; K 0j is the zero bias of the jth accelerometer, with units of pulses / s; K 1j is the scale factor of the accelerometer, with units of pulses / (s·g0); E ij is the installation error angle, which represents the influence of the ith specific force on the jth accelerometer measurement, with units of rad; Δ nj is the asymmetric scale error coefficient of the jth accelerometer, with units of 1. (i, j = x, y, z.) Calibration parameters K 0j , E ij , Δ nj The initial value of K 1j is taken as 0, and the initial value of K ij is taken as the nominal value of the instrument out of the factory.

[0027] (5) Calculate the attitude matrix (direction cosine matrix) of the inertial navigation system from the body coordinate system of each locking position to the local horizontal coordinate system:

[0028]

[0029] where k = 1, 2, … 9; are the measurement values of the outer ring, middle ring, and inner ring frame angle sensors, respectively, with units of rad; are the measurement values of the outer ring, middle ring, and inner ring frame angle sensors at the kth self-calibration locking frame angle position, respectively, with units of rad; are the corresponding frame angle zero biases, with units of rad, j = 1, 2, 3; γ ij are the frame non-orthogonal error angles, with units of rad, i, j = x, y, z.

[0030] (6) Calculate the acceleration of the inertial navigation system in the local horizontal coordinate system g at each locking position:

[0031]

[0032] where k = 1, 2, … 9; α j is the base attitude angle (j = x, z.), with units of rad; is the gravitational acceleration in the local horizontal coordinate system, with units of g0. Since the actual acceleration of the inertial navigation system is 0, is the acceleration error observation of the kth locking position.

[0033] (7) The total least square algorithm is used to obtain the estimated value of error coefficient:

[0034] X = (H T H) -1 H T Z = [X1 X2 … X 20 ] T

[0035] In the formula, Z is the total observation composed of the expression

[0036]

[0037] (8) The estimated value of the calibrated parameter and base attitude angle is corrected by using the least square 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 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 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 xy | (n+1) = γ xy | (n) + X 15

[0059] γ yz | (n+1) = γ yz | (n) + X 16

[0060] γ zx | (n+1) = γ zx | (n) + X 17

[0061] γ zy | (n+1) = γ zy | (n) + X 18

[0062] Frame angle sensor zero offset:

[0063]

[0064] In the above equations, n is the number of iteration calculation, represents the result of the n-th error separation, n = 0, 1, 2, …, wherein n = 0 represents the initial value of the error coefficient.

[0065] (9) Using the modified error coefficient estimate to perform iterative calculation, i.e. repeating steps (4) to (8) until each component X i of the correction X (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. (i = 1, 2, …, 20.) In engineering applications, the number of iterations N can be directly taken as 5-10 times.

[0066] Further, for an inertial navigation system with three input shaft orthogonal installed accelerometers and three rotating frame axes, the error parameters shown in Table 2 can be calibrated.

[0067] Table 2 Parameters that can be calibrated by the method

[0068] Error coefficient Number Accelerometer bias 3 Accelerometer scale factor error 3 Accelerometer asymmetric scale factor error factor 3 Accelerometer installation error 3 Inner ring frame misalignment error angle 2 Middle ring frame misalignment error angle 1 Outer ring frame misalignment error angle 1 Inner ring shaft frame angle bias 1 Middle ring shaft frame angle bias 1

[0069] By compensating the above error coefficients, the specific force measurement accuracy and base attitude angle measurement accuracy of the inertial navigation system can be improved, and the inertial navigation accuracy and carrier attitude measurement accuracy can be improved. The compensation method is as follows:

[0070] For an inertial navigation system with three input shaft orthogonal installed accelerometers, in the 1g gravity field environment of the static base self-calibration, the accelerometer measurement value expression for compensating the error coefficient is

[0071]

[0072] In the formula, f p is the specific force measurement value of the accelerometer combination output, with the unit of g0; K 0jis the zero bias of the j-axis accelerometer, with unit of pulse / s; K 1j is the scale factor error of the j-axis accelerometer, with unit of pulse / s / g0; E ij is the installation error angle of the i-axis accelerometer around the O j axis positive direction, with unit of rad; W j p is the output value of the j-axis accelerometer, with unit of pulse / 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, with unit of 1. Wherein i, j = x, y, z.

