CN113503893A - Initial alignment algorithm of moving base inertial navigation system - Google Patents

Initial alignment algorithm of moving base inertial navigation system Download PDF

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CN113503893A
CN113503893A CN202110613569.5A CN202110613569A CN113503893A CN 113503893 A CN113503893 A CN 113503893A CN 202110613569 A CN202110613569 A CN 202110613569A CN 113503893 A CN113503893 A CN 113503893A
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coordinate system
carrier
representing
matrix
inertial navigation
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庄广琛
郭玉胜
王海军
裴新凯
王大元
王旒军
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Beijing Automation Control Equipment Institute BACEI
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Beijing Automation Control Equipment Institute BACEI
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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

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Abstract

The invention provides an initial alignment algorithm of a moving base inertial navigation system, which decomposes a dynamic initial attitude matrix into a time-varying part and a constant part through coordinate transformation, eliminates the influence of angular motion of a carrier by utilizing the self gyro integral of the inertial navigation system, and converts the solution of the dynamic initial attitude matrix into the solution of the constant matrix; eliminating carrier acceleration and speed errors by using carrier speed information measured by external equipment; and solving the optimal solution of the constant matrix by adopting a quaternion method. The algorithm separates the gravity component in the acceleration sensitively obtained by the inertial navigation system and the interference acceleration generated by angular motion and linear motion, solves the problem of the estimation of the optimal initial attitude under the condition of carrier motion, and improves the accuracy of the initial alignment under the dynamic condition.

Description

Initial alignment algorithm of moving base inertial navigation system
Technical Field
The invention belongs to the technical field of inertial navigation, and particularly relates to an initial alignment algorithm of a moving base inertial navigation system.
Background
The initial alignment of the inertial navigation system is one of the key technologies affecting the use performance of the system, and the accuracy and speed of the alignment are directly related to the accuracy and starting characteristics of the inertial system. With the gradual increase of the demand of the easy use of the navigation system in various industry fields, the demand of the inertial navigation system for completing high-precision initial alignment in a short time under a dynamic state is more and more strong.
The current common method is an alignment method based on gravity vectors, and the initial attitude of the inertial navigation system is obtained by calculating the rotation angle of the gravity vectors in an inertial space. By using recursion algorithms such as Kalman filtering, recursion least squares and the like, the real-time optimal estimation of the attitude can be realized. However, the calculation of the conventional gravity vector method depends on the accurate measurement of the inertial navigation system itself on the gravity acceleration, when the carrier has motion, the attitude cosine matrix is time-varying, and the gravity vector depends on the inertial navigation system itself and cannot be accurately measured, so that improvement needs to be performed on the method.
Disclosure of Invention
Aiming at the problem that acceleration generated by movement cannot be separated under the condition of a moving base in the existing gravity vector alignment algorithm, so that the calculation of a gravity vector is inaccurate, the invention provides an inertial navigation system initial alignment algorithm under the condition of the moving base, which separates gravity components in the acceleration obtained by an inertial navigation system in a sensitive manner and interference acceleration generated by angular movement and linear movement, and solves the problem of estimation of the optimal initial attitude under the condition of carrier movement.
The technical scheme adopted by the invention for solving the technical problems is as follows:
an initial alignment algorithm of a moving base inertial navigation system comprises the following steps
Decomposing the dynamic initial attitude matrix into a time-varying part and a constant part through coordinate transformation, eliminating the influence of angular motion of a carrier by utilizing the self gyro integral of an inertial navigation system, and converting the solution of the dynamic initial attitude matrix into the solution of the constant matrix;
eliminating carrier acceleration and speed errors by using carrier speed information measured by external equipment;
and solving the optimal solution of the constant matrix by adopting a quaternion method.
