CN112798014A - Inertial navigation self-alignment method for compensating vertical line deviation based on gravitational field spherical harmonic model - Google Patents

Inertial navigation self-alignment method for compensating vertical line deviation based on gravitational field spherical harmonic model Download PDF

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CN112798014A
CN112798014A CN202011110959.2A CN202011110959A CN112798014A CN 112798014 A CN112798014 A CN 112798014A CN 202011110959 A CN202011110959 A CN 202011110959A CN 112798014 A CN112798014 A CN 112798014A
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gravity
coordinate system
carrier
alignment
vector
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张志利
周召发
郝诗文
冯磊
赵军阳
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Rocket Force University of Engineering of PLA
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • 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

Abstract

The invention relates to an inertial navigation self-alignment method for compensating vertical line deviation based on a gravitational field spherical harmonic model, which is characterized by comprising the following steps of: the method comprises the following steps of directly calculating the component of the gravity disturbance value of an alignment point by using a high-precision gravity field spherical harmonic model, and projecting the component to a navigation coordinate system by using a quaternion method for compensation, and specifically comprises the following steps: calibrating before starting, and estimating constant drift of a gyro and constant zero offset of an accelerometer; calculating a normal gravity vector of the initial alignment point through a normal gravity model; obtaining the projection of a real gravity vector under an n system after compensating the gravity disturbance; after rotating the angle theta around the rotating shaft u, obtaining a real gravity disturbance vector under a navigation coordinate system n'; solving a true gravity vector after the deviation compensation of the vertical line; obtaining a rough estimation value of a carrier attitude matrix; the compensated real gravity vector is used for fine alignment based on Kalman filtering, and finally the astronomical azimuth angle of the carrier is obtained, so that the alignment performance is improved.

Description

Inertial navigation self-alignment method for compensating vertical line deviation based on gravitational field spherical harmonic model
Technical Field
The invention belongs to the technical field of inertial navigation, and relates to an inertial navigation self-alignment method for compensating vertical line deviation based on a gravitational field spherical harmonic model.
Background
The inertial navigation system is a completely autonomous positioning and orienting device, can determine the attitude, the speed and the position information of a carrier without depending on any external active information, and is widely applied to the fields of navigation positioning, engineering measurement and the like. The method mainly utilizes an inertial measurement element gyroscope and an accelerometer to autonomously measure angular velocity and acceleration information of a carrier relative to an inertial space, and carries out integral calculation under a navigation coordinate system to obtain attitude, velocity and position information of the carrier. The initial alignment is a key step of navigation positioning of the inertial navigation system, and mainly determines the attitude matrix of the carrier at the initial moment, and the accuracy of the initial alignment directly influences the accuracy of the navigation positioning. In an inertial navigation system, for the convenience of navigation calculation, a normal gravity vector artificially defined on a normal of a reference ellipsoid is usually substituted for a true gravity vector of a vertical line of a ground level for calculation, a difference between the true gravity vector and the normal gravity vector is called a gravity disturbance vector, a difference in direction is called a vertical line deviation, and the initial alignment performance is directly influenced by the vertical line deviation. For high precision inertial navigation systems, such errors are often not negligible and need to be compensated for.
In the prior art, the vertical deviation compensation method mainly comprises two modes of actually measured vertical deviation compensation and gravity field model-based compensation. The actual measurement mode by utilizing the gravity gradiometer and the vector gravitometer is limited by various conditions such as high cost, incomplete technology and the like, and the problem of the measurement precision of the vertical line deviation cannot be fundamentally solved, so that the compensation effect is limited, and the method cannot be applied to engineering practice. A direct difference-modeling Method is provided in a published paper of An Accurate quality Compensation Method for High-Accuracy aircraft POS of Beijing university of aerospace housing construction and the like. At present, a plurality of High-Precision Gravity field spherical harmonic models are published around the world, students at home and abroad also use the spherical harmonic models to perform vertical deviation compensation analysis in a dispute, a paper "An Online quality Modeling Method Applied for High Precision Free-INS" published by royal crystal of Beijing aerospace university and the like proposes a simplified two-dimensional second-order polynomial model, which compensates navigation position errors, but mainly analyzes the influence of vertical deviation on navigation calculation, has less compensation research on initial alignment, and the existing compensation initial alignment methods are all compensated and calculated under a navigation coordinate system taking An ellipsoid normal line as a day direction, while An accelerometer actually measures real Gravity in a true vertical line direction, and the condition that the coordinate system of the compensation calculation is inconsistent with the coordinate system actually measured by a measuring device exists on the algorithm, so that the initial alignment performance is influenced. The chinese patents with application numbers 201410697203.0 and 201710894464.5 all adopt an EGM2008 gravity field spherical harmonic model to calculate vertical deviation data, but compensation calculation is performed under a navigation coordinate system taking an ellipsoid normal as a sky direction, and the situation that coordinate systems are inconsistent exists, which affects alignment performance. In 2019, a paper "grade distribution Compensation for Inertial Navigation System" published by IEEE instruments and measurement magazines of naval engineering university and the like analyzes the coupling relationship between vertical deviation and accelerometer error and the improvement of position precision after Compensation in a horizontal Gravity Disturbance Compensation Inertial Navigation System, but has the problem of directly analyzing the improvement of initial alignment performance of the Inertial Navigation System after vertical deviation Compensation.
