CN112033438A - Shaking base self-alignment method based on speed fitting - Google Patents

Shaking base self-alignment method based on speed fitting Download PDF

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CN112033438A
CN112033438A CN202010831817.9A CN202010831817A CN112033438A CN 112033438 A CN112033438 A CN 112033438A CN 202010831817 A CN202010831817 A CN 202010831817A CN 112033438 A CN112033438 A CN 112033438A
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inertial navigation
coordinate system
speed
fitting
velocity
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CN112033438B (en
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胡华峰
刘明
施丽娟
李星善
张阳艳
李旦
穆杰
游浪
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General Designing Institute of Hubei Space Technology Academy
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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 relates to the technical field of inertial navigation, in particular to a shaking base self-alignment method based on speed fitting. The method comprises the following steps: collecting specific force f of inertial measurement unit IMU in system B of body coordinate systemBAnd collecting the projection of the angular velocity of the B system relative to the I system of the earth center inertial coordinate system under the B system
Figure DDA0002638273730000011
According to fBAnd
Figure DDA0002638273730000012
obtaining a posture transformation matrix from a B system of the IMU to an N system of a northeast geographic coordinate system
Figure DDA0002638273730000013
By using
Figure DDA0002638273730000014
Figure DDA0002638273730000015
And fBPerforming reverse pure inertial navigation resolving to obtain pure inertial navigation speed of the IMU at each moment; fitting the pure inertial navigation speed to obtain a fitting inertial navigation speed; obtaining the shaking speed of the IMU at each moment according to the pure inertial navigation speed and the fitting inertial navigation speed, and obtaining a corrected posture conversion matrix according to the shaking speed
Figure DDA0002638273730000016
The problem that the alignment precision is not high in the prior art due to the fact that the shaking base is aligned based on the zero-speed assumed condition or the external high-precision information is used for assisting can be solved, and the problem that extra equipment needs to be added in the prior art.

