CN117346823A - System-level error calibration method of strapdown inertial navigation system considering magnetic field influence - Google Patents

System-level error calibration method of strapdown inertial navigation system considering magnetic field influence Download PDF

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CN117346823A
CN117346823A CN202311457416.1A CN202311457416A CN117346823A CN 117346823 A CN117346823 A CN 117346823A CN 202311457416 A CN202311457416 A CN 202311457416A CN 117346823 A CN117346823 A CN 117346823A
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CN117346823B (en
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于旭东
娄琪欣
李鼎
江奇渊
张燚
孙兵锋
魏国
高春峰
王林
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National University of Defense Technology
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    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices
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Abstract

The invention relates to the technical field of inertial navigation, in particular to a system-level error calibration method of a strapdown inertial navigation system considering magnetic field influence; according to the invention, the conventional IMU error is excited by the rotation of the three-axis turntable, and the first-order magnetic field coefficient of the gyroscope is excited by the variable geomagnetic field sensed by the IMU in the rotation process, so that the influence of an external magnetic field on the output of the gyroscope is calibrated; the invention can accurately calibrate the conventional error parameters of the IMU and the first-order magnetic field coefficient of the gyroscope by utilizing the three-axis turntable and the geomagnetic field; as the system level calibration, the invention does not need a high-precision turntable, and is convenient for completing the calibration under the non-laboratory condition; the geomagnetic field is directly utilized, and an external excitation magnetic field is not required to be additionally added manually, so that auxiliary equipment such as a large-scale coil and the like are not required to be built, and the calibration of the strapdown inertial navigation low-cost magnetic field can be realized; the calibration method provided by the invention is used in the NMRG inertial navigation system, so that the dependence on high-performance magnetic shielding can be reduced, and the cost of the NMRG inertial navigation system is reduced.

Description

System-level error calibration method of strapdown inertial navigation system considering magnetic field influence
Technical Field
The invention relates to the technical field of inertial navigation, in particular to a system-level error calibration method of a strapdown inertial navigation system considering magnetic field influence, which is suitable for error calibration occasions of the strapdown inertial navigation system.
Background
In a strapdown inertial navigation system (hereinafter referred to as inertial navigation), navigation accuracy is closely related to the accuracy of inertial devices (e.g., gyroscopes). At present, various gyroscopes in common use, including laser gyroscopes, fiber-optic gyroscopes, nuclear magnetic resonance gyroscopes and the like, have output accuracy affected by external magnetic field interference to different degrees. In order to improve the navigation precision of the strapdown inertial navigation system, a method capable of reducing the influence of a magnetic field on the output of the gyroscope is needed.
Taking a nuclear magnetic resonance gyro (Nuclear magnetic resonance gyroscope, NMRG) as an example, since the frequency of the atomic pull Mo Jindong is directly related to the magnetic field strength in the direction of the sensitive axis, and the atomic relaxation time is also affected by the magnetic field, its output is more sensitive to external magnetic field disturbances. At present, double isotopes are adopted in the design of the gyroscope to offset the direct influence of axial magnetic field fluctuation on the output of the gyroscope, and a magnetic shielding technology is adopted to weaken an external magnetic field, but the external magnetic field change still has larger interference on the output of the gyroscope. Therefore, compensating for the magnetic field effects using calibration techniques becomes a better way to solve this problem.
The calibration technology is an important means for improving the navigation precision of the strapdown inertial navigation system, and the technology carries out mathematical modeling on various errors in an inertial measurement unit (Inertial Measurement Unit, IMU) formed by an inertial device and the inertial device, and carries out measurement and compensation. The common calibration mode comprises discrete calibration and system-level calibration, wherein the system-level calibration does not depend on a high-precision turntable and has higher calibration precision. Currently, an 18-order system-level calibration method in documents 1[Camberlein L,Mazzanti F.Calibration technique for laser gyro strapdowninertial navigation systems[C, symposium Gyro Technology, stuttgart, westGermany,1985 is widely adopted in strapdown inertial navigation calibration, and can calibrate conventional IMU errors including zero offset, scale factors and installation errors, but the method does not consider the influence of a magnetic field on gyro output and needs to be improved so as to meet the requirement of the current high-precision inertial navigation.
Disclosure of Invention
Considering that various gyroscopes such as a laser gyroscope, an optical fiber gyroscope, an NMRG and the like are sensitive to magnetic fields to different degrees, wherein the NMRG is higher in sensitivity to the external magnetic field, and the geomagnetic field can be regarded as a stable external magnetic field.