Further, the dynamic initial attitude matrix is decomposed into
Figure BDA0003096579820000021
Wherein e is an earth geocentric inertial coordinate system at the initial moment; e.g. of the type0Representing the earth geocentric inertial coordinate system fixedly connected with the earth at the current moment; i.e. i0Representing an inertial coordinate system at an initial moment; n is0Representing an initial time-of-day geographic coordinate system fixedly connected with the earth; n denotes the geographical coordinate system of the current time instant,
Figure BDA0003096579820000022
representing a carrier coordinate system at the initial moment, and b representing a carrier coordinate system at the current moment;
Figure BDA0003096579820000023
the rotation matrix for coordinate transformation represents a rotation matrix converted from a coordinate system of a subscript to a coordinate system of a superscript.
Further, the
Figure BDA0003096579820000024
Performing integral elimination angular motion on the output of the gyroscope through a strapdown inertial navigation attitude updating algorithm; the constant matrix to be solved is
Figure BDA0003096579820000025
Further, the method for eliminating acceleration and speed errors of the carrier by using the carrier speed information measured by the external equipment specifically comprises the following steps
S2.1, measuring the carrier speed v by adopting external equipment;
s2.2, according to the coordinate transformation, have
Figure BDA0003096579820000031
Differentiating it to obtain
Figure BDA0003096579820000032
Figure BDA0003096579820000033
Figure BDA0003096579820000034
Figure BDA0003096579820000035
Wherein v isbRepresenting the component of the carrier velocity v in the system of the carrier coordinate system b,
Figure BDA0003096579820000036
the specific force of the carrier relative to the inertial coordinate system i under the n coordinate system is shown,
Figure BDA0003096579820000037
representing the angular velocity of motion of the e-coordinate system relative to the i-coordinate system under the n-coordinate system,
Figure BDA0003096579820000038
representing the angular velocity of motion of the n-coordinate system relative to the e-coordinate system under the n-coordinate system,
Figure BDA0003096579820000039
representing the motion angular speed of the n coordinate system relative to the i coordinate system under the n coordinate system;
s2.3, the formula of S2.2 is arranged to obtain
Figure BDA00030965798200000310
Figure BDA00030965798200000311
Neglecting the rotation of the earth to obtain
Figure BDA00030965798200000312
Multiplication of both sides of the above formula
Figure BDA00030965798200000313
To obtain
Figure BDA00030965798200000314
Order to
Figure BDA00030965798200000315
Wherein,
Figure BDA00030965798200000316
and
Figure BDA00030965798200000317
respectively representing the measured value of the accelerometer under the carrier coordinate system and the theoretical value of the gravity acceleration under the inertial coordinate system when the carrier motion is not considered;
Figure BDA00030965798200000318
a matrix of rotations is represented, which is,
Figure BDA00030965798200000319
representing the specific force of the carrier in the b coordinate system relative to the inertial coordinate system i,
Figure BDA0003096579820000041
represents the angular velocity of motion of the b coordinate system relative to the i coordinate system under the b coordinate system, vbRepresenting the component of the carrier velocity v in the carrier coordinate system, gnRepresenting the component of gravity plus velocity in the n coordinate system.
Further, the method for solving the optimal solution of the constant matrix by using the quaternion method specifically comprises the following steps
S3.1, constant matrix to be solved
Figure BDA0003096579820000042
Marked as A ', constant matrix A' and attitude quaternion
Figure BDA0003096579820000043
Has a conversion relationship of
Figure BDA0003096579820000044
Figure BDA0003096579820000045
Wherein, theta is a rotation angle,
Figure BDA0003096579820000046
is a rotating shaft;
defining a loss function
Figure BDA0003096579820000047
Let g (a ') -1-L (a ') -tr [ a ' B ]T]Is obtained by
Figure BDA0003096579820000048
Wherein,
Figure BDA0003096579820000049
S＝B+BT；
constructing equations
Figure BDA00030965798200000410
Order to
Figure BDA00030965798200000411
Can obtain the product
Figure BDA00030965798200000412
S3.2, iteratively calculating the maximum characteristic root of K corresponding to each group of attitude matrixes according to the following formula
λmax,i+1＝λmax,i-p(λi)/p′(λi),i＝0,1,...
