CN108318052B - Hybrid platform inertial navigation system calibration method based on double-shaft continuous rotation - Google Patents

Hybrid platform inertial navigation system calibration method based on double-shaft continuous rotation Download PDF

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CN108318052B
CN108318052B CN201810068573.6A CN201810068573A CN108318052B CN 108318052 B CN108318052 B CN 108318052B CN 201810068573 A CN201810068573 A CN 201810068573A CN 108318052 B CN108318052 B CN 108318052B
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gyroscope
error
navigation
angle
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CN108318052A (en
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刘凯
王蕾
赵启坤
朱志刚
胡镌芮
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Beijing Aerospace Control Instrument Institute
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    • G01—MEASURING; TESTING
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Abstract

The invention discloses a hybrid platform inertial navigation system calibration method based on double-shaft continuous rotation, which comprises the following steps: (1) rough alignment is carried out, and a rough initial attitude matrix is obtained; (2) the outer ring shaft and the platform body shaft of the control platform system rotate at the same angular speed, the inner ring shaft is always in a locked state, and the output of a gyroscope and an accelerometer is collected in the rotating process; (3) solving an error state equation and an observation equation, and calibrating a gyroscope scale factor error, a gyroscope installation error and an accelerometer equivalent zero offset; (4) controlling the outer ring frame angle, the inner ring frame angle and the platform body frame angle to be locked to a zero position state, then locking after rotating the platform body shaft for 180 degrees, and acquiring output data of the gyroscope; (5) controlling the outer ring frame angle, the inner ring frame angle and the platform body frame angle to be locked to a zero position state, then locking after rotating the outer ring shaft for 180 degrees, and acquiring output data of the gyroscope; (6) and calculating the constant drift of the gyroscope. The method effectively shortens the calibration time and improves the calibration efficiency.

Description

Hybrid platform inertial navigation system calibration method based on double-shaft continuous rotation
Technical Field
The invention relates to a calibration method of a hybrid platform inertial navigation system, in particular to a system-level navigation self-calibration method adopting double-shaft continuous rotation, and belongs to the field of inertial navigation system calibration.
Background
Chinese patent publication No. CN 106767806a, published as 31/5/2017, entitled "a physical platform for hybrid inertial navigation system", discloses the definition of a hybrid inertial navigation system, and is a novel inertial navigation system that takes advantages of platform type and strapdown type, and adopts a two-frame three-axis structure, and uses an optical gyroscope and a quartz accelerometer as an inertial sensing element on a stage body. Chinese patent publication No. CN 105973271a, published as 2016, 9, 28, describes a calibration scheme of hybrid inertial navigation system in "a self-calibration method of hybrid inertial navigation system", but the calibration method has the following disadvantages:
(1) part of installation errors and scale factor errors cannot be calibrated through one-time rotation, the scale factor errors and the installation errors of two orthogonal gyroscopes can be calibrated through one-time rotation, calibration of error coefficients of all gyroscopes is realized through multiple positions, and a rotating shaft is required to be in a horizontal plane when the gyroscopes rotate forwards and backwards in the calibration process;
(2) the actually used hybrid inertial navigation is a two-frame three-axis structure, but an inner ring axis is used for avoiding the phenomenon of 'lock losing', a stop nail is used for limiting, the rotation range is-45 degrees, and the three-axis rotation calibration requirement provided in the patent cannot be met;
(3) the required transposition steps are multiple, the calibration time is long, and the position arrangement is complex.
The prior platform type inertial navigation system adopts a force feedback method or a static drifting method for calibration, and the method has the following three defects:
(1) before calibration, self-aiming is needed to obtain the platform body direction of the platform;
(2) the calibration time is longer, the calibration is firstly carried out to a preset position accurately, leveling is carried out after the transposition is finished, data are collected after the leveling is finished, and data are not collected in the transposition process;
(3) and the calibrated error items are less, and error coefficients such as installation errors and scale factor errors cannot be calibrated.
From the above analysis, it can be seen that the hybrid platform inertial navigation system cannot adopt a platform-type calibration method, and cannot adopt a dual-axis strapdown inertial navigation system-level calibration method to realize full-parameter calibration. Therefore, a new calibration method needs to be researched to make up for the defects of the calibration method.
Disclosure of Invention
The technical problem solved by the invention is as follows: the method can accurately and quickly calibrate the errors of the gyroscope and the accelerometer, can solve the problems of incomplete calibration parameters, long calibration time and the like of the gyroscope, improves the calibration efficiency and improves the system precision.
The technical scheme of the invention is as follows: a mixed platform inertial navigation system calibration method based on double-shaft continuous rotation comprises the following steps:
(1) the hybrid platform inertial navigation system is placed still, the outer ring frame angle, the inner ring frame angle and the platform body frame angle are locked to a zero position state and kept, the output of a gyroscope and an accelerometer is collected, and coarse alignment is carried out to obtain a coarse initial attitude matrix;
(2) the outer ring shaft and the platform body shaft of the control platform system rotate at the same angular speed, the inner ring shaft is always in a locked state, and the output of a gyroscope and an accelerometer is collected in the rotating process;
(3) establishing a navigation resolving error model, establishing an error state equation and an observation equation of the hybrid platform inertial navigation system by taking the speed of the carrier in the east, north and sky directions under a navigation coordinate system as observed quantity according to the inertial navigation system error model, resolving the error state equation and the observation equation according to the initial attitude matrix and the output of the gyroscope and the accelerometer acquired in the step (2), and calibrating gyroscope scale factor error, gyroscope installation error and accelerometer equivalent zero bias;
(4) controlling the outer ring frame angle, the inner ring frame angle and the platform body frame angle to be locked in a zero position state, then enabling the platform body shaft to rotate 180 degrees and then be locked, locking the outer ring shaft and the inner ring shaft in the zero position state, and acquiring output data of the gyroscope;
(5) controlling the outer ring frame angle, the inner ring frame angle and the platform body frame angle to be locked in a zero position state, then enabling the outer ring shaft to rotate 180 degrees and then be locked, locking the inner ring shaft and the platform body shaft in the zero position state, and collecting output data of the gyroscope;
(6) and (4) returning to the gyroscope output data in the step (1), the step (4) and the step (5) according to the gyroscope scale factor error and the mounting error calibrated in the step (3), and calculating the gyroscope constant drift.