Disclosure of Invention
In view of the above technical situation, an object of the present invention is to provide an inertial navigation self-alignment method for compensating a vertical deviation based on a gravitational field spherical harmonic model, in which a newly published egen-6C 4 gravitational field spherical harmonic model is used to calculate the vertical deviation, an azimuth angle of a carrier is calculated in a navigation coordinate system with a true vertical direction as a sky direction, and initial alignment accuracy and performance of an inertial navigation system are improved.
The technical solution of the present invention is now described as follows:
according to the above object, the present invention provides an inertial navigation self-alignment method for compensating vertical deviation based on a gravity field spherical harmonic model, wherein the inertial navigation self-alignment method for compensating vertical deviation based on a gravity field spherical harmonic model is a method combining vertical deviation compensation coarse alignment and compensation kalman filter fine alignment of a solidification coordinate system, and is characterized in that: the method comprises the following steps of directly calculating the component of a gravity disturbance value of an alignment point under an n system by using a high-precision gravity field spherical harmonic model EIGEN-6C4, projecting the component to a navigation coordinate system n' system by using a quaternion method for compensation, and finally obtaining a carrier astronomical azimuth angle to improve alignment performance, wherein the method specifically comprises the following steps:
step 1: before inertial navigation self-alignment begins, calibrating an inertial navigation system by using a rotary table, accurately estimating gyro constant drift and accelerometer constant zero offset, and deducting corresponding constant errors from output data;
step 2: defining a navigation coordinate system n system and an n 'system, wherein the n system represents a northeast sky coordinate system established by taking the normal of a reference ellipsoid as the sky direction, the n' system represents a northeast navigation coordinate system established by taking the true vertical direction (the true gravity direction) as the sky direction, when the static base is initially aligned, the position coordinate of the carrier is accurately known, the geographic latitude L, the longitude lambda and the elevation h are calculated, and the normal gravity vector gamma of an initial alignment point is calculated through a WGS-84 normal gravity modeln；
γn＝[0 0 -γ]T (1)
And step 3: constructing an EIGEN-6C4 high-precision gravitational field spherical harmonic model, inputting the latitude L, the longitude lambda and the elevation h of the initial alignment point of the inertial navigation system, and calculating the component delta g of the gravity disturbance under an n systemnAfter gravity disturbance is compensated, the projection g of the real gravity vector under the n system can be obtainedn；
gn＝γn+δg (2)
And 4, step 4: the vector g after gravity disturbance compensation calculated in the step 3nAfter the angle theta is rotated around the rotating shaft u, a real gravity disturbance vector g under a navigation coordinate system n' is obtainedn′＝[0 0 -g]TThe method is realized by the following steps;
step 4.1: the gravity disturbance vector delta g calculated according to the step 3nCalculating the deviation eta, xi of the perpendicular line, wherein
Figure BDA0002728585890000031
Figure BDA0002728585890000032
As can be seen from FIG. 1, the equation is based onThe angular function relationship may be calculated as the rotation axis u ═ ux uy uz]TWherein
Figure BDA0002728585890000033
uz＝0；
Step 4.2: the rotation angle can be calculated according to figure 1
Figure BDA0002728585890000034
Step 4.3: a quaternion Q ═ Q of the coordinate system n and the system n' can be constructed from the rotation axis u and the rotation angle θ0 q1 q2q3]TWherein
Figure BDA0002728585890000035
Step 4.4: from the rotational quaternion, the attitude transformation matrix can be calculated from
Figure BDA0002728585890000036
