CN108871378B - Online dynamic calibration method for errors of inner lever arm and outer lever arm of two sets of rotary inertial navigation systems - Google Patents

Online dynamic calibration method for errors of inner lever arm and outer lever arm of two sets of rotary inertial navigation systems Download PDF

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CN108871378B
CN108871378B CN201810697400.0A CN201810697400A CN108871378B CN 108871378 B CN108871378 B CN 108871378B CN 201810697400 A CN201810697400 A CN 201810697400A CN 108871378 B CN108871378 B CN 108871378B
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inertial navigation
navigation system
rins1
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CN108871378A (en
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李魁
吴琪
王蕾
宋天骁
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Beihang University
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Abstract

The invention discloses an online dynamic calibration method for errors of an inner lever arm and an outer lever arm of two sets of rotary inertial navigation systems. Firstly, establishing a measurement model of the error of an inner rod arm and an outer rod arm between two sets of rotary inertial navigation systems and the speed difference between the two sets of rotary inertial navigation systems; secondly, designing two rotation strategies of the rotary inertial navigation system based on the principle and the way of realizing the separation of the inner rod and the arm of each of the two rotary inertial navigation systems by model analysis; thirdly, respectively controlling the frames of the RINS1 and the RINS2 to rotate according to a preset rotation strategy, performing navigation calculation, and outputting two sets of speed information of the rotary inertial navigation in real time; and finally, calculating the speed difference of the two sets of rotary inertial navigation systems, and taking the speed difference as a measurement to construct a Kalman filter so as to realize online dynamic calibration of errors of the inner lever arm and the outer lever arm of the two sets of rotary inertial navigation systems. The calibration method has the advantages of short calibration time, simple calibration process, high calibration precision of the inner lever arm and the outer lever arm, no need of depending on other external reference information, strong autonomy and easy realization.

Description

Online dynamic calibration method for errors of inner lever arm and outer lever arm of two sets of rotary inertial navigation systems
Technical Field
The invention belongs to the technical field of inertial navigation system error parameter calibration, and particularly relates to an online dynamic calibration method for errors of an inner lever arm and an outer lever arm of two sets of rotary inertial navigation systems, which can simultaneously realize online dynamic calibration of the inner lever arm and the outer lever arm between the two sets of rotary inertial navigation systems.
Background
An Inertial Measurement Unit (IMU) of the inertial navigation system consists of three gyroscopes and three accelerometers, the three gyroscopes and the three accelerometers can respectively measure angular velocity components and linear acceleration components of the carrier in three directions, and attitude, velocity and position information of the carrier can be obtained in real time through integration of the angular velocity and the acceleration. However, in a practical inertial navigation system, the accelerometers are solid elements with certain sizes and volumes, so that the installation positions of the three accelerometers cannot be completely overlapped with the central position of the IMU, and due to inevitable installation errors, extension lines of the directions of three acceleration sensitive axes cannot intersect at a point, so that the sensitive measurement points of each accelerometer are different from each other. A connecting line vector from the center of the IMU to each accelerometer measuring point forms a group of inner lever arms, when angular velocity excitation exists, a lever arm effect is generated, acceleration errors are caused, and velocity errors and position errors are caused after integral calculation. Therefore, the calibration and compensation of the parameters of the inner rod arm are one of the key technologies for improving the navigation accuracy of a single set of inertial navigation system.
For a large carrier, in order to ensure safety and reliability, the carrier is generally provided with two or more sets of inertial navigation systems to form a redundant configuration structure, so as to realize emergency disposal under a fault condition. Because the outer lever arm exists between the two sets of inertial navigation systems due to different installation positions, when the carrier has angular motion, the speed information output by the two sets of inertial navigation systems is different under the action of the lever arm effect, and therefore, in order to comprehensively utilize the navigation information of the two sets of systems, the lever arm parameters between the two sets of inertial navigation systems need to be accurately calibrated and compensated.
Aiming at the problems, the invention provides an online dynamic calibration method for errors of inner lever arms and outer lever arms of two sets of rotary inertial navigation systems, which takes the difference between the speeds of the two sets of rotary inertial navigation systems as an observed quantity to construct a Kalman filter and realize online dynamic calibration of parameters of the inner lever arms and the outer lever arms between the two sets of rotary inertial navigation systems.
Disclosure of Invention
The invention provides an online dynamic calibration method for errors of an inner rod arm and an outer rod arm of two sets of rotary inertial navigation systems.
The technical scheme of the invention is as follows: an online dynamic calibration method for errors of an inner lever arm and an outer lever arm of two sets of rotary inertial navigation systems comprises the following specific steps:
step (1) establishing a measurement model of the error of an inner rod arm and an outer rod arm between two sets of rotary inertial navigation systems and the speed difference between the two sets of rotary inertial navigation systems;
step (2) based on the principle and approach of separating inner rods and arms of two sets of rotary inertial navigation systems by model analysis, designing two sets of rotary inertial navigation rotary strategies;
step (3) controlling the rotation of the frames of the RINS1 and the RINS2 by using the rotation strategy of the step (2), performing navigation calculation, and outputting two sets of speed information of the rotational inertial navigation in real time;
and (4) calculating the speed difference of the two sets of rotary inertial navigations obtained in the step (3), and constructing a Kalman filter by using the measurement model in the step (1) to realize online dynamic calibration of errors of the inner lever arm and the outer lever arm of the two sets of rotary inertial navigations.