The invention adopts the technical scheme that: a system-level error calibration method of a strapdown inertial navigation system considering magnetic field influence comprises the following steps:
s1, mounting the IMU on a three-axis turntable (the precision of the turntable is not required, the IMU can complete the rotating path in S3, and the IMU can be manually turned over even on a flat ground without the three-axis turntable, while the traditional discrete calibration method can provide a position reference and complete calibration by using a high-precision turntable), and powering up the system;
if a three-axis turntable is used, the corresponding relation between the axial direction of the three-axis turntable and the axial geometric positions of the X, Y and Z three axes of the strapdown inertial navigation system is that: when the three-axis turntable is in zero position, the axis parallel to the axial direction of the center axis of the turntable is the y axis of inertial navigation, the axis parallel to the axial direction of the inner axis of the turntable is the z axis of inertial navigation, the axial direction of the outer axis of the turntable is also parallel to the z axis of inertial navigation, and the x axis orthogonal to the y axis and the z axis can be obtained by a right-hand coordinate system.
Meanwhile, a navigation coordinate system, a carrier coordinate system, a geocentric inertial coordinate system and an earth coordinate system are determined:
selecting a geographic coordinate system of east-north-sky (E-N-U) as a navigation coordinate system, and marking the geographic coordinate system as an N system; selecting a right-front-upper coordinate system as a carrier coordinate system, and marking as a b system; the geocentric inertial coordinate system is marked as an i system; the earth coordinate system is denoted as e-system.
S2, initial alignment is carried out, the posture of the IMU is obtained and stored in a navigation computer, and the initial alignment time length is determined by specific parameters of the IMU (specific process can refer to the literature Yan Gongmin, weng Jun. The strapdown inertial navigation algorithm and the combined navigation principle [ M ]. The university of northwest industry Press, 2019 ").
S3, the IMU periodically rotates to fully excite various error parameters (such as gyro zero offset, accelerometer zero offset, gyro scale factor error, accelerometer scale factor error, gyro installation error, accelerometer installation error and gyro first-order magnetic field coefficient) of the IMU including the gyro first-order magnetic field coefficient, wherein each rotation period and specific rotation path are as follows:
path 1: forward rotating by 90 degrees around the y axis of the IMU;
path 2: forward rotation 180 ° about IMU y-axis;
path 3: forward rotation 180 ° about IMU y-axis;
path 4: forward rotating 90 ° around IMU z-axis;
path 5: forward rotation 180 ° about IMU z-axis;
path 6: forward rotation 180 ° about IMU z-axis;
path 7: forward rotating by 90 degrees around the IMU x axis;
path 8: forward rotation 180 ° about IMU x-axis;
path 9: forward rotation 180 ° about IMU x-axis;
path 10: forward rotating by 90 degrees around the IMU x axis;
path 11: forward rotating by 90 degrees around the IMU x axis;
path 12: forward rotating by 90 degrees around the IMU x axis;
path 13: forward rotating 90 ° around IMU z-axis;
path 14: forward rotating 90 ° around IMU z-axis;
path 15: forward rotating 90 ° around IMU z-axis;
path 16: forward rotating by 90 degrees around the y axis of the IMU;
path 17: forward rotating by 90 degrees around the y axis of the IMU;
path 18: forward rotating by 90 degrees around the y axis of the IMU;
the paths 1-18 are a period, and the period number of the turntable rotation in the calibration process is determined by the actual error convergence condition. The first-order magnetic field coefficient of the gyroscope can be fully excited because the projection of the earth magnetic field on three axes of the IMU changes in different rotation paths and in the rotation process of the turntable.
In the periodic rotation process, taking the IMU gesture obtained in the step S2 as an initial inertial navigation gesture, carrying out inertial navigation calculation in real time, and storing the following parameters of the IMU in the rotation process to a navigation computer:
namely, b is a posture cosine matrix of n;
V n ＝[V E V N V U ]i.e. projection of IMU velocity on the n-series, including east velocity V E North speed and heaven speed V U ；
The location, i.e., latitude L, longitude λ, and altitude h, where the IMU is located.
(specific navigation resolving process can refer to the literature Yan Gongmin, weng Jun. Strapdown inertial navigation algorithm and combined navigation principle [ M ]. North Industrial university Press, 2019 ").