The inner ring shaft is limited by a stop pin, and the rotatable angle range is-45 degrees to +45 degrees.
In the step (2), the rotation angular velocity of the outer ring shaft and the table body shaft is greater than or equal to 1 degree/s.
The inertial navigation system error model is as follows:
Figure BDA0001557466710000031
wherein phi isnIn order to be an attitude error angle,
Figure BDA0001557466710000032
is the derivative of the attitude error angle,
Figure BDA0001557466710000033
is the projection of the angular velocity of the navigation coordinate system relative to the inertial system under the navigation coordinate system,
Figure BDA0001557466710000034
is the projection of the angular velocity error component of the navigation coordinate system relative to the inertial system under the navigation coordinate system,
Figure BDA0001557466710000035
is a coordinate transformation matrix from the carrier coordinate system to the navigation coordinate system,sfor constant drift of the gyroscope, KgFor the purpose of the gyro scale factor error,
Figure BDA0001557466710000036
in order to prevent the installation error of the gyroscope,
Figure BDA0001557466710000037
is the output of a gyroscope under a coordinate system of a table body, VnIn order to be able to determine the speed error,
Figure BDA0001557466710000038
is the derivative of the speed error; f. ofnFor the accelerometer output in the navigational coordinate system,
Figure BDA0001557466710000039
represents the projection of the angular velocity of the earth rotation in a navigation coordinate system,
Figure BDA00015574667100000310
for the projection of the angular velocity of the navigation coordinate system relative to the terrestrial coordinate system under the navigation coordinate system,
Figure BDA00015574667100000311
the projection of the earth rotation angular velocity error in a navigation coordinate system,
Figure BDA00015574667100000312
projection of the angular velocity error of the navigation coordinate system relative to the terrestrial coordinate system in the navigation coordinate system, VnFor the velocity component in the navigation coordinate system, gnFor the projection of the gravitational acceleration error in the navigation coordinate system, ΔsEquivalent zero offset for the accelerometer;
Figure BDA00015574667100000313
Figure BDA0001557466710000041
in the formula: kgxFor the scale factor error of the gyroscope in the x-direction of the coordinate system of the table body, KgyFor the y-direction gyroscope scale factor error, K, of the coordinate system of the table bodygzFor z-gyro scale factor error, theta, of the gantry coordinate systemgxyIs the installation error angle theta of the gyroscope in the x direction of the table body coordinate system relative to the y axis of the table body coordinate systemgxzIs the installation error angle theta of the gyroscope in the x direction of the table body coordinate system relative to the z axis of the table body coordinate systemgyxIs the installation error angle theta of the gyroscope relative to the x axis of the table coordinate system in the y direction of the table coordinate systemgyzFor the table body coordinate system y-direction gyroscope relative table body coordinate systemMounting error angle of z-axis, thetagzxIs the installation error angle theta of the gyroscope in the z direction of the table body coordinate system relative to the x axis of the table body coordinate systemgzyThe mounting error angle of the gyroscope in the z direction of the table body coordinate system relative to the y axis of the table body coordinate system is shown.
The error state equation of the hybrid platform inertial navigation system is as follows:
Figure BDA0001557466710000042
wherein W (t) is white Gaussian noise of N (0, Q), Q is system noise variance matrix, and
Figure BDA0001557466710000043
ωφE、ωφN、ωφUrespectively measuring noise by the gyroscope in the lower east direction, the north direction and the sky direction of the navigation coordinate system,
Figure BDA0001557466710000044
measuring noise of accelerometers in the east, north and sky directions of a navigation coordinate system respectively;
x is a state quantity, and:
Figure BDA0001557466710000045
in the formula, phiEIs the east misalignment angle phiNIs the north misalignment angle phiUAngle of vertical misalignment, Δ VEFor east velocity error, Δ VNFor north velocity error, Δ VUIn order to be an error in the speed in the direction of the day,
Figure BDA0001557466710000046
outputting equivalent zero offset to the accelerometer for the table body coordinate system x,
Figure BDA0001557466710000047
outputting equivalent zero offset to the accelerometer for the y direction of the table body coordinate system,
Figure BDA0001557466710000048
outputting equivalent zero offset for the z-direction accelerometer of the table body coordinate system;
Figure BDA0001557466710000051
in the formula (I), the compound is shown in the specification,
Figure BDA0001557466710000052
is a coordinate transformation matrix from a table coordinate system to a carrier coordinate system,
Figure BDA0001557466710000053
an initial state transition matrix between a carrier coordinate system and a navigation coordinate system;
Figure BDA0001557466710000054
in the formula: omegaieThe rotational angular velocity of the earth; l is the local geographical latitude;
Figure BDA0001557466710000055
in the formula, RMRadius of curvature, R, of the earth's meridianNThe curvature radius of the earth-unitary mortise is shown, and h is the height of the carrier relative to the local horizontal plane;
Figure BDA0001557466710000056
in the formula, thetaxIs the outer ring frame angle output, θzIs the output of the angle of the frame of the table body,
Figure BDA0001557466710000057
for the angular velocity of the outer ring frame,
Figure BDA0001557466710000058
the angular velocity of the frame of the table body;
Figure BDA0001557466710000059
wherein g is the local gravitational acceleration;
Figure BDA0001557466710000061
the measurement equation is as follows:
Z＝HX+V
Z＝[VEVNVU]T
wherein H is [0 ]3×3I3×303×12]V is system measurement noise, is Gaussian white noise process of N (0, R), R array is measurement noise variance array, VEFor projection of the velocity calculated from the inertial device in the geographical east direction, VNFor projection of the velocity calculated from the inertial device in the geographic north, VUIs the projection of the velocity calculated by the inertial device in the direction of the sky.