Compared with the prior art, the invention has the advantages that:
(1) according to the online dynamic calibration method for the errors of the inner lever arm and the outer lever arm of the two sets of rotary inertial navigation systems, the optimal estimation and dynamic calibration of the parameters of the outer lever arm between 6 inner lever arms and the system of the two sets of rotary inertial navigation systems can be simultaneously realized by fully utilizing the speed difference of the two sets of rotary inertial navigation systems and constructing a Kalman filter.
(2) The method for the online dynamic calibration of the errors of the inner lever arm and the outer lever arm of the two sets of rotary inertial navigation systems, which is provided by the invention, has the advantages of short calibration time, simple calibration process and high calibration precision of the inner lever arm and the outer lever arm, which is better than 2 mm.
(3) According to the online dynamic calibration method for the errors of the inner lever arm and the outer lever arm of the two sets of rotary inertial navigation systems, only the difference between the speeds of the two sets of rotary inertial navigation systems is used as an observed quantity, and other external reference information is not needed, so that the method is strong in autonomy and easy to implement.
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FIG. 1 is a flow chart of an online dynamic calibration method for errors of an inner lever arm and an outer lever arm of two rotary inertial navigation systems according to the invention;
FIG. 2 is a schematic diagram of respective inner lever arms and respective outer lever arms of two rotary inertial navigation systems according to an embodiment of the present invention;
FIG. 3 is a diagram of attitude/heading angle of angular motion of a carrier in an embodiment of the invention;
FIG. 4 illustrates the rotation strategy of RINS1 and RINS2 in an embodiment of the present invention; wherein FIG. 4(a) is the rotation strategy of RINS1, and FIG. 4(b) is the rotation strategy of RINS 2;
FIG. 5 is a convergence curve of error parameters of inner lever arms and outer lever arms of two rotary inertial navigation systems according to an embodiment of the present invention; fig. 5(a) shows the convergence curves of the 9 inner lever arm components of RINS1, fig. 5(b) shows the convergence curves of the 9 inner lever arm components of RINS2, and fig. 5(c) shows the convergence curves of the 3 outer lever arm components between RINS1 and RINS 2.
Detailed Description
The invention is further described with reference to the following figures and specific embodiments.
As shown in FIG. 1, the specific implementation method of the online dynamic calibration method for the errors of the inner lever arm and the outer lever arm of the two sets of rotary inertial navigation systems of the invention is as follows:
1. establishing a measurement model of the error of the inner rod arm and the outer rod arm between the two sets of rotary inertial navigation systems and the speed difference between the two sets of rotary inertial navigation systems;
fig. 2 is a schematic diagram of the inner lever arm and the outer lever arm between the two rotary inertial navigation systems according to the present invention. Wherein, Ob1-Xb1Yb1Zb1、Ob2-Xb2Yb2Zb2Body coordinate systems RINS1 and RINS2, respectively, origin Ob1、Ob2Coincident with the IMU centers of RINS1, RINS2, respectively, On-XnYnZnFor navigating the coordinate system, its origin OnCoincident with the center of mass of the carrier, Ob1To Ob2Vector of (2)
Figure BDA0001713924650000031
The outer lever arm between RINS1 and RINS 2. O isx1,Oy1,Oz1Respectively, the mounting positions of the x, y and z accelerometers of RINS1,
Figure BDA0001713924650000032
three inner lever arms of RINS 1; o isx2,Oy2,Oz2Respectively, the mounting positions of the x, y and z accelerometers of RINS2,
Figure BDA0001713924650000033
three inner lever arms of RINS 2.
The lever arm error model was developed using the x-accelerometer of RINS1 as an example. As shown in FIG. 2, the spatial distance of RINS1 from the carrier's centroid constitutes a set of outer lever arms
Figure BDA0001713924650000034
Meanwhile, the x accelerometer and the IMU center form a group of inner rod arms
Figure BDA0001713924650000035
When there is angular motion of the carrier and rotational motion of RINS1 about the frame, the acceleration to which the x-accelerometer is sensitive is equal to the vector sum of the bulk acceleration, the relative acceleration, and the coriolis acceleration.