S4, an IMU error model is established:
s4.1 establishing a first-order magnetic field coefficient B comprising a gyroscope B The gyro error model of (1) is:
in the formula (1), the components are as follows,indicating the angular increment of the spinning topA quantity output error; />Representing the actual angular increment input of the gyroscope (namely, the ideal angular increment output-the gyroscope is taken as a measuring device, and the actual physical input value is the ideal measuring output value); b (B) g ＝[B gx B gy B gz ] T The constant zero offset of the x, y and z axis gyroscopes in the IMU is represented; epsilon g ＝[ε gx ε gy ε gz ] T Representing random zero offset of the x, y and z axis gyroscopes in the IMU; b= [ B ] x B y B z ] T Representing the magnetic field strength component of an external magnetic field (including but not limited to geomagnetic fields) in the IMUx, y, z axes, which can be measured by the NMRG itself in an NMRG inertial navigation system, and by a magnetometer in other inertial navigation systems;
δK g for gyro scale factor error, the expression is shown as formula (2), wherein δK gx ,δK gy ,δK gz The scale factor errors of the x, y and z axis gyroscopes in the IMU are respectively shown:
δM g for gyro installation error, the expression is shown as formula (3), wherein δM gyx ,δM gzx ,δM gzy The components of the gyro installation error along different directions of the gyro sensitive axis are respectively represented:
using gyro first-order magnetic field coefficient B B Modeling the zero bias of the gyroscope caused by the magnetic field, wherein the expression is shown as a formula (4), and B Bxx Representing the influence of the field intensity component of an external magnetic field on the IMUx axis on zero offset of the x-axis gyroscope, B Bxy Representing the effect of the field strength component of the external magnetic field on the IMUy axis on the zero bias of the x-axis gyroscope, …, the significance of the remaining parameters and so on:
s4.2, an accelerometer error model is established as follows:
δf b ＝(δK a +δM a )f b +B a +ε a (5)
in formula (5), δf b Representing a specific force increment output error of the accelerometer; f (f) b An actual specific force delta input (i.e., an ideal specific force delta output) representing the accelerometer; b (B) a ＝[B ax B ay B az ] T Representing constant zero offset of the x, y and z axis accelerometers in the IMU; epsilon a ＝[ε ax ε ay ε az ] T Representing the random zero offset of the x, y and z-axis accelerometers in the IMU;
in formula (5), δK a For the scale factor error of the accelerometer, the expression is shown as formula (6), wherein δK ax ,δK ay ,δK az Scale factor errors for x, y, z-axis accelerometers in IMU are shown, respectively:
in formula (5), δM a For accelerometer installation errors, the expression is shown as formula (7), wherein δM axy ,δM axz ,δM ayx ,δM ayz ,δM azx ,δM azy The components of the accelerometer installation error along different directions of the accelerometer sensitive axis are respectively represented:
s5, establishing a Kalman filtering system state equation and an observation equation under continuous time:
s5.1, the state equation of the Kalman filtering system under continuous time is as follows:
in the formula (8), the amino acid sequence of the compound,the differentiation of the 39-dimensional state vector X is that:
in the formula (9), the amino acid sequence of the compound,projection of the attitude errors of the IMU in the east, north and sky directions, delta V E ,δV N ,δV U Speed errors of the IMU in the east, north and sky directions are respectively shown, and delta L, delta lambda and delta h are respectively shown as latitude errors, longitude errors and altitude errors of the IMU; other parameters have been defined above.
F is a state transition matrix at continuous time, and its expression is as follows:
wherein 0 is m×n Representing an m multiplied by n dimensional 0 matrix, wherein the rest of the block matrixes are all 3 multiplied by 3 dimensional square matrixes, and the expression is as follows:
wherein,
in the formulae (11) to (29), R M ,R N The main curvature radius of the earth meridian circle and the mortise unitary circle are respectively; omega ie Is the rotation angular rate of the earth;respectively projecting the angular velocities of the IMUx, y and z axes in a b system, namely outputting by an x, y and z axis gyroscope; />Representation->Values of the j-th row and k-th column of the matrix; f (f) E ,f N ,f U Respectively outputting projections of specific force in the east direction, the north direction and the sky direction for an accelerometer in the IMU; f (f) b x ,f b y ,f b z IMUx respectivelyProjection of y, z-axis specific force in the b-system, i.e., x, y, z-axis accelerometer output;
in the formula (8), G is an inertial navigation system noise driving matrix, and the expression is:
w (t) is an inertial navigation system noise matrix, and the expression is:
in the formula (31), W gj (t) (j=x, y, z) is zero-mean white noise of the x, y, z axis gyro output in the IMU, W aj (t) (j=x, y, z) is zero-mean white noise output by the x, y, z-axis accelerometer in the IMU; the system noise covariance matrix Q is shown below:
Q＝diag{(Q gx ) 2 (Q gy ) 2 (Q gz ) 2 (Q ax ) 2 (Q ay ) 2 (Q az ) 2 } (32)
in formula (32), diag represents a diagonal matrix, Q gj (j=x, y, z) is zero mean white noise variance of the x, y, z axis gyro output in IMU, Q aj (j=x, y, z) is zero mean white noise variance of the x, y, z axis accelerometer output in the IMU, satisfying the following condition:
where E represents the desire to solve for.