The specific calculation method of the gyroscope constant drift comprises the following steps:
Figure BDA0001557466710000062
Figure BDA0001557466710000063
Figure BDA0001557466710000064
in the formula (I), the compound is shown in the specification,
Figure BDA0001557466710000065
is the gyroscope output of step (2)
Figure BDA0001557466710000066
Figure BDA0001557466710000067
Is the gyroscope output of step (4)
Figure BDA0001557466710000068
Is the gyroscope output of step (5)
Figure BDA0001557466710000069
Gyroscope output of step (1)
Figure BDA00015574667100000610
Gyroscope output of step (4)
Figure BDA00015574667100000611
And the gyroscope output of step (5)
Figure BDA00015574667100000612
Taking the average value in a preset period of time.
Compared with the prior art, the invention has the following advantages:
(1) according to the invention, all error parameters of the gyroscope and the accelerometer are excited through continuous rotation of the double shafts, the installation errors and scale factor errors of the gyroscope and the accelerometer can be completely calibrated through one-time rotation, compared with the calibration method of the traditional platform type inertial navigation system and the strap-down type inertial navigation system, the calibration time can be saved, the required transposition steps are few, the position arrangement is relatively simple, one-time rapid error coefficient calibration can be realized before the weapon system is launched, and the correction efficiency is greatly improved.
(2) The indexing mechanism has simple requirements on the indexing mechanism, can run fully automatically according to the design of a preset scheme, does not need to add too much manual participation, can correct error parameters of acquired data according to a program, has clear and simple theory and is easy to realize programming.
Drawings
FIG. 1 is a flow chart of an implementation of a calibration method of a hybrid platform inertial navigation system according to the present invention;
FIG. 2 is a graph of the output of a gyroscope during rotation in accordance with an embodiment of the present invention;
FIG. 3 is a graph of the output of an accelerometer during rotation according to an embodiment of the invention;
FIG. 4(a) is a diagram illustrating an east misalignment angle estimation error during calibration according to an embodiment of the present invention;
FIG. 4(b) is a block diagram illustrating an error in estimating the north misalignment angle during calibration according to an embodiment of the present invention;
FIG. 4(c) is a diagram illustrating an estimation error of a misalignment angle during calibration according to an embodiment of the present invention;
FIG. 4(d) is an east-direction velocity estimation error during calibration according to an embodiment of the present invention;
FIG. 4(e) is a diagram illustrating the estimation error of the north velocity during the calibration process according to the embodiment of the present invention;
FIG. 4(f) is a diagram illustrating an estimation error of the speed in the sky during the calibration process according to the embodiment of the present invention;
FIG. 5(a) is a diagram illustrating an x-gyroscope scale factor estimation error in a stage coordinate system during calibration according to an embodiment of the present invention;
FIG. 5(b) is a diagram illustrating the y-gyroscope scale factor estimation error in the stage coordinate system during calibration according to an embodiment of the present invention;
FIG. 5(c) is a diagram illustrating an error in estimating a scale factor of a z-gyroscope in a stage coordinate system during calibration according to an embodiment of the present invention;
FIG. 5(d) is a diagram illustrating an error in estimating an installation error of an x-gyroscope around a y-axis in a stage coordinate system during calibration according to an embodiment of the present invention;
FIG. 5(e) is a diagram illustrating an error in estimating an installation error of an x-gyroscope around a z-axis in a stage coordinate system during calibration according to an embodiment of the present invention;
FIG. 5(f) is a diagram illustrating an error in estimating a mounting error of a y-gyroscope around an x-axis in a stage coordinate system during calibration according to an embodiment of the present invention;
FIG. 5(g) is a diagram illustrating an error in estimating a mounting error of a y-gyroscope around a z-axis in a stage coordinate system during calibration according to an embodiment of the present invention;
FIG. 5(h) is a diagram illustrating an error in estimating a mounting error of a z-gyroscope around a y-axis in a stage coordinate system during calibration according to an embodiment of the present invention;
FIG. 5(i) shows an error in estimating an installation error of a z-gyroscope around an x-axis in a stage coordinate system during calibration according to an embodiment of the present invention;
FIG. 6(a) shows an error of zero offset estimation of an x-accelerometer in a stage coordinate system during calibration according to an embodiment of the present invention;
FIG. 6(b) is a diagram illustrating a zero offset estimation error of a y accelerometer in a stage coordinate system during calibration according to an embodiment of the present invention;
FIG. 6(c) is a diagram illustrating a zero offset estimation error of a z accelerometer in a stage coordinate system during calibration according to an embodiment of the present invention;
FIG. 7 is a comparison curve of latitude change of navigation solution before and after error compensation in the calibration process according to the embodiment of the present invention;
FIG. 8 is a comparison graph of longitude variation of navigation solutions before and after error compensation during calibration according to an embodiment of the present invention;
FIG. 9 is a comparison curve of the course angle variation of the navigation solution before and after the error compensation in the calibration process according to the embodiment of the present invention.
Detailed Description
The invention is described in detail below with reference to the figures and specific examples.