Figure BDA0003096579820000051
S3.3, rewriting the formula of the step S3.2 according to the Kalimett theorem
[(λ+σ)I-S]-1＝γ-1(αI+βS+S2)
Wherein α ═ λ2-σ2+κ，β＝λ-σ，γ＝α(λ+σ)-Δ，
Figure BDA0003096579820000052
κ ═ tr (adj (S)), Δ ═ S |, I is the identity matrix;
is obtained by calculation
Figure BDA0003096579820000053
The attitude-optimized solution of the constant matrix A' is
Figure BDA0003096579820000054
Wherein,
Figure BDA0003096579820000055
compared with the prior art, the invention has the beneficial effects that:
aiming at the problem that acceleration generated by base movement cannot be separated under the condition of a moving base in the traditional gravity vector alignment algorithm, so that gravity vector calculation is inaccurate, the invention provides the inertial navigation system initial alignment algorithm under the condition of the moving base, which separates gravity components in the acceleration obtained by the inertial navigation system sensitively and interference acceleration generated by angular movement and linear movement, solves the problem of optimal initial attitude estimation under the condition of carrier movement, and improves alignment accuracy.
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The accompanying drawings, which are included to provide a further understanding of the embodiments of the invention and are incorporated in and constitute a part of this specification, illustrate embodiments of the invention and together with the description serve to explain the principles of the invention. It is obvious that the drawings in the following description are only some embodiments of the invention, and that for a person skilled in the art, other drawings can be derived from them without inventive effort.
FIG. 1 is a coordinate relationship diagram provided by an embodiment of the present invention, wherein the left diagram is an initial time coordinate system, and the right diagram is a rotation ωieA post-t coordinate system;
fig. 2 is a posture curve of the lake test alignment process according to an embodiment of the present invention.
Detailed Description
The following provides a detailed description of specific embodiments of the present invention. In the following description, for purposes of explanation and not limitation, specific details are set forth in order to provide a thorough understanding of the present invention. However, it will be apparent to one skilled in the art that the present invention may be practiced in other embodiments that depart from these specific details.
It should be noted that, in order to avoid obscuring the present invention with unnecessary details, only the device structures and/or processing steps closely related to the scheme of the present invention are shown in the drawings, and other details not so related to the present invention are omitted.
The traditional gravity vector method mainly solves the problem of the carrierThe method has the advantages that the problem of optimal estimation of the initial attitude of the inertial navigation system under the static condition is solved, when the carrier moves, the attitude cosine matrix is time-varying, and the measured value of an accelerometer under a carrier coordinate system
Figure BDA0003096579820000062
The invention provides an improved initial alignment algorithm of a moving base inertial navigation system aiming at initial alignment of a moving base by depending on the fact that the inertial navigation system cannot accurately measure, which mainly comprises the following steps:
s1, decomposing the dynamic initial attitude matrix into a time-varying part and a constant part through coordinate transformation, eliminating the influence of angular motion of a carrier by utilizing the self gyro integral of the inertial navigation system, and converting the solution of the dynamic initial attitude matrix into the solution of the constant matrix;
s2, eliminating the acceleration and speed error of the carrier by using the carrier speed information measured by external equipment, and eliminating the influence of carrier linear motion;
and S3, solving the optimal solution of the constant matrix by adopting a quaternion method.
The invention is explained in detail below with reference to a specific embodiment.
The movement of the carrier is divided into two types, angular movement and linear movement. The influence of the two motions on the inertial navigation system is eliminated first, and then the attitude optimal estimation is carried out.
1. Dynamic initial attitude matrix
Figure BDA0003096579820000071
The method is decomposed into a time-varying part and a constant part, angular motion influence can be eliminated by utilizing the self gyroscope integral of the inertial navigation system, and a dynamic initial attitude matrix is subjected to
Figure BDA0003096579820000072
The solution of (2) is converted into a solution of the constant matrix. The specific method comprises the following steps:
the attitude cosine matrix can be divided into two matrix multiplication forms: the decomposition is carried out into two parts of time-varying part and constant, the time-varying part
Figure BDA0003096579820000073
Can be obtained by theoretical calculation and measurement, and the unknown part is in the constant part
Figure BDA0003096579820000074
In (1).