Figure BDA0002728585890000037
And 5: calculated attitude transformation matrix
Figure BDA0002728585890000038
Obtaining the true gravity vector g after the vertical deviation compensationn′
gn′＝Cn ′ng (4)
Step 6: the compensated true gravity vector gn′Used in the coarse alignment method based on the solidification coordinate system to obtain the rough estimation value of the carrier attitude matrix
Figure BDA0002728585890000039
The resolving process is carried out under a navigation coordinate system n', and b represents a carrier coordinate system;
step 6.1: i.e. in′0To solidifyA navigation coordinate system which represents a navigation coordinate system n' aligned with the initial time and keeps unchanged relative to the inertial space;
Figure BDA00027285858900000310
reflects the n's relative in′0The rotation of the system can be obtained by calculation according to the latitude information L and the time interval t of the position of the carrier;
Figure BDA00027285858900000311
representing the motion of the carrier relative to a coordinate system of the solidified carrier, the initial value of which is an identity matrix,
Figure BDA00027285858900000312
Figure BDA00027285858900000313
can be output by a gyroscope
Figure BDA00027285858900000314
Updating in real time by using a quaternion method;
Figure BDA00027285858900000315
Figure BDA00027285858900000316
step 6.2:
Figure BDA00027285858900000317
the key point of the solution is that
Figure BDA00027285858900000318
In the method, the speed is respectively selected to be ib0,in′0Vector of two different time instants under coordinate system
Figure BDA0002728585890000041
Solving as reference vector
Figure BDA0002728585890000042
Figure BDA0002728585890000043
Figure BDA0002728585890000044
Figure BDA00027285858900000413
In the formula (I), the compound is shown in the specification,
Figure BDA0002728585890000045
represents tkOutputting a value by the accelerometer at the moment;
step 6.3: will find
Figure BDA0002728585890000046
Respectively carry in (5), the rough estimation value of the attitude matrix can be obtained
Figure BDA0002728585890000047
Measuring the accelerometer value fb(t) projection onto ib0In the process of the curing process,
Figure BDA0002728585890000048
the carrier attitude change caused by the carrier shaking interference can be tracked, and the carrier shaking interference can be effectively inhibited;
and 7: the compensated true gravity vector gn′The method is used in a fine alignment method based on Kalman filtering;
and 8: aligning the Kalman filter in the step 7 with the misalignment angle
Figure BDA0002728585890000049
Is compensated into a coarse estimate of the coarse alignment
Figure BDA00027285858900000410
In (1),
Figure BDA00027285858900000411
finally obtaining an accurate attitude matrix estimation value
Figure BDA00027285858900000412
The initial alignment is completed.
Drawings
FIG. 1: navigation coordinate system n' system and gravity vector schematic diagram after vertical deviation compensation
FIG. 2: the invention relates to a flow chart of an inertial navigation self-alignment method for compensating vertical line deviation
FIG. 3: azimuth angle error compensation effect using method in static base alignment test
Detailed Description
The embodiments of the present invention will now be further described with reference to the accompanying drawings.
The basic idea of the invention is to calculate the gravity disturbance vector through the EIGEN-6C4 high-precision gravity field spherical harmonic model, compensate the gravity disturbance vector into the normal gravity vector, and compensate the gravity vector g after compensationnConverting the gravity vector into a navigation coordinate system n' system to obtain a real gravity vector gn′(ii) a On the basis, the compensated real gravity vector is applied to the coarse alignment process and the fine alignment process of Kalman filtering based on a solidification coordinate system, and the astronomical azimuth angle of the carrier is finally calculated, wherein the calculation process is carried out under a navigation coordinate system n'.
The technical solution of the present invention is described in detail by embodiments with reference to the accompanying drawings.