The hybrid platform inertial navigation system generally adopts a two-frame three-axis structure and comprises a gyroscope, an accelerometer, an outer ring frame, an inner ring frame and a platform body; the gyroscope and the accelerometer are arranged on the platform body, the outer ring frame, the inner ring frame and the platform body can respectively rotate around an outer ring shaft, an inner ring shaft and the platform body shaft, single-degree-of-freedom rotation in three directions of pitching, rolling and yawing is respectively realized, in order to prevent the generation of a locking effect, the inner ring shaft is limited by a stop pin, and the rotatable angle range is-45 degrees- +45 degrees.
The invention provides a calibration method of a hybrid platform inertial navigation system, which utilizes the advantages of the hybrid platform inertial navigation system, a motor drives a ring frame to rotate to provide certain angular velocity excitation for a gyroscope on a platform body, and all error coefficients of 3 axial gyroscopes can be excited through the simultaneous rotation of an outer ring shaft and a platform shaft, so that a calibration result is achieved. The method has the advantages of short calibration time, simple and clear thought, easy realization in engineering and the like, can realize the whole calibration of the error parameters of the gyroscope through one-time rotation, improves the calibration efficiency and saves the calibration time.
As shown in FIG. 1, the calibration process of the present invention is as follows:
(1) placing the hybrid platform inertial navigation system on a marble flat plate, electrifying and heating to stabilize the internal temperature field of the inertial device, locking the outer ring frame angle, the inner ring frame angle and the platform body frame angle to a zero position state and keeping the zero position state after reaching a stable temperature point, collecting the output of a gyroscope and an accelerometer, and performing coarse alignment to obtain a coarse initial attitude matrix, namely the relationship between a platform body coordinate system where the inertial device is located and a navigation system;
when the frame stops rotating and is in a static state, the output of the gyroscope is the local ground speed, namely the rotational angular velocity of the earth: wherein, the value is a gyroscope equivalent constant value zero offset. Let the position at this time be s1The gyroscope output at this position is therefore:
Figure BDA0001557466710000094
the carrier coordinate system (system b) is fixedly connected with a hybrid platform inertial navigation system base system (system bm), and the carrier coordinate system and the platform base system are in rigid connection, namely the coordinate conversion relation between the system b and the system bm is fixed.
OX of outer ring shaft and base system of hybrid platform inertial navigation systembInner ring axis OY of hybrid platform inertial navigation system with fixedly-connected shaftsInner partOY of shaft and outer ring shaftOuter coverPlatform body axis OZ of hybrid platform inertial navigation system with fixedly-connected axisTable (Ref. Table)OZ of axis and inner ring axisInner partThe shaft is fixedly connected.
Under the condition of not considering the shafting installation error, according to the relation, when the frame angles of the three axes of the platform are all zero, the carrier coordinate system (system b) is superposed with the platform coordinate system (system s) of the hybrid platform inertial navigation system. When any frame angle in the three shaft frame angles is not zero, the coordinate conversion matrix from the carrier coordinate system (system b) to the platform coordinate system (system s)
Figure BDA0001557466710000101
Comprises the following steps:
Figure BDA0001557466710000102
wherein, thetax、θyAnd thetazRespectively an outer ring frame angle, an inner ring frame angle and a platform body frameAn angle; cx (theta)x) Representing rotation theta of the outer ring frame about the x-axis of the outer ring axis of the platformxConversion matrix between the outer annular coordinate system and the base coordinate system after each angle, Cy (theta)y) Showing the rotation theta of the inner ring frame around the y-axis of the inner ring of the platformyTransformation matrix between inner and outer annular coordinate systems after an angle, Cz (theta)z) Representing a rotation theta of the stage body about the z-axis of the stage body axiszAnd a transformation matrix between the angle background body coordinate system and the inner ring coordinate system.
The navigation coordinate system n adopts a northeast coordinate system, and an initial state transition matrix between the stage body coordinate system s system and the navigation coordinate system n system can be obtained by analytic coarse alignment under the state
Figure BDA0001557466710000103
The method specifically comprises the following steps:
Figure BDA0001557466710000104
from the above formula, one can obtain:
Figure BDA0001557466710000105
wherein, gnRepresenting the projection of the local gravity values in the navigation coordinate system, gn＝[0 0 -g]T；
Figure BDA0001557466710000106
Represents the projection of the angular velocity of the earth rotation in a navigation coordinate system,
Figure BDA0001557466710000111
l represents the local geographic latitude; f. ofsAnd ωsRespectively representing accelerometer output and angular velocity output in a table coordinate system.
Due to the coarse alignment, the hybrid platform system is in a zero-locking state, namely: the frame angles of the three axes of the platform are all zero, at the moment, a carrier coordinate system (system b) is coincident with a platform coordinate system s of the hybrid platform inertial navigation system, and the carrier coordinate system and the navigation coordinate system are in parallel connectionInitial state transition matrix between
Figure BDA0001557466710000119
And
Figure BDA00015574667100001110
are equal.