The involved acceleration is:
Figure BDA0001713924650000036
in the formula (1), the vector
Figure BDA0001713924650000037
Can be further expressed as:
Figure BDA0001713924650000038
the relative acceleration is:
Figure BDA0001713924650000039
the coriolis acceleration is:
Figure BDA00017139246500000310
therefore, under the action of the inner lever arm and the outer lever arm, the acceleration error included in the acceleration information output by the x-accelerometer is as follows:
Figure BDA00017139246500000311
the above formula is expanded as:
Figure BDA00017139246500000312
in the formula (1) - (5),
Figure BDA00017139246500000313
respectively the carrier angular velocity and the frame angular velocity of RINS1,
Figure BDA00017139246500000314
respectively a carrier angular velocity differential and a frame rotational angular velocity differential,
Figure BDA00017139246500000315
is the inner lever arm between the x-accelerometer of RINS1 and the center of the IMU,
Figure BDA0001713924650000041
is the lever arm between the x-accelerometer and the center of mass of the carrier,
Figure BDA0001713924650000042
is an outer lever arm between the IMU center and the carrier center of mass of RINS1, and has
Figure BDA0001713924650000043
In the formula (5), the lever arm vector
Figure BDA0001713924650000044
Can be expressed as components along three coordinate axis directions in a space three-dimensional coordinate system, i.e.
Figure BDA0001713924650000045
Rx1In the lower corner of (1) x represents
Figure BDA0001713924650000046
Projection in the x-direction, 1 denotes the rotational inertial navigation System No. 1 (i.e., RINS1), rxx1The first x in the subscript of (1) represents
Figure BDA0001713924650000047
Projection in the x direction, the second x represents the x accelerometer of inertial navigation system # 1, and 1 represents the rotational inertial navigation system # 1 (i.e., RINS 1).
Similarly, the acceleration error caused by the outer lever arm and the inner lever arm of the x-accelerometer of RINS2 is:
Figure BDA0001713924650000048
in the formula (6), the reaction mixture is,
Figure BDA0001713924650000049
respectively the carrier angular velocity and the frame angular velocity of RINS2,
Figure BDA00017139246500000410
respectively a carrier angular velocity differential and a frame rotational angular velocity differential,
Figure BDA00017139246500000411
is the inner lever arm between the x-accelerometer of RINS2 and the center of the IMU,
Figure BDA00017139246500000412
the outer lever arm between the IMU center and the carrier center of mass of RINS 2.
Because two sets of rotary inertial navigation systems are fixedly connected with the carrier at the same time, RINS1 and RINS2 sensitive
Figure BDA00017139246500000413
Similarly, by subtracting the formula (5) from the formula (6), the acceleration error under the common action of the inner lever arm and the outer lever arm between the two sets of rotational inertial navigations can be obtained as follows:
Figure BDA00017139246500000414
in the formula (7), the reaction mixture is,
Figure BDA00017139246500000415
is the outer lever arm vector between RINS1 and RINS 2.
Further, a measurement model for obtaining respective errors of the inner rod arm and the outer rod arm between the two sets of rotational inertial navigation systems and the speed difference between the two sets of rotational inertial navigation systems is as follows:
Figure BDA00017139246500000416
in the formula (8), the reaction mixture is,
Figure BDA00017139246500000417
a rotation transformation matrix representing the sensitive axis coordinate system of RINS1, RINS2 to the navigation coordinate system,
Figure BDA00017139246500000418
indicating RINS1 inner lever arm
Figure BDA00017139246500000419
The resulting error in the acceleration is, in turn,
Figure BDA00017139246500000420
indicating RINS2 inner lever arm
Figure BDA00017139246500000421
The resulting error in the acceleration is, in turn,
Figure BDA00017139246500000422
representing the outer lever arm between RINS1 and RINS2
Figure BDA00017139246500000423
The resulting acceleration error.
2. Analyzing the principle and the way of separating inner rods and arms of the two sets of rotary inertial navigation systems, and designing two sets of rotary strategies of the rotary inertial navigation;
as shown in the formula (7), the outer lever arm between RINS1 and RINS2
Figure BDA0001713924650000051
By angular movement of the carrier only
Figure BDA0001713924650000052
Actuation, inner lever arms of RINS1, RINS2
Figure BDA0001713924650000053
While being moved angularly by the carrier
Figure BDA0001713924650000054
And rotational movement of the frame
Figure BDA0001713924650000055
Excited, therefore, when there is angular movement of the carrier, i.e. when there is angular movement of the carrier
Figure BDA0001713924650000056
At the same time, the RINS1 and RINS2 have the rotation movement of the frame and satisfy
Figure BDA0001713924650000057
In time, the outer lever arm can be realized
Figure BDA0001713924650000058
Inner lever arm
Figure BDA0001713924650000059
Separation and estimation of (2).