[0073] For the inertial navigation system with three rotating frame axes 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 each frame rotating axis should be parallel to the corresponding axis 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 the frame axis system.

[0074] Suppose the frame orientation of the three-axis frame type inertial navigation system is X, Y, Z from outside to inside, when each rotating frame is at zero position, the frame rotating axes are mutually orthogonal, and the input axes of each axis accelerometer are approximately parallel to the corresponding frame rotating axis direction. As shown in Figure 1 .

[0075] 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 three-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

[0076]

[0077] In the formula, m3 is the inner ring frame coordinate system, m2 is the middle ring frame coordinate system, and m1 is the outer ring frame coordinate system. The expressions of the matrix factors are as follows:

[0078] (1) The direction cosine matrix from the platform coordinate system to the inner ring frame coordinate system is

[0079]

[0080] In the formula, γ zx , γ zy are the non-orthogonal error angles of the inner ring frame.

[0081] (2) The direction cosine matrix from the inner ring frame coordinate system to the middle ring frame coordinate system is

[0082]

[0083] where γ yz is the non-orthogonality error angle of the middle ring frame, is the middle ring frame angle sensor measurement value, is the middle ring frame angle sensor zero offset.

[0084] (3) The direction cosine matrix from the middle ring frame coordinate system to the outer ring frame coordinate system is

[0085]

[0086] where γ xy is the non-orthogonality error angle of the middle ring frame, is the middle ring frame angle sensor measurement value, is the middle ring frame angle sensor zero offset.

[0087] (4) The direction cosine matrix from the outer ring frame coordinate system to the base coordinate system is

[0088]

[0089] where γ is the outer ring frame angle sensor measurement value.

[0090] Compared with the prior art, the present application has the following beneficial effects:

[0091] The present application realizes complete self-calibration of the non-orthogonality error coefficient of the shaft system of the frame type inertial navigation system, including the non-orthogonality error of the frame and the zero offset of the frame angle, and can also calibrate all error coefficients of the commonly used accelerometer error model. Through the self-calibration and compensation of the error coefficients, the carrier or base attitude measurement precision of the frame type 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 the condition of a static base, thereby improving the performance of the inertial navigation system self-calibration, initial alignment and inertial navigation related to the table body attitude precision. BRIEF DESCRIPTION OF DRAWINGS

[0092] Figure 1 is the frame orientation of the frame type inertial navigation system of the present application.

[0093] Figure 2 is the flowchart of the method of the present application. DETAILED DESCRIPTION

[0094] To make the purpose, technical scheme and advantages of the present application clearer, the embodiments of the present application will be further described in detail below with reference to the drawings.

[0095] Based on the simulation test, the specific embodiments and application effects of the present application are given. Assuming that the frame orientation of the inertial navigation system is as shown inFigure 1 The error coefficients of the inertial navigation system shown in Table 2 are all normal distribution random constants: the equivalent value range of the accelerometer is 5000±50 pulses / (s·g0), the accelerometer zero offset value range is [-0.25, 0.25] pulses / s, the accelerometer asymmetric scale error value range is [-5e-6, 5e-6], the accelerometer installation error value range is [-180, 180] angle seconds, the frame non-orthogonal error angle value range is [-180, 180] angle seconds, the frame angle sensor zero offset value range is [-180, 180] angle seconds, the inertial navigation system base horizontal attitude angle value range is [-3°, 3°], and the base azimuth angle is uniformly distributed in the range of [0°, 360°).

[0096] The self-calibration lock frame angle position used in self-calibration is shown in Table 3.