(2) The outer ring shaft and the platform body shaft of the control platform system rotate at the same angular speed, the inner ring shaft is always in a locked state, and the output of a gyroscope and an accelerometer is collected in the rotating process;
this step can obtain the ideal output of the gyroscope at this time, specifically:
according to the constraint relation between the shafting definition and the frame in the step (1), the derivation process is omitted, and the angular speed of the platform body of the platform can be obtained
Figure BDA0001557466710000112
And angular velocity of table body base
Figure BDA0001557466710000113
And frame angular velocity
Figure BDA0001557466710000114
The relationship between them is:
Figure BDA0001557466710000115
because the inner ring is locked in the zero position state theta y0, i.e. no change in inner ring frame angle
Figure BDA0001557466710000116
The outer ring shaft and the platform body shaft of the hybrid platform inertial navigation system rotate at a certain angular speed at the same time, and the angular speed output of a platform body coordinate system is changed into:
Figure BDA0001557466710000117
from the above formula, the angular velocity projection of the table coordinate system relative to the table base system can be obtained
Figure BDA0001557466710000118
(3) Establishing a navigation resolving error model, establishing an error state equation and an observation equation of the hybrid platform inertial navigation system by taking the speed of the carrier in the east, north and sky directions under a navigation coordinate system as observed quantity according to the inertial navigation system error model, resolving the error state equation and the observation equation according to the initial attitude matrix and the output of the gyroscope and the accelerometer acquired in the step (2), and calibrating gyroscope scale factor error, gyroscope installation error and accelerometer equivalent zero bias;
the inertial navigation system error model is as follows:
Figure BDA0001557466710000121
wherein phi isnIn order to be an attitude error angle,
Figure BDA0001557466710000122
is the derivative of the attitude error angle,
Figure BDA0001557466710000123
is the projection of the angular velocity of the navigation coordinate system relative to the inertial system under the navigation coordinate system,
Figure BDA0001557466710000124
is the projection of the angular velocity error component of the navigation coordinate system relative to the inertial system under the navigation coordinate system,
Figure BDA0001557466710000125
is a coordinate transformation matrix from the carrier coordinate system to the navigation coordinate system,sfor constant drift of the gyroscope, KgFor the purpose of the gyro scale factor error,
Figure BDA0001557466710000126
in order to prevent the installation error of the gyroscope,
Figure BDA0001557466710000127
as coordinates of table bodyIs the output of a gyroscope, VnIn order to be able to determine the speed error,
Figure BDA0001557466710000128
is the derivative of the speed error; f. ofnFor the accelerometer output in the navigational coordinate system,
Figure BDA0001557466710000129
represents the projection of the angular velocity of the earth rotation in a navigation coordinate system,
Figure BDA00015574667100001210
for the projection of the angular velocity of the navigation coordinate system relative to the terrestrial coordinate system under the navigation coordinate system,
Figure BDA00015574667100001211
the projection of the earth rotation angular velocity error in a navigation coordinate system,
Figure BDA00015574667100001212
the projection of the angular velocity error of the navigation coordinate system relative to the earth coordinate system in the navigation coordinate system is VnFor the velocity component in the navigation coordinate system, gnFor the projection of the gravitational acceleration error in the navigation coordinate system, ΔsEquivalent zero offset for the accelerometer;
Figure BDA00015574667100001213
Figure BDA00015574667100001214
in the formula: kgxFor the scale factor error of the gyroscope in the x-direction of the coordinate system of the table body, KgyFor the y-direction gyroscope scale factor error, K, of the coordinate system of the table bodygzFor z-gyro scale factor error, theta, of the gantry coordinate systemgxyIs the installation error angle theta of the gyroscope in the x direction of the table body coordinate system relative to the y axis of the table body coordinate systemgxzIs the installation error angle theta of the gyroscope in the x direction of the table body coordinate system relative to the z axis of the table body coordinate systemgyxIs a table bodyInstallation error angle theta of gyroscope in y direction of coordinate system relative to x axis of table coordinate systemgyzIs the installation error angle theta of the gyroscope relative to the z axis of the table body coordinate system in the y direction of the table body coordinate systemgzxIs the installation error angle theta of the gyroscope in the z direction of the table body coordinate system relative to the x axis of the table body coordinate systemgzyThe mounting error angle of the gyroscope in the z direction of the table body coordinate system relative to the y axis of the table body coordinate system is shown.
Due to the fact that
Figure BDA0001557466710000131
When the two shafts rotate simultaneously and the rotation angular velocity is much greater than the ground velocity, i.e. when
Figure BDA0001557466710000132
When the rotation angular velocity is larger than or equal to 1 degree/s, the equivalent zero offset of the gyroscope can be simplified as follows:
Figure BDA0001557466710000133
in the above formula, matrix
Figure BDA00015574667100001310
、
Figure BDA00015574667100001311
May be derived from the initial alignment and frame angle outputs respectively,
Figure BDA0001557466710000134
and
Figure BDA0001557466710000135
the method can be respectively obtained through output difference of an outer ring frame angle and a platform body frame angle, zero drift of a gyroscope, scale factor errors and installation errors are unknown variables, and according to an error model of the hybrid inertial navigation system, an 18-dimensional error state equation of the hybrid platform inertial navigation system can be obtained as follows:
Figure BDA0001557466710000136
wherein W (t) is white Gaussian noise of N (0, Q), and
Figure BDA0001557466710000137
ωφE、ωφN、ωφUrespectively measuring noise by the gyroscope in the lower east direction, the north direction and the sky direction of the navigation coordinate system,
Figure BDA0001557466710000138
and respectively measuring noise of the accelerometers in the east, north and sky directions under the navigation coordinate system.