Therefore, the design of the rotation strategies of RINS1 and RINS2 needs to be satisfied
Figure BDA00017139246500000510
Principle of (1). Since angular velocity is a vector with both magnitude and direction, there are three ways to provide different angular velocities: first, RINS1 and RINS2 have the same rotational axis direction but different rotational angular velocities; secondly, RINS1 and RINS2 have the same rotational angular velocity but different rotational axis directions; third, RINS1 and RINS2 are different in the rotation axis direction and the rotational angular velocity. The following analysis was performed from these three aspects, respectively:
(a) RINS1 and RINS2 have the same rotation axis direction but different rotation angular velocities;
suppose that both RINS1 and RINS2 rotate around the inner frame shaft, but the rotation angular velocities are different, namely, the requirement of satisfying
Figure BDA00017139246500000511
In this case, the acceleration errors caused by the inner lever arms of RINS1 and RINS2 are:
Figure BDA00017139246500000512
at this time, the rotation matrices of RINS1 and RINS2 are:
Figure BDA00017139246500000513
when equations (9) and (10) are substituted into equation (7) and expanded, the acceleration error under the common action of the inner lever arms of RINS1 and RINS2 can be obtained as follows:
Figure BDA00017139246500000514
in the formulae (9) to (11),
Figure BDA00017139246500000515
the rotation angles of the inner frames of RINS1 and RINS2 are respectively
Figure BDA00017139246500000516
Figure BDA00017139246500000517
And angular velocity of rotation
Figure BDA00017139246500000518
There is an integral relationship between, as follows:
Figure BDA00017139246500000519
according to the formulae (11) and (12), when
Figure BDA0001713924650000061
Rotation angle at different sizes
Figure BDA0001713924650000062
And a rotation matrix
Figure BDA0001713924650000063
Figure BDA0001713924650000064
The variation period of the two-way valve is different, and the separation of the inner lever arms of the RINS1 and the RINS2 can be realized according to the difference of the periods.
(b) RINS1 and RINS2 have the same rotational angular velocity but different rotational axis directions;
assuming that RINS1 rotates about the inner frame axis and RINS2 rotates about the middle frame axis, i.e., satisfies
Figure BDA0001713924650000065
Figure BDA0001713924650000066
And is
Figure BDA0001713924650000067
In this case, the acceleration errors caused by the inner lever arms of RINS1 and RINS2 are:
Figure BDA0001713924650000068
at this time, the process of the present invention,
Figure BDA0001713924650000069
can be respectively expressed as:
Figure BDA00017139246500000610
wherein the content of the first and second substances,
Figure BDA00017139246500000611
indicates the rotation angle of the inner frame of RINS1,
Figure BDA00017139246500000612
Indicating the middle box rotation angle of RINS 2.
Similarly, when equations (13) and (14) are replaced with equation (7) and expanded, the acceleration error under the common action of the inner lever arms of RINS1 and RINS2 can be found as follows:
Figure BDA00017139246500000613
from the equation (15), when the rotational axis directions of RINS1 and RINS2 are different, the inner lever arm component of RINS1 and the inner lever arm component of RINS2 are in the same direction
Figure BDA00017139246500000614
The two arms are divided into sine and cosine, and the separation of the inner lever arms of the RINS1 and the RINS2 can be realized according to the difference of the sine and the cosine.
(c) The rotational axis directions and rotational angular velocities of RINS1 and RINS2 are different from each other;
when the rotation axis direction and the rotation angular velocity of RINS1 and RINS2 are different, that is, the first two implementation approaches are satisfied simultaneously, it can be seen from the foregoing analysis that the inner lever arm components of RINS1 and RINS2 have both the difference in period and the difference in sine and cosine in the representation of the acceleration error, and the separation of the inner lever arms of RINS1 and RINS2 can be realized according to the difference in the two aspects.
3. And calculating the speed difference of the two sets of rotary inertial navigation systems, and taking the speed difference as a measurement to construct a Kalman filter so as to realize online dynamic calibration of errors of the inner lever arm and the outer lever arm of the two sets of rotary inertial navigation systems.
1) The state model of the kalman filter is:
Figure BDA0001713924650000071
in the formula (16), the compound represented by the formula,
Figure BDA0001713924650000072
indicating RINS1 inner lever arm
Figure BDA0001713924650000073
The resulting error in the acceleration is, in turn,
Figure BDA0001713924650000074
indicating RINS2 inner lever arm
Figure BDA0001713924650000075
The resulting error in the acceleration is, in turn,
Figure BDA0001713924650000076
representing the outer lever arm between RINS1 and RINS2
Figure BDA0001713924650000077
The resulting acceleration error.
Selecting the state variables as follows according to the state model:
Figure BDA0001713924650000078
wherein, delta phiE,δφN,δφUEast platform deflection angle, north platform deflection angle and sky direction of RINS1 and RINS2 respectivelyDifference in platform deflection angle; delta VE,δVNThe difference between the east and north speeds of RINS1, RINS2, respectively; epsilonx1,εy1,εz1、εx2,εy2,εz2Gyro drift for RINS1, RINS2, respectively;
Figure BDA0001713924650000079
accelerometers with zero offset for RINS1, RINS2, respectively; r isxx1,rxy1,rxz1、ryx1,ryy1,ryz1、rzx1,rzy1,rzz19 inner lever arm components of RINS1, rxx2,rxy2,rxz2、ryx2,ryy2,ryz2、rzx2,rzy2,rzz2Is 9 inner lever arm components, R, of RINS2x,Ry,RzIs the 3 outer lever arm components between RINS1 and RINS 2.