Step 1: before inertial navigation self-alignment begins, calibrating an inertial navigation system by using a rotary table, accurately estimating gyro constant drift and accelerometer constant zero offset, and deducting corresponding constant errors from output data;
step 2: as shown in FIG. 1, a navigation coordinate system n system is definedAnd n' system, the origin of coordinates of the n system is the position of the carrier, xnAxis and ynThe axes are in the tangent plane of the local ellipsoid and point to east and north, z respectivelynThe axes are collinear with the normal line of a reference ellipsoid at the position of the carrier and point to the sky, the three axes meet the right-hand orthogonal law, and the WGS-84 ellipsoid model is selected as the reference ellipsoid; the origin of coordinates of the n' system is at the position of the carrier, xn′Axis and yn′The axes are in the horizontal plane of the ground and point to the east and north poles, zn′The axis being collinear with the perpendicular to the position of the carrier, i.e. with the true gravity vector gn′Collinear, three-axis pointing satisfies the right-hand orthogonal law. And defining a carrier coordinate system b system, wherein the coordinate origin is at the mass center of the inertial navigation system, and the three axes of the carrier coordinate system b system point to the pitch axis, the roll axis and the course axis respectively along the inertial navigation system. The latitude L, longitude lambda and elevation h of the initial alignment point are accurately known by the GPS, and the normal gravity vector gamma of the initial alignment point is calculated through the WGS-84 normal gravity modeln；
γn＝[0 0 -γ]T (1)
γ＝9.7803267714×(1+5.27904×10-3×sin2L+2.97381×10-5sin4L)-3.0877×10-6×h
And step 3: constructing an EIGEN-6C4 high-precision gravitational field spherical harmonic model, inputting the latitude L, the longitude lambda and the elevation h of the initial alignment point of the inertial navigation system, and calculating the horizontal component of the gravity disturbance under an n system
Figure BDA0002728585890000051
After gravity disturbance is compensated, the projection g of a real gravity vector under an n system can be obtainedn；
gn＝γn+δgn (2)
And 4, step 4: the vector g after gravity disturbance compensation calculated in the step 3nAfter the angle theta is rotated around the rotating shaft u, a real gravity disturbance vector g under a navigation coordinate system n' is obtainedn′＝[0 0 -g]TThe method is realized by the following steps;
step 4.1: the gravity disturbance vector delta g calculated according to the step 3nCalculating the deviation of the vertical lineThe difference eta, xi, wherein
Figure BDA0002728585890000052
Figure BDA0002728585890000053
As can be seen from fig. 1, the rotation axis u ═ u can be calculated from the trigonometric function relationshipx uy uz]TWherein
Figure BDA0002728585890000054
uz＝0；
Step 4.2: the rotation angle can be calculated according to figure 1
Figure BDA0002728585890000055
Step 4.3: a quaternion Q ═ Q of the coordinate system n and the system n' can be constructed from the rotation axis u and the rotation angle θ0 q1 q2q3]TWherein
Figure BDA0002728585890000061
Step 4.4: from the rotational quaternion, the attitude transformation matrix can be calculated from
Figure BDA0002728585890000062
Figure BDA0002728585890000063
And 5: the attitude transformation matrix calculated according to the step 4
Figure BDA0002728585890000064
Obtaining the true gravity vector g after the vertical deviation compensationn′
Figure BDA0002728585890000065
Step 6: the true gravity vector g after the vertical deviation compensation is obtained in the step 5n′For coarse alignment based on a solidification coordinate system to obtain a coarse estimation value of a posture matrix
Figure BDA0002728585890000066
Figure BDA0002728585890000067
Step 6.1: i.e. ib0A condensed carrier coordinate system, which represents the carrier coordinate system aligned at the initial moment and remains unchanged with respect to the inertial space; i.e. in′0The navigation coordinate system is a solidified navigation coordinate system and represents a navigation coordinate system n' aligned with the initial moment, and the relative inertia space is kept unchanged;
Figure BDA0002728585890000068
reflects the n's relative in′0The rotation of the system can be obtained by calculation according to the latitude information L and the time interval t of the position of the carrier;
Figure BDA0002728585890000069
representing the motion of the carrier relative to a coordinate system of the solidified carrier, the initial value of which is an identity matrix,
Figure BDA00027285858900000610
Figure BDA00027285858900000611
can be output by a gyroscope
Figure BDA00027285858900000612
And updating in real time by utilizing a quaternion method.
Figure BDA00027285858900000613
Figure BDA00027285858900000614
Step 6.2: thus, it is possible to provide
Figure BDA00027285858900000615
The key point of the solution is that
Figure BDA00027285858900000616
In the algorithm, the speed is respectively selected to be ib0,in′0Vector of two different time instants under coordinate system
Figure BDA00027285858900000617
Solving as reference vector
Figure BDA00027285858900000618
Figure BDA0002728585890000071
Figure BDA0002728585890000072
Figure BDA0002728585890000073
In the formula (I), the compound is shown in the specification,
Figure BDA0002728585890000074
represents tkAnd outputting a value by the accelerometer at the moment.