Figure BDA0003096579820000075
As shown in FIG. 1, wherein e0An earth geocentric inertial coordinate system at an initial moment; e represents the earth geocentric inertial coordinate system fixedly connected with the earth at the current moment; i.e. i0Representing an inertial coordinate system at an initial moment; n is0Representing an initial time geographic coordinate system fixedly connected with the earth; n represents a geographic coordinate system of the current time;
Figure BDA0003096579820000076
representing a carrier coordinate system at an initial moment; b denotes the current time carrier coordinate system. From the coordinate transformation, the time-varying part can be divided
Figure BDA0003096579820000077
Is decomposed into
Figure BDA0003096579820000078
Will be constant part
Figure BDA0003096579820000079
Is decomposed into
Figure BDA00030965798200000710
Wherein,
Figure BDA00030965798200000711
Figure BDA00030965798200000712
the expression meaning of each rotation matrix is as follows: the rotation matrix is transformed from the coordinate system of the subscript to the coordinate system of the superscript.
Wherein the cornerIn which the motion mainly affects the constant part
Figure BDA00030965798200000713
The gyroscope output can be integrated through a strapdown inertial navigation attitude updating algorithm, and further the angular motion influence is eliminated. At this time, the unknown part is left
Figure BDA00030965798200000714
For dynamic initial attitude matrix
Figure BDA0003096579820000081
Is converted into a solution constant matrix
Figure BDA0003096579820000082
2. The acceleration and speed errors of the carrier are eliminated by utilizing the carrier speed information measured by external equipment, namely the influence of linear motion is eliminated, and the specific method is as follows:
2.1, measuring the carrier speed v by adopting external equipment such as a GPS (global positioning system), an odometer and the like, and eliminating the acceleration generated by movement by utilizing external speed information.
2.2 according to the coordinate transformation, have
Figure BDA0003096579820000083
Differentiating it to obtain
Figure BDA0003096579820000084
Figure BDA0003096579820000085
Figure BDA0003096579820000086
Figure BDA0003096579820000087
Wherein the superscript denotes the coordinate system used for the calculation, e.g. vbRepresenting the component of the vector velocity v in the vector coordinate system b, vnRepresenting the component of the vehicle velocity v in the system of geographical coordinates n. In other similar terms, f represents specific force, omega represents angular motion, g represents gravitational acceleration, the upper and lower marks respectively represent coordinate system relations, a specific coordinate system is shown in figure 1,
Figure BDA0003096579820000088
representing the specific force of the carrier in relation to the inertial frame i in the n-frame,
Figure BDA0003096579820000089
representing the angular velocity of motion of the e-coordinate system relative to the i-coordinate system under the n-coordinate system,
Figure BDA00030965798200000810
representing the angular velocity of motion of the n-coordinate system relative to the e-coordinate system under the n-coordinate system,
Figure BDA00030965798200000811
representing the angular velocity of motion of the n-coordinate system relative to the i-coordinate system under the n-coordinate system.
2.3 the formula of the finishing step 2.2 can be obtained
Figure BDA00030965798200000812
Figure BDA0003096579820000091
2.4 in the formula (7),
Figure BDA0003096579820000092
representing the rotational angular velocity of the earth in the coordinate system of the carrier, which differs by several orders of magnitude with respect to the rotational velocity of the carrier, and neglecting here, equation (7) is approximated as
Figure BDA0003096579820000093
Multiply the left and right sides of the above formula simultaneously
Figure BDA0003096579820000094
To obtain
Figure BDA0003096579820000095
At this time, remove
Figure BDA0003096579820000096
Are all known externally, let
Figure BDA0003096579820000097
Wherein,
Figure BDA0003096579820000098
a matrix of rotations is represented, which is,
Figure BDA0003096579820000099
representing the specific force of the carrier in the b coordinate system relative to the inertial coordinate system i,
Figure BDA00030965798200000910
represents the angular velocity of motion of the b coordinate system relative to the i coordinate system under the b coordinate system, vbRepresenting the component of the carrier velocity v in the carrier coordinate system b, gnThe component of the gravitational acceleration in the n coordinate system is represented. At this time, the process of the present invention,
Figure BDA00030965798200000911
and
Figure BDA00030965798200000912
respectively representing the measured value of the accelerometer under the carrier coordinate system and the theoretical value of the gravity acceleration under the inertial coordinate system when the carrier motion is not considered.