2) The measurement model of the kalman filter is:
Figure BDA00017139246500000710
in the formula (17), δ VE,δVNThe difference between the east and north speeds of RINS1, RINS2, respectively; in the subscript, INS1 and INS2 represent speed information output by RINS1 and RINS2, respectively.
Therefore, a Kalman filter is constructed by taking the speed difference of two sets of rotary inertial navigation systems as a measurement value, and taking the platform deflection angles and speed errors of the two sets of rotary inertial navigation systems, and the inner rod arms and the inter-system outer rod arms of the two sets of rotary inertial navigation systems as state quantities, so that the estimation of 9 inner rod arm components of RINS1, 9 inner rod arm components of RINS2 and 3 outer rod arm components between RINS1 and RINS2 is realized.
4. And designing a simulation experiment, and performing simulation verification on the two sets of online dynamic calibration methods for errors of the rotary inertial navigation inner lever arm and the outer lever arm.
In the simulation example, the angular motion of the carrier is set to respectively accord with the following rules:
carrier pitch angle:
Figure BDA00017139246500000711
carrier roll angle:
Figure BDA0001713924650000081
carrier course angle:
Figure BDA0001713924650000082
wherein, aiAccording to a normal distribution with a mean of 4 DEG and a variance of 2 DEG, TθiNormal distribution with mean of 5s and variance of 3s is conformed; biAccording to a normal distribution with a mean of 5 DEG and a variance of 2 DEG, TγiNormal distribution with mean of 6s and variance of 4s is conformed; c. CiAccording to a normal distribution with a mean of 3 DEG and a variance of 2 DEG, TψiFit a normal distribution with a mean of 8s and a variance of 3 s.
Figure BDA0001713924650000087
Coincidence interval [ 02 pi]M ═ 20. As shown in fig. 3, is a course/attitude change curve of the carrier.
Fig. 4 shows the rotation strategies of RINS1 and RINS2 in the simulation example of the present invention, wherein fig. 4(a) shows the rotation strategy of RINS1 and fig. 4(b) shows the rotation strategy of RINS 2. As shown in the figure, the frame rotation angles of RINS1 and RINS2 follow the cosine change law
Figure BDA0001713924650000083
Wherein T is the period. The cosine period of the rotation angle of the RINS1 frame is 60s, and the frame rotation sequence is: inner frame-outer frame-middle frame; the cosine period of the rotation angle of the RINS2 frame is 48s, and the frame rotation sequence is: inner frame-outer frame-middle frame.
In addition, the gyro drift and the accelerometer zero offset are added in the simulation example respectively as follows: the random constant drift of the gyro is 0.01 degree/h, and the random walk is
Figure BDA0001713924650000084
Adding a constant value of zero offset to 50 mu g and random walk to
Figure BDA0001713924650000085
Under the simulation conditions, the two sets of online dynamic calibration methods for errors of the rotary inertial navigation inner lever arm and the outer lever arm provided by the invention are verified, and the simulation results are shown in fig. 5: fig. 5(a) shows the convergence curves of the 9 inner lever arm components of RINS1, fig. 5(b) shows the convergence curves of the 9 inner lever arm components of RINS2, and fig. 5(c) shows the convergence curves of the 3 outer lever arm components between RINS1 and RINS 2. As can be seen from the convergence curves, the convergence speed of each component of the inner lever arm and the outer lever arm of the two sets of rotary inertial navigation systems is high, and the convergence process is stable. In order to quantitatively analyze the calibration precision, 6 times of repeated experiments are carried out on the online dynamic calibration of the inner lever arm and the outer lever arm of the two sets of rotary inertial navigation systems, and the average value and the standard deviation of the obtained estimation results are shown in table 1. As can be seen from Table 1, the calibration precision of the online dynamic calibration of the inner lever arm and the outer lever arm of the two sets of rotary inertial navigation systems provided by the invention is superior to 1mm, and the effectiveness of the invention is proved.
TABLE 1 Online dynamic calibration result of error parameters of inner lever arm and outer lever arm of two sets of rotary inertial navigation systems
Figure BDA0001713924650000086
Figure BDA0001713924650000091
In a word, the method can realize the online dynamic calibration of the errors of the inner lever arm and the outer lever arm of the two sets of rotary inertial navigation systems, and has important significance for improving the navigation information interaction and transmission precision of the two sets of rotary inertial navigation systems.
Portions of the invention not disclosed in detail are well within the skill of the art.
Although illustrative embodiments of the present invention have been described above to facilitate the understanding of the present invention by those skilled in the art, it should be understood that the present invention is not limited to the scope of the embodiments, and various changes may be made apparent to those skilled in the art as long as they are within the spirit and scope of the present invention as defined and defined by the appended claims, and all matters of the invention which utilize the inventive concepts are protected.