Step 6.3: will find
Figure BDA0002728585890000075
Respectively carry in (5), the rough estimation value of the attitude matrix can be obtained
Figure BDA0002728585890000076
Measuring the accelerometer value fb(t) projection onto ib0In the process of the curing process,
Figure BDA0002728585890000077
the carrier attitude change caused by the carrier shaking interference can be tracked, and the carrier shaking interference can be effectively inhibited.
And 7: establishing a 12-state Kalman filter for fine alignment, wherein the filter state comprises a misalignment angle
Figure BDA0002728585890000078
Speed error δ vn′Deviation of gyro drift epsilonbAnd accelerometer zero offset error
Figure BDA0002728585890000079
The state quantity of the Kalman filtering model after the vertical deviation compensation is shown as the following formula:
Figure BDA00027285858900000710
the kalman filter state equation and the measurement equation are as follows:
Figure BDA00027285858900000711
the Kalman filter state matrix is as follows:
Figure BDA00027285858900000712
Figure BDA00027285858900000713
Figure BDA00027285858900000714
Figure BDA00027285858900000715
Figure BDA0002728585890000081
wherein L, h represents the latitude and height of the inertial navigation system, RNAnd RMThe radius of curvature of the prime circle and the radius of curvature of the prime circle are respectively the radius of curvature of the prime circle at the location of the inertial navigation system.
G(t)＝[01×3 δgn′T 01×6]T (14)
Figure BDA0002728585890000082
Figure BDA0002728585890000083
In the formula (I), the compound is shown in the specification,
Figure BDA0002728585890000084
and
Figure BDA0002728585890000085
respectively, the measurement noise of the gyro and accelerometer, and v (t) the metrology noise, assumed to be white.
And in the initial alignment of the static base, selecting the speed output value of the inertial navigation system as a measurement value.
Figure BDA0002728585890000086
H＝[03×3 I3×3 03×6] (18)
And 8: aligning the Kalman filter in the step 7 with the misalignment angle
Figure BDA0002728585890000087
The estimated value of (A) is compensated into a coarse estimate obtained by coarse alignmentValue of
Figure BDA0002728585890000088
Finally, obtaining accurate attitude matrix estimation value
Figure BDA0002728585890000089
The initial alignment is completed.
Figure BDA00027285858900000810
When the compensation method is used in the initial alignment process of the static-base strapdown inertial navigation system, the course angle of the strapdown inertial navigation system is measured by the pendulum type gyro north finder to serve as a theoretical true value, the course angle errors before and after compensation are shown in figure 3, the solid line is the azimuth angle error before the uncompensated vertical deviation, and the dotted line is the azimuth angle error after the compensation of the method, so that the initial alignment azimuth angle error is obviously reduced, the alignment performance is obviously improved, the course angle error before the uncompensated is 35.3 ', and the course angle error is reduced to 28.6' after the compensation of the method.

Claims (3)

1. The inertial navigation self-alignment method for compensating the vertical deviation based on the gravity field spherical harmonic model is a method combining the vertical deviation compensation coarse alignment and the compensation Kalman filtering fine alignment of a solidification coordinate system, and is characterized in that: the method comprises the following steps of directly calculating the component of a gravity disturbance value of an alignment point under an n system by using a high-precision gravity field spherical harmonic model, projecting the component to a navigation coordinate system n' by using a quaternion method for compensation, and finally obtaining a carrier astronomical azimuth angle to improve alignment performance, wherein the method specifically comprises the following steps:
step 1: before inertial navigation self-alignment begins, calibrating an inertial navigation system by using a rotary table, accurately estimating gyro constant drift and accelerometer constant zero offset, and deducting corresponding constant errors from output data;
step 2: defining n and n' systems of navigation coordinate system, wherein n is expressed byThe method comprises the steps of establishing a northeast coordinate system by taking an ellipsoid normal as a sky direction, representing a northeast navigation coordinate system by taking a true vertical line direction (a true gravity direction) as the sky direction by using an n' system, accurately knowing the position coordinates of a carrier when a static base is initially aligned, calculating a normal gravity vector gamma of an initial alignment point through a normal gravity model, and calculating the normal gravity vector gamma of the initial alignment point by using a geographical latitude L, a longitude lambda and an elevation hn；
γn＝[0 0 -γ]T (1)
And step 3: constructing a high-precision gravity field spherical harmonic model, inputting the latitude L, the longitude lambda and the elevation h of the initial alignment point of the inertial navigation system, and calculating the component delta g of gravity disturbance under an n systemnAfter gravity disturbance is compensated, the projection g of the real gravity vector under the n system can be obtainedn；
gn＝γn+δg (2)
And 4, step 4: the vector g after gravity disturbance compensation calculated in the step 3nAfter the angle theta is rotated around the rotating shaft u, a real gravity disturbance vector g under a navigation coordinate system n' is obtainedn′＝[0 0 -g]T；
And 5: calculated attitude transformation matrix
Figure FDA0002728585880000011
Obtaining the true gravity vector g after the vertical deviation compensationn′
Figure FDA0002728585880000012
Step 6: the compensated true gravity vector gn′Used in the coarse alignment method based on the solidification coordinate system to obtain the rough estimation value of the carrier attitude matrix
Figure FDA0002728585880000013
The resolving process is carried out under a navigation coordinate system n', and b represents a carrier coordinate system;
and 7: the compensated true gravity vector gn′For based on kalmanIn the fine alignment method of filtering, the accurate estimation value of the carrier attitude matrix is finally obtained
Figure FDA0002728585880000021
And finishing the initial alignment process of the inertial navigation system.