Through the processing of the formula (10), the acceleration generated by the motion in the acceleration information of the inertial navigation measurement is removed, and only the acceleration generated by the gravity is reserved.
3. And solving the optimal solution of the constant matrix by adopting a quaternion method.
3.1 constant matrix to be solved
Figure BDA00030965798200000913
Marked as A ', constant matrix A' and attitude quaternion
Figure BDA00030965798200000914
Has a conversion relationship of
Figure BDA00030965798200000915
Wherein
Figure BDA0003096579820000101
Theta is a rotation angle of the rotary shaft,
Figure BDA0003096579820000102
is a rotating shaft.
To achieve an optimal estimate of the pose, the following loss function is defined:
Figure BDA0003096579820000103
order:
g(A′)＝1-L(A′)＝tr[A′BT] (14)
to achieve the minimum loss function, it is only necessary to satisfy g (A') max.
The formula (11) is introduced into formula (14) to obtain:
Figure BDA0003096579820000104
wherein,
Figure BDA0003096579820000105
each intermediate variable is
Figure BDA0003096579820000106
Figure BDA0003096579820000107
Figure BDA0003096579820000108
S＝B+BT (20)
Wherein,
Figure BDA0003096579820000111
and
Figure BDA0003096579820000112
respectively, the measured value of the accelerometer in the body coordinate system and the theoretical value of the gravity acceleration in the reference coordinate system, in the present invention,
Figure BDA0003096579820000113
and
Figure BDA0003096579820000114
the calculation is performed by using equation (10). Alpha is alphaiIs a weight coefficient, and
Figure BDA0003096579820000115
0＜αiand (3) less than 1, wherein n weight coefficients correspond to n groups of gravity vector measurement values. Characteristic value lambda of KjAnd a feature vector qjWherein j is 1,2,3, 4.
Having unique constraints on elements of quaternion
Figure BDA0003096579820000116
To find the maximum value of equation (15) under the constraint of equation (21), the equation is reconstructed:
Figure BDA0003096579820000117
order to
Figure BDA0003096579820000118
Can obtain the product
Figure BDA0003096579820000119
As can be seen from the above formula analysis, λ is a characteristic root of K,
Figure BDA00030965798200001110
are corresponding feature vectors and thus
Figure BDA00030965798200001111
Is an optimal estimate of attitude.
3.2, maximum one λ of all eigenvalues of KmaxSo 1 can be used as the initial value to perform iterative calculation to obtain the maximum eigenvalue λ of Kmax. Will be lambdamax,0Iteration is carried out with the following formula as 1:
λmax,i+1＝λmax,i-p(λi)/p′(λi),i＝0,1,... (24)
wherein
Figure BDA00030965798200001112
3.3, in order to increase the speed and stability of the calculation, according to the Karley Hamilton theorem, the matrix part in the formula (25) is rewritten into
[(λ+σ)I-S]-1＝γ-1(αI+βS+S2) (26)
Wherein α ═ λ2-σ2+ κ, β ═ λ - σ, γ ═ α (λ + σ) - Δ, where
Figure BDA0003096579820000121
κ ═ tr (adj (S)), Δ ═ S |, and I is an identity matrix.