Claims (2)

1. An online dynamic calibration method for errors of an inner lever arm and an outer lever arm of two sets of rotary inertial navigation systems is characterized by comprising the following implementation steps:
step (1) establishing a measurement model of the error of an inner rod arm and an outer rod arm between two sets of rotary inertial navigation systems and the speed difference between the two sets of rotary inertial navigation systems;
step (2) based on the principle and the way of separating inner rods and arms of the two sets of rotary inertial navigation systems by model analysis in the step (1), designing two sets of rotary strategies of rotary inertial navigation;
step (3) respectively controlling the frame rotation of the No. 1 rotary inertial navigation system RINS1 and the No. 2 rotary inertial navigation system RINS2 by using the rotation strategy of the step (2), performing navigation calculation, and outputting two sets of speed information of rotary inertial navigation in real time;
step (4) calculating the speed difference of the two sets of rotational inertial navigation obtained in the step (3), and constructing a Kalman filter by using the measurement model in the step (1) to realize online dynamic calibration of errors of inner lever arms and outer lever arms of the two sets of rotational inertial navigation systems;
in the step (1), the building process of the measurement model of the difference between the error of the inner rod arm and the outer rod arm between the two sets of rotary inertial navigation systems and the speed between the two sets of rotary inertial navigation systems is as follows:
for the lever arm error model of the x accelerometer of the rotational inertial navigation system RINS1 No. 1, the spatial distance between the rotational inertial navigation system RINS1 No. 1 and the mass center of the carrier forms a group of outer lever arms, meanwhile, the x accelerometer and the IMU center form a group of inner lever arms, and when angular motion of the carrier and rotational motion of the rotational inertial navigation system RINS1 No. 1 around the frame exist, the sensitive acceleration of the x accelerometer is equal to the vector sum of the involved acceleration, the relative acceleration and the Coriolis acceleration;
the involved acceleration is:
Figure FDA0003057405470000011
in the formula (1), the vector
Figure FDA0003057405470000012
Further expressed as:
Figure FDA0003057405470000013
the relative acceleration is:
Figure FDA0003057405470000014
the coriolis acceleration is:
Figure FDA0003057405470000015
therefore, under the action of the inner lever arm and the outer lever arm, the acceleration error included in the acceleration information output by the x-accelerometer is as follows:
Figure FDA0003057405470000016
the above formula is expanded as:
Figure FDA0003057405470000021
in the formula (1) - (5),
Figure FDA0003057405470000022
frame rotation of carrier angular velocity and No. 1 rotary inertial navigation System RINS1 respectivelyThe angular velocity of the light beam is measured,
Figure FDA0003057405470000023
respectively a carrier angular velocity differential and a frame rotational angular velocity differential,
Figure FDA0003057405470000024
is an inner rod arm between an x accelerometer and the IMU center of a No. 1 rotational inertial navigation system RINS1,
Figure FDA0003057405470000025
is the lever arm between the x-accelerometer and the center of mass of the carrier,
Figure FDA0003057405470000026
is an outer lever arm between the IMU center and the carrier mass center of the No. 1 rotational inertial navigation system RINS1, and has the following components according to the vector synthesis principle
Figure FDA0003057405470000027
Simultaneous lever arm vector
Figure FDA0003057405470000028
Expressed in a spatial three-dimensional coordinate system as components along three coordinate axes, i.e.
Figure FDA0003057405470000029
Rx1In the lower corner of (1) x represents
Figure FDA00030574054700000210
Projection in x direction, 1 denotes the rotational inertial navigation system No. 1 RINS1, rxx1The first x in the subscript of (1) represents
Figure FDA00030574054700000211
Projection in the x direction, the second x represents the x accelerometer of the inertial navigation system No. 1, and 1 represents the rotational inertial navigation system No. 1 RINS 1;
similarly, the lever arm error of the x-accelerometer of the No. 2 rotational inertial navigation system RINS2 is:
Figure FDA00030574054700000212
in the formula (6), the reaction mixture is,
Figure FDA00030574054700000213
respectively the carrier angular velocity and the frame rotation angular velocity of the No. 2 rotational inertial navigation system RINS2,
Figure FDA00030574054700000214
respectively a carrier angular velocity differential and a frame rotational angular velocity differential,
Figure FDA00030574054700000215
is an inner rod arm between an x accelerometer and the IMU center of a No. 2 rotational inertial navigation system RINS2,
Figure FDA00030574054700000216
an outer lever arm between the IMU center of the No. 2 rotational inertial navigation system RINS2 and the carrier center of mass; in the same way, the method for preparing the composite material,
Figure FDA00030574054700000217
Rx2in the lower corner of (1) x represents
Figure FDA00030574054700000218
Projection in x-direction, 2 denotes the rotational inertial navigation System No. 2 (RINS2), rxx2The first x in the subscript of (1) represents
Figure FDA00030574054700000219
Projection in the x direction, the second x represents the x accelerometer of the inertial navigation system No. 2, and 2 represents the rotational inertial navigation system No. 2 RINS 2;
because the two sets of rotary inertial navigation systems are fixedly connected with the carrier at the same time, the No. 1 rotary inertial navigation system RINS1 and the No. 2 rotary inertial navigation system RINS2 are sensitive
Figure FDA00030574054700000220