2. The inertial navigation self-alignment method for compensating vertical deviation based on the gravitational field spherical harmonic model according to claim 1, characterized in that: step 4, obtaining the true gravity disturbance vector g under the navigation coordinate system nn′＝[0 0 -g]T(ii) a "is specifically realized by the following steps;
step 4.1: the gravity disturbance vector delta g calculated according to the step 3nCalculating the deviation eta, xi of the perpendicular line, wherein
Figure FDA0002728585880000022
As can be seen from fig. 1, the rotation axis u ═ u can be calculated from the trigonometric function relationshipx uy uz]TWherein
Figure FDA0002728585880000023
uz＝0；
Step 4.2: the rotation angle can be calculated according to figure 1
Figure FDA0002728585880000024
Step 4.3: quaternion of coordinate system n and n' system can be constructed according to rotation axis u and rotation angle theta
Figure FDA0002728585880000025
Wherein
Figure FDA0002728585880000026
Step 4.4: from the rotational quaternion, the attitude transformation matrix can be calculated from
Figure FDA0002728585880000027
Figure FDA0002728585880000028
3. The inertial navigation self-alignment method for compensating vertical deviation based on the gravitational field spherical harmonic model according to any one of claims 1 and 2, characterized in that: carrying out rough estimation on carrier attitude matrix under navigation coordinate system n
Figure FDA0002728585880000029
The resolving process is as follows:
step 6.1:
Figure FDA00027285858800000210
in the formula in′0The navigation coordinate system is a solidified navigation coordinate system and represents a navigation coordinate system n' aligned with the initial moment, and the relative inertia space is kept unchanged;
Figure FDA00027285858800000211
reflects the n's relative in′0The rotation of the system can be obtained by calculation according to the latitude information L and the time interval t of the position of the carrier;
Figure FDA0002728585880000031
in the formula (I), the compound is shown in the specification,
Figure FDA0002728585880000032
representing the motion of the carrier relative to a coordinate system of the solidified carrier, the initial value of which is an identity matrix,
Figure FDA0002728585880000033
Figure FDA0002728585880000034
can be output by a gyroscope
Figure FDA0002728585880000035
Updating in real time by using a quaternion method;
step 6.2:
Figure FDA0002728585880000036
the key point of the solution is that
Figure FDA0002728585880000037
In the method, the speed is respectively selected to be ib0,in′0Vector of two different time instants under coordinate system
Figure FDA0002728585880000038
Solving as reference vector
Figure FDA0002728585880000039
Figure FDA00027285858800000310
Figure FDA00027285858800000311
Figure FDA00027285858800000312
In the formula (I), the compound is shown in the specification,
Figure FDA00027285858800000313
represents tkOutputting a value by the accelerometer at the moment;
step 6.3: will find
Figure FDA00027285858800000314
Respectively carry in (5), the rough estimation value of the attitude matrix can be obtained
Figure FDA00027285858800000315
Measuring the accelerometer value fb(t) projection onto ib0In the process of the curing process,
Figure FDA00027285858800000316
the carrier attitude change caused by the carrier shaking interference can be tracked, and the carrier shaking interference can be effectively inhibited.
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CN113885101A (en) * 2021-09-28 2022-01-04 中国船舶重工集团公司第七0七研究所 Method for constructing gravity gradient reference map based on ellipsoid model
CN115077520A (en) * 2022-08-22 2022-09-20 中国船舶重工集团公司第七0七研究所 Attitude compensation method based on resonant inertial navigation system

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