Substitution of α, β and γ into formula (25) can give:
p(λ)＝λ4-(a+b)λ2-cλ+(ab+cσ-d)＝0 (27)
wherein a ═ σ2-κ，
Figure BDA0003096579820000122
This gives:
Figure BDA0003096579820000123
from this, the attitude-optimized solution of the constant matrix a' can be obtained:
Figure BDA0003096579820000124
wherein,
Figure BDA0003096579820000125
solving the equations (24) and (29) to obtain the optimal attitude estimation under the condition of the moving base.
The method effectively separates the gravity component in the acceleration obtained by the sensing of the guide system and the interference acceleration generated by the angular motion and the linear motion, and solves the problem of the estimation of the optimal initial attitude under the condition of carrier motion.
The precision indexes of the optical fiber strapdown inertial navigation system are as follows: the gyro drifts 0.05 degree/h and walks randomly
Figure BDA0003096579820000126
Accelerometer zero 100 μ g, random walk
Figure BDA0003096579820000127
The lake trial alignment attitude error is shown in fig. 2. Alignment accuracy pairs for the three bars are shown in table 1.
TABLE 1 inertial navigation System initial alignment accuracy
Figure BDA0003096579820000128
Figure BDA0003096579820000131
The initial alignment algorithm of the moving base inertial navigation system provided by the invention can quickly complete initial alignment under a dynamic condition, and the alignment precision is improved by about 50% compared with the prior method.
Features that are described and/or illustrated above with respect to one embodiment may be used in the same way or in a similar way in one or more other embodiments and/or in combination with or instead of the features of the other embodiments.
It should be emphasized that the term "comprises/comprising" when used herein, is taken to specify the presence of stated features, integers, steps or components but does not preclude the presence or addition of one or more other features, integers, steps, components or groups thereof.
The many features and advantages of these embodiments are apparent from the detailed specification, and thus, it is intended by the appended claims to cover all such features and advantages of these embodiments which fall within the true spirit and scope thereof. Further, since numerous modifications and changes will readily occur to those skilled in the art, it is not desired to limit the embodiments of the invention to the exact construction and operation illustrated and described, and accordingly, all suitable modifications and equivalents may be resorted to, falling within the scope thereof.
The above description is only a preferred embodiment of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, or improvement made within the spirit and principle of the present invention should be included in the protection scope of the present invention.
The invention has not been described in detail and is in part known to those of skill in the art.

Claims (5)

1. An initial alignment algorithm of a moving base inertial navigation system is characterized by comprising the following steps
Decomposing the dynamic initial attitude matrix into a time-varying part and a constant part through coordinate transformation, eliminating the influence of angular motion of a carrier by utilizing the self gyro integral of an inertial navigation system, and converting the solution of the dynamic initial attitude matrix into the solution of the constant matrix;
eliminating carrier acceleration and speed errors by using carrier speed information measured by external equipment;
and solving the optimal solution of the constant matrix by adopting a quaternion method.
2. The dynamic-base inertial navigation system initial alignment algorithm of claim 1, wherein the dynamic initial attitude matrix is decomposed into
Figure FDA0003096579810000011
Wherein e is an earth geocentric inertial coordinate system at the initial moment; e.g. of the type0Representing the earth geocentric inertial coordinate system fixedly connected with the earth at the current moment; i.e. i0Representing an inertial coordinate system at an initial moment; n is0Representing an initial time geographic coordinate system fixedly connected with the earth; n denotes the geographical coordinate system of the current time instant,
Figure FDA0003096579810000012
representing a carrier coordinate system at the initial moment, and b representing the carrier coordinate system;
Figure FDA0003096579810000013
the rotation matrix for coordinate transformation represents a rotation matrix converted from a coordinate system of a subscript to a coordinate system of a superscript.