X is a state quantity, and:
Figure BDA0001557466710000139
in the formula, phiEIs the east misalignment angle phiNIs the north misalignment angle phiUAngle of vertical misalignment, Δ VEFor east velocity error, Δ VNFor north velocity error, Δ VUIn order to be an error in the speed in the direction of the day,
Figure BDA0001557466710000147
outputting equivalent zero offset to the accelerometer for the table body coordinate system x,
Figure BDA0001557466710000148
outputting equivalent zero offset to the accelerometer for the y direction of the table body coordinate system,
Figure BDA0001557466710000149
outputting equivalent zero offset for the z-direction accelerometer of the table body coordinate system;
Figure BDA0001557466710000141
in the formula (I), the compound is shown in the specification,
Figure BDA0001557466710000142
is a coordinate transformation matrix from a table coordinate system to a carrier coordinate system,
Figure BDA0001557466710000143
an initial state transition matrix between a carrier coordinate system and a navigation coordinate system;
Figure BDA0001557466710000144
in the formula: omegaieThe rotational angular velocity of the earth; l is the local geographical latitude;
Figure BDA0001557466710000145
in the formula, RMRadius of curvature, R, of the earth's meridianNThe curvature radius of the earth-unitary fourth of twelve earthly branches, h is the height of the carrier relative to the local horizontal plane
Figure BDA0001557466710000146
In the formula, thetazIs the inner ring frame angle, θxIs the outer ring frame angle, thetazIs a corner of a frame of the table body,
Figure BDA0001557466710000151
the angular velocity of the outer ring frame can be obtained by outputting difference through the angle of the outer ring frame;
Figure BDA0001557466710000152
the angular velocity of the table body frame can be obtained by outputting difference through the table body frame angle.
Figure BDA0001557466710000153
Wherein g is the local gravitational acceleration.
Figure BDA0001557466710000154
In the process of rotary calibration, the base is in a static state
Figure BDA0001557466710000155
And the inner ring shaft is in a locking state, and the attitude transfer matrix from the table body coordinate system to the base system can be obtained by reading the values of the outer ring frame angle and the table body frame angle
Figure BDA0001557466710000156
And
Figure BDA0001557466710000157
the rotation angular velocities of the outer ring shaft and the table body shaft are preset respectively;
Figure BDA0001557466710000158
can be obtained by analytic coarse alignment in step (1).
Because the hybrid inertial navigation system is under the condition of a static base, the speed solved by the inertial device is caused by various errors, and the observed quantity can select the speed component under the navigation coordinate system.
Thus, the measurement equation is:
Z＝HX+V
Z＝[VEVNVU]T
wherein H is [0 ]3×3I3×303×12]V is the system measurement noise, is the Gaussian white noise process of N (0, R), VEFor projection of the velocity calculated from the inertial device in the geographical east direction, VNFor projection of the velocity calculated from the inertial device in the geographic north, VUIs the projection of the velocity calculated by the inertial device in the direction of the sky.
After the initial value of the filter is set, error parameters needing to be calibrated can be obtained by adopting Kalman filtering.
(4) Controlling the outer ring frame angle, the inner ring frame angle and the platform body frame angle to be locked in a zero position state, enabling the platform body shaft to rotate forwards by 180 degrees according to a right hand rule and then be locked, locking the outer ring shaft and the inner ring shaft in the zero position state, and acquiring output data of the gyroscope;
setting the current position as s2Relative to s1The position is rotated 180 about the z-axis. In thatThe position gyroscope output is
Figure BDA0001557466710000161
(5) Controlling the outer ring frame angle, the inner ring frame angle and the platform body frame angle to be locked in a zero position state, enabling the outer ring shaft to rotate forwards by 180 degrees according to a right-hand rule, then locking, locking the inner ring shaft and the platform body shaft in the zero position state, and acquiring output data of the gyroscope;
setting the current position as s3Relative to s1The position is rotated 180 about the x-axis. The gyroscope output is
Figure BDA0001557466710000162
(6) And (4) returning to the gyroscope output data in the step (1), the step (4) and the step (5) according to the gyroscope scale factor error and the mounting error calibrated in the step (3), and calculating the gyroscope constant drift.
The specific calculation method of the gyroscope constant drift comprises the following steps:
Figure BDA0001557466710000163
Figure BDA00015574667100001613
Figure BDA0001557466710000164
in the formula (I), the compound is shown in the specification,
Figure BDA0001557466710000165
is the gyroscope output of step (2)
Figure BDA0001557466710000166
Figure BDA0001557466710000167
Gyroscope output of step (4)
Figure BDA0001557466710000168
Is the gyroscope output of step (5)
Figure BDA0001557466710000169
Gyroscope output of step (1)
Figure BDA00015574667100001610
Gyroscope output of step (4)
Figure BDA00015574667100001611
And the gyroscope output of step (5)
Figure BDA00015574667100001612
Taking the average value within a preset period of time (such as 10min and above).
The calibration work of the hybrid platform inertial navigation system can be completed through the method.
Example (b):
in the calibration of the primary mixed platform inertial navigation system, the constant drift of the gyroscope is set to be 0.02 degree/h, the random drift is set to be 0.02 degree/h, the constant zero offset of the accelerometer is set to be 100 mu g, the random offset is set to be 50 mu g, and the error of the scale factor of the gyroscope is set to be
Figure BDA0001557466710000171
(unit: ppm) and the mounting error of each axis is
Figure BDA0001557466710000172
(unit: angular division). The geographic latitude is 33.912 °, the geographic longitude is 0 °, and the initial attitude angle is (0 °, 0 °, 30 °).