[0097] Table 3 Lock frame angle position used in self-calibration of the inertial navigation system

[0098] Position number Outer ring frame angle (°) Middle ring frame angle (°) Inner ring frame angle (°) 1 0 0 0 2 90 0 0 3 90 30 0 4 90 330 0 5 180 0 0 6 270 0 0 7 0 0 90 8 0 0 180 9 0 0 270

[0099] 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 three-axis frame inertial navigation system, the gravity acceleration is projected into the platform 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.

[0100] 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 10, and the self-calibration result obtained is shown in Table 4.

[0101] Table 4 Self-calibration simulation test result

[0102]

[0103] The simulation test result verifies the effectiveness of the method of the present application.

[0104] The contents not described in detail in the specification of the present application are the known technology of those skilled in the art.

[0105] Although the present application has been disclosed with reference to the 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 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 self-calibration and compensation of a triad frame inertial navigation system, characterized in that, The method comprises the following steps: (1) placing the three-axis frame inertial navigation system to be measured on a stable base with shock isolation, so that the base attitude angle of the inertial navigation system is less than 3°; (2) controlling the rotating frame of the inertial navigation system, locking the table body at 9 frame angle positions, and collecting the accelerometer measurement values after locking and stabilizing; (3) calculating the error coefficient observation matrix of each calibration and locking 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 accelerometer 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; (7) obtaining the estimation value of the error coefficient by using the total least square algorithm; (8) correcting the estimation values of the calibrated parameters and the base attitude angle by using the least square estimation result; (9) performing iterative calculation by using the corrected estimation values, 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 triad frame-based INS 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 triad frame-based INS error self-calibration and compensation method according to claim 2, 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 locking and stabilizing.

4. The triad frame-based INS error self-calibration and compensation method according to claim 3, wherein, In step (2), the self-calibration locking frame angle positions of the inertial navigation system are as follows: The sequence of the frame angle positions in the table data collection locking has no requirement.

5. The triad frame-based INS error self-calibration and compensation method according to claim 4, characterized in that, In step (3), the total error coefficient observation matrix is: The error coefficient observation matrix H of the kth self-calibration locking position is (k) The calculation method of H is as follows: H (k) = [H 1(k) H 2(k) H 3(k) H 4(k) ] where H 1(k) The middle c ij The calculation result of the kth position; c ij The element of the direction cosine matrix, The outer ring, middle ring, and inner ring frame angle measurements of the kth position, respectively.

6. The triad 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,... 9; K 0j is the accelerometer bias in j direction; K 1j is the accelerometer scale factor; E ij is the installation error angle, representing the effect of the i direction 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 triad frame-based INS 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: where k = 1, 2,... 9; for the corresponding frame angle zero offset, j = 1, 2, 3; γ ij for the frame non-orthogonality error angle, i, j = x, y, z.

8. The triad frame-based INS error self-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, … 9; a j is the base attitude angle, j = x, z; is the gravity acceleration in the local horizontal coordinate system, since the actual acceleration of the inertial navigation system in the local horizontal coordinate system g at each locking position is zero, thus can be used as the acceleration error observation of the kthlocking position.

9. The triad frame-based INS error self-calibration and compensation method according to claim 8, wherein, In step (7), the estimation value of the error coefficient is obtained by using the total least square algorithm: X = (H T H) -1 H T Z = [X1 X2...X 20 ] T In the formula, Z is The total observed quantity of the composition is expressed by 10. The triad frame-based inertial navigation system error self-calibration and compensation method according to claim 9, characterized in that, In step (8), the estimation values of the calibrated parameters and the base attitude angle are 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 xy | (n+1) = gamma xy | (n) + X 15 gamma yz | (n+1) = gamma yz | (n) + X 16 gamma zx | (n+1) = gamma zx | (n) + X 17 gamma zy | (n+1) = gamma zy | (n) + X 18 Frame angle sensor zero offset: In the above formulas, n is the number of iterative 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.

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