3. The dynamic base inertial navigation system initial alignment algorithm of claim 2, wherein the initial alignment algorithm is based on a linear interpolation of the initial alignment algorithm
Figure FDA0003096579810000014
Performing integral elimination angular motion on the output of the gyroscope through a strapdown inertial navigation attitude updating algorithm; the constant matrix to be solved is
Figure FDA0003096579810000015
4. The initial alignment algorithm for the moving base inertial navigation system according to claim 3, wherein the method for eliminating acceleration and velocity errors of the carrier by using the carrier velocity information measured by the external device specifically comprises the following steps
S2.1, measuring the carrier speed v by adopting external equipment;
s2.2, according to the coordinate transformation, have
Figure FDA0003096579810000021
Differentiating it to obtain
Figure FDA0003096579810000022
Figure FDA0003096579810000023
Figure FDA0003096579810000024
Figure FDA0003096579810000025
Wherein v represents the velocity of the carrier,
Figure FDA0003096579810000026
representing the specific force of the carrier in relation to the inertial frame i in the n-frame,
Figure FDA0003096579810000027
representing the angular velocity of motion of the e-coordinate system relative to the i-coordinate system under the n-coordinate system,
Figure FDA0003096579810000028
representing the angular velocity of movement of the e-coordinate system relative to the n-coordinate system under the n-coordinate system,
Figure FDA0003096579810000029
representing the motion angular speed of the i coordinate system relative to the n coordinate system under the n coordinate system;
s2.3, the formula of S2.2 is arranged to obtain
Figure FDA00030965798100000210
Figure FDA00030965798100000211
Neglecting the rotation of the earth to obtain
Figure FDA00030965798100000212
Multiplication of both sides of the above formula
Figure FDA00030965798100000213
To obtain
Figure FDA00030965798100000214
Order to
Figure FDA00030965798100000215
Wherein,
Figure FDA00030965798100000216
and
Figure FDA00030965798100000217
respectively representing the measured value of the accelerometer under the carrier coordinate system and the theoretical value of the gravity acceleration under the inertial coordinate system when the carrier motion is not considered;
Figure FDA0003096579810000031
a matrix of rotations is represented, which is,
Figure FDA0003096579810000032
representing the specific force of the carrier in the b coordinate system relative to the inertial coordinate system i,
Figure FDA0003096579810000033
represents the angular velocity of motion of the b coordinate system relative to the i coordinate system under the b coordinate system, vbRepresenting the component of the carrier velocity v in the carrier coordinate system, gnRepresenting the component of the gravitational acceleration in the n coordinate system.
5. The initial alignment algorithm for the inertial navigation system with moving base according to claim 4, wherein the method for solving the optimal solution of the constant matrix by using the quaternion method specifically comprises the following steps
S3.1, constant matrix to be solved
Figure FDA0003096579810000034
Marked as A ', constant matrix A' and attitude quaternion
Figure FDA00030965798100000314
Has a conversion relation of
Figure FDA0003096579810000035
Figure FDA0003096579810000036
Wherein, theta is a rotation angle,
Figure FDA0003096579810000037
is a rotating shaft;
defining a loss function
Figure FDA0003096579810000038
Let g (a ') -1-L (a ') -tr [ a ' B ]T]Is obtained by
Figure FDA0003096579810000039
Wherein,
Figure FDA00030965798100000310
S＝B+BT；
constructing equations
Figure FDA00030965798100000311
Order to
Figure FDA00030965798100000312
Can obtain the product
Figure FDA00030965798100000313
S3.2, iteratively calculating the maximum characteristic root of K corresponding to each group of attitude matrixes according to the following formula
λmax,i+1＝λmax,i-p(λi)/p′(λi),i＝0,1,...
Figure FDA0003096579810000041
S3.3, rewriting the formula of the step S3.2 according to the Kalimett theorem
[(λ+σ)I-S]-1＝γ-1(αI+βS+S2)
Wherein α ═ λ2-σ2+κ，β＝λ-σ，γ＝α(λ+σ)-Δ，
Figure FDA0003096579810000042
κ ═ tr (adj (S)), Δ ═ S |, I is the identity matrix;
is obtained by calculation
Figure FDA0003096579810000043
The attitude-optimized solution of the constant matrix A' is
Figure FDA0003096579810000044
Wherein,
Figure FDA0003096579810000045
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