Setting a filtering initial condition, wherein the initial value X (0) of the state vector X is 0, the initial estimation mean square error array P (0), the system noise array Q and the measurement noise array R are respectively as follows:
P(0)＝diag[(0.1°)2(0.1°)2(0.1°)2(0.1m/s)2(0.1m/s)2(0.1m/s)2(0.01)2(0.01)2(0.01)2(20”)2(20”)2(20”)2(20”)2(20”)2(20”)2(100μg)2(100μg)2(100μg
Q＝[(0.02°/h)2(0.02°)2(0.02°)2(50μg)2(50μg)2(50μg)2012×1]
R＝diag[(0.1)2(0.1)2(0.1)2]
the transposition scheme adopts the steps, the rotation angular speed of the outer ring and the table body is 6 degrees/s, and the transposition time is 10 minutes. Fig. 2 shows the output of the gyroscope during the two-axis rotation, which can be derived as follows:
Figure BDA0001557466710000173
fig. 3 shows the output of the accelerometer during the two-axis rotation, which is known from the derivation:
Figure BDA0001557466710000174
fig. 4(a) -4 (f) show three directional misalignment angles and the east, north and sky speed estimation errors estimated by filtering. Fig. 5(a) to 5(i) show the estimated errors of 3 scale factor errors and 6 mounting errors of the filtered estimated gyroscope. Fig. 6(a) -6 (c) show the estimated accelerometer zero offset estimation error. FIG. 7 is a latitude versus altitude plot of navigation solutions before and after error compensation. FIG. 8 is a graph of longitude variation versus navigation solution before and after error compensation. FIG. 9 is a comparison of course angle changes for navigation before and after error compensation.
As can be seen from FIGS. 5(a) -5 (i) and 6(a) -6 (c), the calibration method is proved to be effective by the convergence of the scale factor error and the installation error estimation result of the gyroscope and the equivalent zero offset estimation error of the accelerometer through Kalman filtering estimation, the scale factor estimation precision of the gyroscope reaches 25ppm, the installation error angle estimation precision reaches 1.5 arc seconds, and as can be seen from FIGS. 6(a) -6 (c), the equivalent zero offset estimation precision of the accelerometer can reach 4 × 10-5g. Under the condition of a static base, the output of an inertial device is collected for a certain time, and the calibration method mentioned herein is utilized to compensate and compensate the error termAnd performing navigation calculation after compensation, and outputting uncompensated inertial devices for navigation calculation, wherein the latitude calculation difference, longitude calculation difference and azimuth calculation difference before and after compensation are respectively displayed in the images of fig. 7, 8 and 9. As can be seen from the figure, the output of the uncompensated inertia device has larger deviation of the calculation result due to the accumulation of errors, the variation of the calculation result after compensation is obviously better than that of the uncompensated calculation result, and the variation is obviously slowed down, so that the errors of the inertia device are accurately calibrated after the method is applied.
The present invention has not been described in detail as is known to those skilled in the art.

Claims (8)

1. A hybrid platform inertial navigation system calibration method based on biaxial continuous rotation is characterized by comprising the following steps:
(1) the hybrid platform inertial navigation system is placed still, the outer ring frame angle, the inner ring frame angle and the platform body frame angle are locked to a zero position state and kept, the output of a gyroscope and an accelerometer is collected, and coarse alignment is carried out to obtain a coarse initial attitude matrix;
(2) controlling an outer ring shaft and a platform body shaft of the hybrid platform inertial navigation system to rotate at the same angular speed, keeping an inner ring shaft in a locked state all the time, and collecting the output of a gyroscope and an accelerometer in the rotating process;
(3) establishing a navigation resolving error model, establishing an error state equation and an observation equation of the hybrid platform inertial navigation system by taking the speed of the carrier in the east, north and sky directions under a navigation coordinate system as observed quantity according to the inertial navigation system error model, resolving the error state equation and the observation equation according to the initial attitude matrix and the output of the gyroscope and the accelerometer acquired in the step (2), and calibrating gyroscope scale factor error, gyroscope installation error and accelerometer equivalent zero bias;
(4) controlling the outer ring frame angle, the inner ring frame angle and the platform body frame angle to be locked in a zero position state, then enabling the platform body shaft to rotate 180 degrees and then be locked, locking the outer ring shaft and the inner ring shaft in the zero position state, and acquiring output data of the gyroscope;
(5) controlling the outer ring frame angle, the inner ring frame angle and the platform body frame angle to be locked in a zero position state, then enabling the outer ring shaft to rotate 180 degrees and then be locked, locking the inner ring shaft and the platform body shaft in the zero position state, and collecting output data of the gyroscope;
(6) and (4) returning to the gyroscope output data in the step (1), the step (4) and the step (5) according to the gyroscope scale factor error and the mounting error calibrated in the step (3), and calculating the gyroscope constant drift.
2. The method for calibrating a hybrid platform inertial navigation system based on biaxial continuous rotation as claimed in claim 1, wherein: the inner ring shaft is limited by a stop pin, and the rotatable angle range is-45 degrees to +45 degrees.
3. The method for calibrating a hybrid platform inertial navigation system based on biaxial continuous rotation as claimed in claim 1, wherein: in the step (2), the rotation angular velocity of the outer ring shaft and the table body shaft is greater than or equal to 1 degree/s.