S5.2, the Kalman filtering observation equation under continuous time is as follows:
Z＝HX+ν(t) (35)
in the formula (35), Z is an observed quantity containing navigation resolving speed error and position error, and the expression is as follows:
Z＝[δV E δV N δV U δL δλ δh] T (36)
in equation (36), since the IMU does not generate linear displacement during the whole calibration process, it can be considered that the velocity (V E ,V N ,V U ) Is the velocity error (delta V) E ,δV N ,δV U ) Navigating the calculated position (L, lambda, h) with the actual position (L 0 ,λ 0 ,h 0 ) The difference is the position error (δl, δλ, δh), namely:
in the formula (35), H is an observation matrix, and the expression is shown as a formula (38), wherein I 3×3 Representing a 3 x 3 dimensional identity matrix:
v (t) is an observation noise matrix, and the expression is:
ν(t)＝[ν E (t) ν N (t) ν U (t) ν L (t) ν λ (t) ν h (t)] T (40)
in formula (40), v E (t),ν N (t),ν U (t) the east, north and sky direction speed observation noise, v L (t),ν λ (t),ν h (t) observed noise at latitude L, longitude λ, and altitude h positions, respectively; the observed noise covariance matrix R is shown below:
R＝diag{(R E ) 2 (R N ) 2 (R U ) 2 (R L ) 2 (R λ ) 2 (R h ) 2 } (41)
in the formula (41), R E ,R N ,R U Observing noise variance for east, north and sky speeds respectively, R L ,R λ ,R h Observed noise variances at latitude, longitude, and altitude, respectively, each satisfying the following conditions:
s6, a discrete Kalman filter system state equation and an observation equation are constructed, and each state parameter is estimated by using the discrete Kalman filter:
s6.1, the state equation and the observation equation of the Kalman filtering system established in the step S5 are time continuous, and discretization processing is needed for the state equation and the observation equation of the Kalman filtering system to be calculated by using a navigation computer:
the equivalent discretized form of the Kalman filtering system state equation (8) is:
X k ＝Φ k/k-1 X k-1 +G k-1 W k-1 (44)
wherein X is k-1 X is the state quantity at time k-1 k As the state quantity at time k, G k-1 For the system noise driving matrix at time k-1, W k-1 Is the system noise matrix at time k-1. Phi k/k-1 For a state one-step transition matrix from time k-1 to time k:
f is a continuous time state transition matrix shown in formula (10), I is an identity matrix with the same dimension as F, and T is a filtering period.
The equivalent discretized form of the Kalman filter observation equation (35) is:
Z k ＝HX k +ν k (46)
wherein Z is k V is the observed quantity at time k k Is the observed noise matrix at time k.
S6.2, constructing a discrete Kalman filter based on the state equation and the observation equation of the discretization system constructed in the S6.1, and estimating the state quantity:
state quantity estimation at known k-1 time according to the basic principle of discrete Kalman filterBased on (a), the state quantity X at the k moment can be estimated k Thus, after the state quantity at the initial time is given, the state quantity at any time can be recursively estimated; the five basic equations for discrete Kalman filtering are as follows:
state one-step prediction equation:
state one-step prediction mean square error matrix equation:
the filter gain calculation equation: k (K) k ＝P k/k-1 H T (HP k/k-1 H T +R) -1 (49)
State quantity estimation equation:
state estimation mean square error matrix equation:
in the formulae (47) to (51),representing the state quantity X at time k-1 k-1 Setting the initial value as the estimated value of (2) A one-step predicted value representing a state quantity from a k-1 time to a k time; p (P) k-1 The mean square error matrix corresponding to the state quantity estimated value at the moment k-1 is represented, and the initial value setting is determined by specific IMU parameters; p (P) k/k-1 Representing a mean square error matrix corresponding to the one-step predicted value of the state quantity from the k-1 moment to the k moment; k (K) k The filtering gain is k time; the system noise covariance matrix Q has been defined in equation (32), its value being related to the specific IMU parameters; the observed noise covariance matrix R has been defined in equation (41), whose value is related to the specific IMU parameters;
s7, recording state vector estimation valueThe final value of (2) is used as a calibration result, an IMU output model is established by using the calibration result, and a calculation formula is as follows, wherein +.>Representation->The m-th element of (a):
gyro constant zero bias:
constant zero offset of accelerometer:
gyro scale factor:
accelerometer scale factor:
gyro installation error:
accelerometer mounting error:
first order magnetic field coefficient of gyro:
the calibrated gyro output is shown in formula (59), whereinFor the actual output of the gyro +.>Representing an estimate of the actual input (i.e., ideal output) of the gyroscope, b= [ B ] x B y B z ] T Representing the magnetic field strength component, T, of an external magnetic field in the x, y and z axes of the IMU IMU Sampling interval for IMU:
the calibrated accelerometer output is shown in equation (60), whereFor the accelerometer to actually output, +.>An estimate representing the actual input (i.e., ideal output) of the accelerometer:
in the actual navigation process, the calibrated navigation system is usedAnd->And performing correlation calculation.