Similarly, the difference between the formula (5) and the formula (6) is obtained to obtain the acceleration error of the two sets of rotational inertial navigation x accelerometers under the common action of the inner lever arm and the outer lever arm between systems as follows:
Figure FDA00030574054700000221
in the formula (7), the reaction mixture is,
Figure FDA00030574054700000222
is an outer lever arm vector between the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS 2;
further, a measurement model for obtaining the difference between the error of the inner lever arm and the error of the outer lever arm between the two sets of rotational inertial navigation x accelerometers and the speed between the two sets of rotational inertial navigation systems is as follows:
Figure FDA0003057405470000031
in the formula (8), the reaction mixture is,
Figure FDA0003057405470000032
a rotation transformation matrix from a sensitive axis coordinate system of the No. 1 rotation inertial navigation system RINS1 and the No. 2 rotation inertial navigation system RINS2 to a navigation coordinate system is shown,
Figure FDA0003057405470000033
represents the acceleration error caused by the lever arm in the No. 1 rotary inertial navigation system RINS1,
Figure FDA0003057405470000034
represents the acceleration error caused by the lever arm in the No. 2 rotary inertial navigation system RINS2,
Figure FDA0003057405470000035
denotes No. 1Acceleration error caused by an outer lever arm between the rotational inertial navigation system RINS1 and the rotational inertial navigation system RINS 2;
in the step (2), the design process for realizing the analysis process and the rotation strategy for separating the inner rod and the arm of each of the two sets of rotary inertial navigation systems is as follows:
1) analyzing the principle and the way of separating the inner rod and the arm of the two sets of rotary inertial navigation systems: the outer rod arm between the No. 1 rotary inertial navigation system RINS1 and the No. 2 rotary inertial navigation system RINS2 is obtained by the formula (7)
Figure FDA0003057405470000036
By angular movement of the carrier only
Figure FDA0003057405470000037
Exciting inner lever arm of No. 1 rotary inertial navigation system RINS1 and No. 2 rotary inertial navigation system RINS2
Figure FDA0003057405470000038
While being moved angularly by the carrier
Figure FDA0003057405470000039
And rotational movement of the frame
Figure FDA00030574054700000310
Excited, therefore, when there is angular movement of the carrier, i.e. when there is angular movement of the carrier
Figure FDA00030574054700000311
At the same time, the RINS1 and RINS2 have the rotation movement of the frame and satisfy
Figure FDA00030574054700000312
In time, realize the outer lever arm
Figure FDA00030574054700000313
Inner lever arm
Figure FDA00030574054700000314
Separation and estimation of;
2) the design principle and the specific implementation of the rotation strategy are as follows: the design of the rotation strategies of the No. 1 rotation inertial navigation system RINS1 and the No. 2 rotation inertial navigation system RINS2 needs to meet the requirement
Figure FDA00030574054700000315
Since the angular velocity is a vector with both magnitude and direction, there are three ways to provide different angular velocities: first, the rotational axis directions of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 are the same, but the rotational angular velocities are different; secondly, the rotational angular velocities of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 are the same, but the rotational axis directions are different; third, the rotational axis direction and the rotational angular velocity of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 are different, and the following three aspects are analyzed:
(a) the rotational axis directions of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 are the same, but the rotational angular velocities are different;
suppose that the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 both rotate around the inner frame axis, but the rotational angular velocities are different, namely the requirement of satisfying
Figure FDA00030574054700000316
In the meantime, the acceleration errors caused by the inner lever arm of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 are respectively as follows:
Figure FDA00030574054700000317
in the formula (9), rxx1,rxy1,rxz1、ryx1,ryy1,ryz1、rzx1,rzy1,rzz1Is 9 inner lever arm components of the No. 1 rotary inertial navigation system RINS1,
at this time, the rotation matrices of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 are respectively:
Figure FDA0003057405470000041
the equations (9) and (10) are substituted into the equation (7) and expanded, and the acceleration error under the common action of the inner rod arms of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 is obtained as follows:
Figure FDA0003057405470000042
in the formulae (9) to (11),
Figure FDA0003057405470000043
the rotation angles of the inner frame of the No. 1 rotary inertial navigation system RINS1 and the No. 2 rotary inertial navigation system RINS2 are respectively
Figure FDA0003057405470000044
And angular velocity of rotation
Figure FDA0003057405470000045
There is an integral relationship between, as follows:
Figure FDA0003057405470000046
obtained from the formula (11) and the formula (12) when
Figure FDA0003057405470000047
Rotation angle at different sizes
Figure FDA0003057405470000048
And a rotation matrix
Figure FDA0003057405470000049
Figure FDA00030574054700000410
The change periods of the two-way valve are different, and the separation of lever arms in a No. 1 rotational inertial navigation system RINS1 and a No. 2 rotational inertial navigation system RINS2 is realized according to the difference of the periods;
(b) the rotational angular velocities of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 are the same, but the rotational axis directions are different;