4. The method for calibrating a hybrid platform inertial navigation system based on biaxial continuous rotation of claim 1, wherein the inertial navigation system error model is:
Figure FDA0002500624580000021
Figure FDA0002500624580000022
wherein phi isnIn order to be an attitude error angle,
Figure FDA0002500624580000023
is the derivative of the attitude error angle,
Figure FDA0002500624580000024
is the projection of the angular velocity of the navigation coordinate system relative to the inertial system under the navigation coordinate system,
Figure FDA0002500624580000025
is the projection of the angular velocity error component of the navigation coordinate system relative to the inertial system under the navigation coordinate system,
Figure FDA0002500624580000026
is a coordinate transformation matrix from the carrier coordinate system to the navigation coordinate system,sfor constant drift of the gyroscope, KgFor the purpose of the gyro scale factor error,
Figure FDA0002500624580000027
in order to prevent the installation error of the gyroscope,
Figure FDA0002500624580000028
is the output of a gyroscope under a coordinate system of a table body, VnIn order to be able to determine the speed error,
Figure FDA0002500624580000029
is the derivative of the speed error; f. ofnFor the accelerometer output in the navigational coordinate system,
Figure FDA00025006245800000210
represents the projection of the angular velocity of the earth rotation in a navigation coordinate system,
Figure FDA00025006245800000211
for the projection of the angular velocity of the navigation coordinate system relative to the terrestrial coordinate system under the navigation coordinate system,
Figure FDA00025006245800000212
the projection of the earth rotation angular velocity error in a navigation coordinate system,
Figure FDA00025006245800000213
projection of the angular velocity error of the navigation coordinate system relative to the terrestrial coordinate system in the navigation coordinate system, VnFor the velocity component in the navigation coordinate system, gnFor the projection of the gravitational acceleration error in the navigation coordinate system, ΔsEquivalent zero offset for the accelerometer;
Figure FDA00025006245800000214
Figure FDA00025006245800000215
in the formula: kgxFor the scale factor error of the gyroscope in the x-direction of the coordinate system of the table body, KgyFor the y-direction gyroscope scale factor error, K, of the coordinate system of the table bodygzFor z-gyro scale factor error, theta, of the gantry coordinate systemgxyIs the installation error angle theta of the gyroscope in the x direction of the table body coordinate system relative to the y axis of the table body coordinate systemgxzIs the installation error angle theta of the gyroscope in the x direction of the table body coordinate system relative to the z axis of the table body coordinate systemgyxIs the installation error angle theta of the gyroscope relative to the x axis of the table coordinate system in the y direction of the table coordinate systemgyzIs the installation error angle theta of the gyroscope relative to the z axis of the table body coordinate system in the y direction of the table body coordinate systemgzxIs the installation error angle theta of the gyroscope in the z direction of the table body coordinate system relative to the x axis of the table body coordinate systemgzyThe mounting error angle of the gyroscope in the z direction of the table body coordinate system relative to the y axis of the table body coordinate system is shown.
5. The method for calibrating a hybrid platform inertial navigation system based on biaxial continuous rotation of claim 4, wherein the error state equation of the hybrid platform inertial navigation system is as follows:
Figure FDA0002500624580000031
wherein W is white Gaussian noise of N (0, Q), Q is system noise variance matrix, and
Figure FDA0002500624580000032
Figure FDA0002500624580000033
respectively measuring noise by the gyroscope in the lower east direction, the north direction and the sky direction of the navigation coordinate system,
Figure FDA0002500624580000034
measuring noise of accelerometers in the east, north and sky directions of a navigation coordinate system respectively;
x is a state quantity, and:
Figure FDA0002500624580000035
in the formula, phiEIs the east misalignment angle phiNIs the north misalignment angle phiUAngle of vertical misalignment, Δ VEFor east velocity error, Δ VNFor north velocity error, Δ VUIn order to be an error in the speed in the direction of the day,
Figure FDA0002500624580000036
outputting equivalent zero offset to the accelerometer for the table body coordinate system x,
Figure FDA0002500624580000037
outputting equivalent zero offset to the accelerometer for the y direction of the table body coordinate system,
Figure FDA0002500624580000038
outputting equivalent zero offset for the z-direction accelerometer of the table body coordinate system;
Figure FDA0002500624580000041
in the formula (I), the compound is shown in the specification,
Figure FDA0002500624580000042
is a coordinate transformation matrix from a table coordinate system to a carrier coordinate system,
Figure FDA0002500624580000043
as a carrier coordinate system and guideAn initial state transition matrix between the navigation coordinate systems;
Figure FDA0002500624580000044
in the formula: omegaieThe rotational angular velocity of the earth; l is the local geographical latitude;
Figure FDA0002500624580000045
in the formula, RMRadius of curvature, R, of the earth's meridianNThe curvature radius of the earth-unitary mortise is shown, and h is the height of the carrier relative to the local horizontal plane;
Figure FDA0002500624580000046
in the formula, thetaxIs the outer ring frame angle output, θzIs the output of the angle of the frame of the table body,
Figure FDA0002500624580000047
for the angular velocity of the outer ring frame,
Figure FDA0002500624580000048
the angular velocity of the frame of the table body;
Figure FDA0002500624580000049
wherein g is the local gravitational acceleration;
Figure FDA0002500624580000051
6. the method for calibrating a hybrid platform inertial navigation system based on biaxial continuous rotation as claimed in claim 5, wherein the observation equation is:
Z＝HX+V
Z＝[VEVNVU]T
wherein H is [0 ]3×3I3×303×12]V is system measurement noise, is Gaussian white noise process of N (0, R), R array is measurement noise variance array, VEFor projection of the velocity calculated from the inertial device in the geographical east direction, VNFor projection of the velocity calculated from the inertial device in the geographic north, VUIs the projection of the velocity calculated by the inertial device in the direction of the sky.
7. The method for calibrating a hybrid platform inertial navigation system based on biaxial continuous rotation as claimed in claim 1, wherein: the specific calculation method of the gyroscope constant drift comprises the following steps:
Figure FDA0002500624580000052
Figure FDA0002500624580000053
Figure FDA0002500624580000054
in the formula (I), the compound is shown in the specification,
Figure FDA0002500624580000055
is the gyroscope output of step (2)
Figure FDA0002500624580000056
Figure FDA0002500624580000057
Is the gyroscope output of step (4)
Figure FDA0002500624580000058
Figure FDA0002500624580000059
Is the gyroscope output of step (5)
Figure FDA00025006245800000510
8. The method for calibrating a hybrid platform inertial navigation system based on biaxial continuous rotation as claimed in claim 1, wherein: gyroscope output of step (1)
Figure FDA00025006245800000511
Gyroscope output of step (4)
Figure FDA0002500624580000061
And the gyroscope output of step (5)
Figure FDA0002500624580000062
Taking the average value in a preset period of time.
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