The invention has the following technical effects:
1. the invention utilizes the three-axis turntable and the geomagnetic field, and can accurately calibrate the conventional error parameters of the IMU (such as zero bias of the gyroscope, zero bias of the accelerometer, scale factor error of the gyroscope, scale factor error of the accelerometer, installation error of the gyroscope and installation error of the accelerometer) and the first-order magnetic field coefficient of the gyroscope;
2. as the system level calibration, the invention does not need a high-precision turntable, and is convenient for completing the calibration under the non-laboratory condition;
3. the geomagnetic field is directly utilized, and an external excitation magnetic field is not required to be additionally added manually, so that auxiliary equipment such as a large-scale coil and the like are not required to be built, and the calibration of the strapdown inertial navigation low-cost magnetic field can be realized;
4. the calibration method provided by the invention is used in the NMRG inertial navigation system, so that the dependence on high-performance magnetic shielding can be reduced, and the cost of the NMRG inertial navigation system is reduced;
5. the method provided by the invention can be used for various inertial navigation systems, and can improve the navigation precision under the influence of an external magnetic field (including but not limited to a geomagnetic field).
Drawings
Fig. 1: the invention provides a calibration method implementation flow
Fig. 2: gyroscope zero offset estimation curve
Fig. 3: zero offset estimation curve of accelerometer
Fig. 4: gyro scale factor estimation curve
Fig. 5: accelerometer scale factor estimation curve
Fig. 6: gyro installation error estimation curve
Fig. 7: accelerometer installation error estimation curve
Fig. 8: first-order magnetic field coefficient estimation curve of x-axis gyroscope
Fig. 9: first-order magnetic field coefficient estimation curve of y-axis gyroscope
Fig. 10: first-order magnetic field coefficient estimation curve of z-axis gyroscope
Fig. 11: the calibration method of the invention and the navigation error comparison chart after calibration by the common calibration method
Detailed Description
What is not described in detail in this specification is prior art known to those skilled in the art.
In order to make the technical method and advantages of the present application more apparent, the present invention is further described below with reference to the accompanying drawings, and the specific embodiments described herein are used for explaining the present application and are not limiting the present application.
The implementation flow of the system-level calibration method of the strapdown inertial navigation system containing magnetic field influence provided by the invention is shown in figure 1.
It should be noted that, considering that the east component of the geomagnetic field is small (the geomagnetic field reference model "international geomagnetic reference field (International Geomagnetic Reference Gield, IGRF)") in each place, if the x, y, z three axes of the IMU and the n system three coordinate axes in the initial position are substantially coincident, there will be a small geomagnetic field intensity projection in the direction of the sensitive axis in each position in the rotation path. Therefore, in order to improve the convergence speed and the calibration accuracy of the magnetic field coefficient in the calibration process, before step S2, the initial posture of the IMU may be checked and adjusted, so that all three sensitive axes of the IMU have an included angle greater than 30 ° with the eastern direction of geography.
To demonstrate the feasibility of the invention, simulation experiments were performed. In the experiment, the initial longitude is 112.993 degrees, the latitude is 28.222 degrees, the height is 0m, and the initial posture of the IMU is (0 degrees, 0 degrees and 135 degrees); initial alignment includes coarse alignment 240s and two-position fine alignment 740s; the gyro random walk is set asThe accelerometer random walk is set to +>The sampling frequency of the output information of the inertial device is set to be 200Hz; the filter period of the Kalman filter is set to 200Hz; setting the angular speed of the turntable to be 9 degrees/s in the calibration process according to engineering experience, and standing for 180s between every two rotations to rotate for 6 cycles;
for Kalman filtering, the initial value of the state estimation mean square error matrix is set as shown in equation (52), where r= 6378137m is the earth long half-axis length:
setting a system noise covariance matrix as shown in formula (53):
setting an observed noise covariance matrix as shown in formula (54):
the remaining parameters and calibration results are shown in table 1:
table 1 simulation experiment part parameter set values and calibration estimation values
/>
From fig. 2 to 10, it can be seen that the error parameters are sufficiently converged, and therefore it can be considered that 6 cycles of rotation of the turntable are sufficient. If the error parameter convergence degree is found to be not ideal (if the error parameter convergence degree is not still stabilized near a certain value), the period number of the turntable rotation can be increased, and the calibration time can be prolonged.
In order to further illustrate the advantages and technical effects of the present invention, error calibration is performed on the same simulation data by using a conventional calibration method without considering the first-order magnetic field coefficient of the gyroscope, and navigation simulation experiments with the duration of 20h are performed respectively by using the calibration result obtained by the error calibration method and the calibration result obtained by the error calibration method, and the results are shown in fig. 11. It can be observed that the influence of the magnetic field on the gyroscope is not considered in the conventional calibration method, so that the IMU error parameter cannot be accurately calibrated, and the maximum position error in the navigation process is close to 46.1 sea; the maximum position error of the calibration method in the navigation process does not exceed 1.1 sea, and the calibration precision is considered to be superior to that of the conventional calibration method.