assuming that the No. 1 rotary inertial navigation system RINS1 rotates around the inner frame axis and the No. 2 rotary inertial navigation system RINS2 rotates around the middle frame axis, namely the requirement is met
Figure FDA00030574054700000411
And is
Figure FDA00030574054700000412
In the meantime, the acceleration errors caused by the inner lever arm of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 are respectively as follows:
Figure FDA00030574054700000413
at this time, the process of the present invention,
Figure FDA00030574054700000414
respectively expressed as:
Figure FDA00030574054700000415
wherein the content of the first and second substances,
Figure FDA00030574054700000510
indicates the rotation angle of the inner frame of the No. 1 rotary inertial navigation system RINS1,
Figure FDA00030574054700000511
The middle frame rotation angle of the No. 2 rotary inertial navigation system RINS2 is shown;
similarly, equations (13) and (14) are substituted into equation (7) and expanded to obtain the acceleration error under the common action of the inner lever arms of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 as follows:
Figure FDA0003057405470000051
as obtained from equation (15), when the rotational axis directions of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 are different, the inner lever arm component of the No. 1 rotational inertial navigation system RINS1 and the inner lever arm component of the No. 2 rotational inertial navigation system RINS2 are in the same direction
Figure FDA0003057405470000052
The system has sine and cosine, and realizes the separation of lever arms in a No. 1 rotary inertial navigation system RINS1 and a No. 2 rotary inertial navigation system RINS2 according to the difference of sine and cosine;
(c) the rotation axis direction and the rotation angular velocity of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 are different;
when the rotation axis direction and the rotation angular velocity of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 are different, that is, the former two implementation approaches are satisfied simultaneously, the previous analysis shows that the inner lever arm components of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 have both periodic difference and sine and cosine difference in the aspect of the acceleration error, and the separation of the inner lever arms of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 is realized according to the difference between the two aspects.
2. The online dynamic calibration method for the errors of the inner lever arm and the outer lever arm of the two rotary inertial navigation systems according to claim 1, characterized in that: in the step (4), the kalman filter is constructed as follows:
1) the state model of the kalman filter is:
Figure FDA0003057405470000053
in the formula (16), the compound represented by the formula,
Figure FDA0003057405470000054
inner lever arm for indicating No. 1 rotary inertial navigation system RINS1
Figure FDA0003057405470000055
The resulting error in the acceleration is, in turn,
Figure FDA0003057405470000056
inner lever arm for indicating No. 2 rotary inertial navigation system RINS2
Figure FDA0003057405470000057
The resulting error in the acceleration is, in turn,
Figure FDA0003057405470000058
represents an outer lever arm between the No. 1 rotary inertial navigation system RINS1 and the No. 2 rotary inertial navigation system RINS2
Figure FDA0003057405470000059
Induced acceleration error;
selecting the state variables as follows according to the state model:
Figure FDA0003057405470000061
wherein, delta phiE,δφN,δφUDifferences between an east platform deflection angle, a north platform deflection angle and a sky platform deflection angle of the No. 1 rotary inertial navigation system RINS1 and the No. 2 rotary inertial navigation system RINS2 are respectively; delta VE,δVNThe difference between the east speed and the north speed of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 respectively; epsilonx1,εy1,εz1、εx2,εy2,εz2No. 1 rotary inertial navigation system RINS1 and No. 2 rotary inertial navigation systemGyro drift of system RINS 2;
Figure FDA0003057405470000062
the accelerometers of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 have zero offset respectively; r isxx1,rxy1,rxz1、ryx1,ryy1,ryz1、rzx1,rzy1,rzz1Is 9 inner rod arm components, r, of No. 1 rotary inertial navigation system RINS1xx2,rxy2,rxz2、ryx2,ryy2,ryz2、rzx2,rzy2,rzz2Is 9 inner lever arm components, R, of No. 2 rotary inertial navigation system RINS2x,Ry,Rz3 outer lever arm components between No. 1 rotational inertial navigation System RINS1 and No. 2 rotational inertial navigation System RINS 2;
2) the measurement model of the kalman filter is:
Figure FDA0003057405470000063
in the formula (17), δ VE,δVNThe difference between the east speed and the north speed of the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS2 respectively; the INS1 and the INS2 in the lower corner mark respectively represent speed information output by the No. 1 rotational inertial navigation system RINS1 and the No. 2 rotational inertial navigation system RINS 2;
therefore, a Kalman filter is constructed by taking the speed difference of two sets of rotary inertial navigation systems as a measurement value, and taking the platform deflection angles and speed errors of the two sets of rotary inertial navigation systems, and the inner rod arms and the inter-system outer rod arms of the two sets of rotary inertial navigation systems as state quantities, so that the estimation of 9 inner rod arm components of the No. 1 rotary inertial navigation system RINS1, 9 inner rod arm components of the No. 2 rotary inertial navigation system RINS2 and 3 outer rod arm components between the No. 1 rotary inertial navigation system RINS1 and the No. 2 rotary inertial navigation system RINS2 is realized.
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