Claims (5)

1. A system-level error calibration method of a strapdown inertial navigation system considering magnetic field influence is characterized by comprising the following steps:
s1, mounting an IMU on a three-axis turntable, and powering up a system;
correspondence between axial directions of the three-axis turntable and axial geometrical positions of the X, Y and Z three axes of the strapdown inertial navigation system: when the three-axis turntable is in a zero position, an axis parallel to the axial direction of the center shaft of the turntable is a y axis of inertial navigation, an axis parallel to the axial direction of the inner shaft of the turntable is a z axis of inertial navigation, at the moment, the axial direction of the outer shaft of the turntable is also parallel to the z axis of inertial navigation, and an x axis orthogonal to the y axis and the z axis can be obtained by a right-hand coordinate system;
meanwhile, a navigation coordinate system, a carrier coordinate system, a geocentric inertial coordinate system and an earth coordinate system are determined:
selecting an east-north-sky geographic coordinate system as a navigation coordinate system, and marking the geographic coordinate system as an n system; selecting a right-front-upper coordinate system as a carrier coordinate system, and marking as a b system; the geocentric inertial coordinate system is marked as an i system; the earth coordinate system is marked as an e system;
s2, initial alignment is carried out, and the gesture of the IMU is obtained and stored in a navigation computer;
s3, periodically rotating the three-axis turntable to fully excite each error parameter of the IMU including the first-order magnetic field coefficient of the gyroscope, wherein each rotation period and a specific rotation path are as follows:
path 1: forward rotating by 90 degrees around the y axis of the IMU;
path 2: forward rotation 180 ° about IMU y-axis;
path 3: forward rotation 180 ° about IMU y-axis;
path 4: forward rotating 90 ° around IMU z-axis;
path 5: forward rotation 180 ° about IMU z-axis;
path 6: forward rotation 180 ° about IMU z-axis;
path 7: forward rotating by 90 degrees around the IMU x axis;
path 8: forward rotation 180 ° about IMU x-axis;
path 9: forward rotation 180 ° about IMU x-axis;
path 10: forward rotating by 90 degrees around the IMU x axis;
path 11: forward rotating by 90 degrees around the IMU x axis;
path 12: forward rotating by 90 degrees around the IMU x axis;
path 13: forward rotating 90 ° around IMU z-axis;
path 14: forward rotating 90 ° around IMU z-axis;
path 15: forward rotating 90 ° around IMU z-axis;
path 16: forward rotating by 90 degrees around the y axis of the IMU;
path 17: forward rotating by 90 degrees around the y axis of the IMU;
path 18: forward rotating by 90 degrees around the y axis of the IMU;
the paths 1-18 are a period, and the period number of the turntable rotation in the calibration process is determined by the actual error convergence condition;
in the periodic rotation process, taking the IMU gesture obtained in the step S2 as an initial inertial navigation gesture, carrying out inertial navigation calculation in real time, and storing the following parameters of the IMU in the rotation process to a navigation computer:
namely, b is a posture cosine matrix of n;
V n ＝[V E V N V U ]i.e. projection of IMU velocity on n-series, packageIncluding eastern speed V E North speed and heaven speed V U ；
The position, namely the latitude L, longitude lambda and height h of the IMU;
s4, an IMU error model is established:
s4.1 establishing a first-order magnetic field coefficient B comprising a gyroscope B The gyro error model of (1) is:
in the formula (1), the components are as follows,indicating the angular increment output error of the gyroscope; />Representing the actual angular increment input of the gyroscope; b (B) g ＝[B gx B gy B gz ] T The constant zero offset of the x, y and z axis gyroscopes in the IMU is represented; epsilon g ＝[ε gx ε gy ε gz ] T Representing random zero offset of the x, y and z axis gyroscopes in the IMU; b= [ B ] x B y B z ] T Representing the magnetic field strength components of the external magnetic field in the IMUx, y, z axes;
δK g for gyro scale factor error, the expression is shown as formula (2), wherein δK gx ,δK gy ,δK gz The scale factor errors of the x, y and z axis gyroscopes in the IMU are respectively shown:
δM g for gyro installation error, the expression is shown as formula (3), wherein δM gyx ,δM gzx ,δM gzy The components of the gyro installation error along different directions of the gyro sensitive axis are respectively represented:
using gyro first-order magnetic field coefficient B B Modeling the zero bias of the gyroscope caused by the magnetic field, wherein the expression is shown as a formula (4), and B Bxx Representing the influence of the field intensity component of an external magnetic field on the IMUx axis on zero offset of the x-axis gyroscope, B Bxy Representing the effect of the field strength component of the external magnetic field on the IMUy axis on the zero bias of the x-axis gyroscope, …, the significance of the remaining parameters and so on:
s4.2, an accelerometer error model is established as follows:
δf b ＝(δK a +δM a )f b +B a +ε a (5)
in formula (5), δf b Representing a specific force increment output error of the accelerometer; f (f) b An actual specific force delta input representing an accelerometer; b (B) a ＝[B ax B ay B az ] T Representing constant zero offset of the x, y and z axis accelerometers in the IMU; epsilon a ＝[ε ax ε ay ε az ] T Representing the random zero offset of the x, y and z-axis accelerometers in the IMU;
in formula (5), δK a For the scale factor error of the accelerometer, the expression is shown as formula (6), wherein δK ax ,δK ay ,δK az Scale factor errors for x, y, z-axis accelerometers in IMU are shown, respectively:
in formula (5), δM a For accelerometer installation errors, the expression is shown as formula (7), wherein δM axy ,δM axz ,δM ayx ,δM ayz ,δM azx ,δM azy The components of the accelerometer installation error along different directions of the accelerometer sensitive axis are respectively represented:
s5, establishing a Kalman filtering system state equation and an observation equation under continuous time:
s5.1, the state equation of the Kalman filtering system under continuous time is as follows:
in the formula (8), the amino acid sequence of the compound,the differentiation of the 39-dimensional state vector X is that:
in the formula (9), the amino acid sequence of the compound,projection of the attitude errors of the IMU in the east, north and sky directions, delta V E ,δV N ,δV U Speed errors of the IMU in the east, north and sky directions are respectively shown, and delta L, delta lambda and delta h are respectively shown as latitude errors, longitude errors and altitude errors of the IMU;
f is a state transition matrix at continuous time, and its expression is as follows:
wherein 0 is m×n Representing an m multiplied by n dimensional 0 matrix, wherein the rest of the block matrixes are all 3 multiplied by 3 dimensional square matrixes, and the expression is as follows:
wherein,
in the formulae (11) to (29), R M ,R N Respectively the earth meridian,The primary curvature radius of the mortise unitary ring; omega ie Is the rotation angular rate of the earth;respectively projecting the angular velocities of the IMUx, y and z axes in a b system, namely outputting by an x, y and z axis gyroscope; />Representation ofValues of the j-th row and k-th column of the matrix; f (f) E ,f N ,f U Respectively outputting projections of specific force in the east direction, the north direction and the sky direction for an accelerometer in the IMU; f (f) b x ,f b y ,f b z The projections of IMUx, y and z axis specific forces in the b system are respectively, namely the output of the x, y and z axis accelerometers;
in the formula (8), G is an inertial navigation system noise driving matrix, and the expression is:
w (t) is an inertial navigation system noise matrix, and the expression is:
in the formula (31), W gj (t) (j=x, y, z) is zero-mean white noise of the x, y, z axis gyro output in the IMU, W aj (t) (j=x, y, z) is zero-mean white noise output by the x, y, z-axis accelerometer in the IMU; the system noise covariance matrix Q is shown below:
Q＝diag{(Q gx ) 2 (Q gy ) 2 (Q gz ) 2 (Q ax ) 2 (Q ay ) 2 (Q az ) 2 } (32)
in formula (32), diag represents a diagonal matrix，Q gj (j=x, y, z) is zero mean white noise variance of the x, y, z axis gyro output in IMU, Q aj (j=x, y, z) is zero mean white noise variance of the x, y, z axis accelerometer output in the IMU, satisfying the following condition:
wherein E represents the desire;
s5.2, the Kalman filtering observation equation under continuous time is as follows:
Z＝HX+ν(t) (35)
in the formula (35), Z is an observed quantity containing navigation resolving speed error and position error, and the expression is as follows:
Z＝[δV E δV N δV U δL δλ δh] T (36)
in equation (36), since the IMU does not generate linear displacement during the whole calibration process, the velocity (V E ,V N ,V U ) Is the velocity error (delta V) E ,δV N ,δV U ) Navigating the calculated position (L, lambda, h) with the actual position (L 0 ,λ 0 ,h 0 ) The difference is the position error (δl, δλ, δh), namely:
in the formula (35), H is an observation matrix, and the expression is shown as a formula (38), wherein I 3×3 Representing a 3 x 3 dimensional identity matrix:
v (t) is an observation noise matrix, and the expression is:
ν(t)＝[ν E (t) ν N (t) ν U (t) ν L (t) ν λ (t) ν h (t)] T (40)
in formula (40), v E (t),ν N (t),ν U (t) the east, north and sky direction speed observation noise, v L (t),ν λ (t),ν h (t) observed noise at latitude L, longitude λ, and altitude h positions, respectively; the observed noise covariance matrix R is shown below:
R＝diag{(R E ) 2 (R N ) 2 (R U ) 2 (R L ) 2 (R λ ) 2 (R h ) 2 } (41)
in the formula (41), R E ,R N ,R U Observing noise variance for east, north and sky speeds respectively, R L ,R λ ,R h Observed noise variances at latitude, longitude, and altitude, respectively, each satisfying the following conditions:
s6, a discrete Kalman filter system state equation and an observation equation are constructed, and each state parameter is estimated by using the discrete Kalman filter:
s6.1 equivalent discretized form of Kalman filtering system state equation (8) is:
X k ＝Φ k/k-1 X k-1 +G k-1 W k-1 (44)
wherein X is k-1 X is the state quantity at time k-1 k As the state quantity at time k, G k-1 For the system noise driving matrix at time k-1, W k-1 System noise matrix of k-1 time phi k/k-1 For a state one-step transition matrix from time k-1 to time k:
f is a continuous time state transition matrix shown in formula (10), I is an identity matrix with the same dimension as F, and T is a filtering period;
the equivalent discretized form of the Kalman filter observation equation (35) is:
Z k ＝HX k +ν k (46)
wherein Z is k V is the observed quantity at time k k An observation noise matrix at the moment k;
s6.2, constructing a discrete Kalman filter based on the state equation and the observation equation of the discretization system constructed in the S6.1, and estimating the state quantity:
the five basic equations for discrete Kalman filtering are as follows:
state one-step prediction equation:
state one-step prediction mean square error matrix equation:
the filter gain calculation equation: k (K) k ＝P k/k-1 H T (HP k/k-1 H T +R) -1 (49)
State quantity estimation equation:
state estimation mean square error matrix equation:
in the formulae (47) to (51),representing the state quantity X at time k-1 k-1 Is a function of the estimated value of (2); />A one-step predicted value representing a state quantity from a k-1 time to a k time; p (P) k-1 Representing a mean square error matrix corresponding to the state quantity estimation value at the time of k-1; p (P) k/k-1 Representing a mean square error matrix corresponding to the one-step predicted value of the state quantity from the k-1 moment to the k moment; k (K) k The filtering gain is k time; the system noise covariance matrix Q has been defined in equation (32); the observation noise covariance matrix R has been defined in the formula (41);
s7, recording state vector estimation valueThe final value of (2) is used as a calibration result, an IMU output model is established by using the calibration result, and a calculation formula is as follows, wherein +.>Representation->The m-th element of (a):
gyro constant zero bias:
constant zero offset of accelerometer:
gyro scale factor:
accelerometer scale factor:
gyro installation error:
accelerometer mounting error:
first order magnetic field coefficient of gyro:
the calibrated gyro output is shown in formula (59), whereinFor the actual output of the gyro +.>Representing an estimate of the actual input of the gyro, b= [ B ] x B y B z ] T Representing the magnetic field strength component, T, of an external magnetic field in the IMUx, y, z axes IMU Sampling interval for IMU:
the calibrated accelerometer output is shown in equation (60), whereFor the accelerometer to actually output, +.>An estimate representing the actual input of the accelerometer:
in the actual navigation process, the calibrated navigation system is usedAnd->And performing correlation calculation.
2. A method for calibrating systematic errors of a strapdown inertial navigation system taking magnetic field influence into consideration as set forth in claim 1, wherein the method comprises the steps of: s2, when initial alignment is carried out, the initial alignment time length is determined by the specific parameters of the IMU.
3. A method for calibrating systematic errors of a strapdown inertial navigation system taking magnetic field influence into consideration as set forth in claim 1, wherein the method comprises the steps of: and S3, determining the period number of the turntable rotation in the calibration process by the actual error convergence condition.
4. A method for calibrating systematic errors of a strapdown inertial navigation system taking magnetic field influence into consideration as set forth in claim 1, wherein the method comprises the steps of: s6.2 in the formulas (47) - (51), the state quantity X at the time of k-1 is set k-1 Estimate of (2)The initial value is->State quantity estimation at time k-1Corresponding mean square error matrix P k-1 The initial value of (a) is determined by the specific IMU parameters, the value of the system noise covariance matrix is related to the specific IMU parameters, and the value of the observed noise covariance matrix R is related to the specific IMU parameters.
5. A method for calibrating systematic errors of a strapdown inertial navigation system taking magnetic field influence into consideration according to any one of claims 1 to 4, wherein: in order to improve the convergence speed and the calibration precision of the magnetic field coefficient in the calibration process, the initial posture of the IMU can be checked and adjusted before S2, so that an included angle larger than 30 degrees exists between three sensitive axes of the IMU and the eastern direction of the geography.
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