Description

Shaking base self-alignment method based on speed fitting
Technical Field
The invention relates to the technical field of inertial navigation, in particular to a shaking base self-alignment method based on speed fitting.
Background
The N system (INS) of the inertial northeast geographic coordinate system navigation system can provide completely autonomous navigation information, has the advantages of short reaction time, high reliability, small volume, light weight and the like, is widely applied to the military and civil navigation fields of airplanes, ships, missiles and the like, and has important national defense significance and great economic benefit.
The initial alignment provides an initial attitude for inertial navigation, the accuracy of the initial alignment directly influences the accuracy of subsequent inertial navigation of navigation, an external aiming mode is traditionally used for providing an initial direction for the initial alignment of the inertial navigation, and in recent years, with the development of inertial devices, high-accuracy rapid self-alignment becomes a key for guaranteeing the initial alignment as a core technology of an inertial northeast geographic coordinate system navigation system N system.
For high-precision fast self-alignment, in addition to the requirement for alignment precision, the alignment time needs to be shortened, and the alignment precision and the alignment time are interrelated and mutually restricted, and generally a longer alignment time is required to ensure the alignment precision. In addition, self-alignment is required to meet various actual environment requirements, and different alignment environments also affect the convergence of alignment, and finally affect the alignment accuracy. Under the condition of slight shaking (quasi-static base), such as vehicle-mounted shaking, inertial system alignment is usually adopted, the inertial system alignment method can overcome interference, theoretically, the inertial system alignment can completely overcome angular shaking, but is sensitive to line shaking interference. Under the condition of obvious shaking, such as wind waves and strong gust interference on a ship, the alignment precision and convergence time of the inertial system are obviously influenced, so that the self-alignment method under the condition of shaking the base becomes a hotspot for research.
At present, in the prior art, shaking base alignment is mostly carried out based on a zero-speed assumed condition, or external high-precision information is used for assistance, the former has the problem of low alignment precision, the latter needs to add additional equipment, and the latter has higher requirements on speed measurement precision.
Disclosure of Invention
Aiming at the defects in the prior art, the invention aims to provide a shaking base self-alignment method based on speed fitting, which can solve the problems that the shaking base alignment is performed based on a zero-speed assumed condition or is assisted by external high-precision information in the prior art, the former has low alignment precision, and the latter needs additional equipment.
In order to achieve the above purposes, the technical scheme adopted by the invention is as follows:
the invention provides a shaking base self-alignment method based on speed fitting, which comprises the following steps of:
collecting specific force f of inertial measurement unit IMU in system B of body coordinate systemBAnd collecting the projection of the angular velocity of the B system relative to the I system of the earth center inertial coordinate system under the B system
Figure BDA0002638273710000021
According to fBAnd
Figure BDA0002638273710000022
obtaining a posture transformation matrix from a B system of the IMU to an N system of a northeast geographic coordinate system
Figure BDA0002638273710000023
By using
Figure BDA0002638273710000024
And fBPerforming reverse pure inertial navigation resolving to obtain pure inertial navigation speed of the IMU at each moment;
fitting the pure inertial navigation speed to obtain a fitting inertial navigation speed;
obtaining the shaking speed of the IMU at each moment according to the pure inertial navigation speed and the fitting inertial navigation speed, and obtaining a corrected posture conversion matrix according to the shaking speed
Figure BDA0002638273710000025
On the basis of the technical scheme, according to fBAnd
Figure BDA0002638273710000026
obtaining an attitude transformation matrix from a B system to an N system of an IMU
Figure BDA0002638273710000027
The method specifically comprises the following steps:
obtaining an initial time earth inertia coordinate system E'I0Attitude transformation matrix to N system
Figure BDA0002638273710000028
According to
Figure BDA0002638273710000031
And fBObtaining a strapdown inertial navigation inertial coordinate system B of a system B at the current time relative to the initial timeI0Of the rotation matrix
Figure BDA0002638273710000032
And an initial moment strapdown inertial navigation inertial coordinate system BI0Specific speed of
Figure BDA0002638273710000033
Based on
Figure BDA0002638273710000034
And
Figure BDA0002638273710000035
obtaining an initial moment strapdown inertial navigation inertial coordinate system BI0Earth inertial coordinate system to initial timeE′I0Attitude transformation matrix of
Figure BDA0002638273710000036
According to
Figure BDA0002638273710000037
And
Figure BDA0002638273710000038
obtaining an initial attitude transformation matrix of the IMU
Figure BDA0002638273710000039
Based on the technical scheme, the earth inertia coordinate system E 'at the initial time is obtained'I0Attitude transformation matrix to N system
Figure BDA00026382737100000310
The method specifically comprises the following steps:
according to the formula
Figure BDA00026382737100000311
Determining
Figure BDA00026382737100000312
Wherein L is0To align the start t0Moment strapdown inertial measurement unitLatitude, ωIEIs the rotational angular velocity of the earth.
On the basis of the technical scheme, the method is as follows
Figure BDA00026382737100000313
And fBObtaining a strapdown inertial navigation inertial coordinate system B of a system B at the current time relative to the initial timeI0Of the rotation matrix
Figure BDA00026382737100000314
And an initial moment strapdown inertial navigation inertial coordinate system BI0Specific speed of
Figure BDA00026382737100000315
The method specifically comprises the following steps:
according to
Figure BDA00026382737100000316
Updating through strapdown inertial navigation attitude
Figure BDA00026382737100000317
Calculating a strapdown inertial navigation inertial coordinate system B of the system B at the current time relative to the initial timeI0Of the rotation matrix
Figure BDA00026382737100000323
Wherein the content of the first and second substances,
Figure BDA00026382737100000318
i is an identity matrix;
according to the formula
Figure BDA00026382737100000319
Calculating to obtain an initial moment strapdown inertial navigation inertial coordinate system BI0Specific speed of
Figure BDA00026382737100000320
τ is a variable of the integral expression.
On the basis of the technical scheme, the method is based on
Figure BDA00026382737100000321
And
Figure BDA00026382737100000322
obtaining an initial moment strapdown inertial navigation inertial coordinate system BI0To initial time earth inertia coordinate system E'I0Attitude transformation matrix of
Figure BDA0002638273710000041
The method specifically comprises the following steps:
according to the formula
Figure BDA0002638273710000042
Calculating to obtain an initial time earth inertia coordinate system E'I0Specific speed of
Figure BDA0002638273710000043
Wherein f isNIs a specific force under the N series,
Figure BDA0002638273710000044
is composed of
Figure BDA0002638273710000045
Transposing;
strapdown inertial navigation inertial coordinate system B based on initial timeI0Specific speed of
Figure BDA0002638273710000046
And an initial time earth inertia coordinate system E'I0Specific speed of
Figure BDA0002638273710000047
According to the formula
Figure BDA0002638273710000048
Calculating to obtain an initial moment strapdown inertial navigation inertial coordinate system BI0Earth inertial coordinate system to initial timeE′I0Attitude transformation matrix of
Figure BDA0002638273710000049
Wherein the content of the first and second substances,
Figure BDA00026382737100000410
is composed of
Figure BDA00026382737100000411
Middle t0Take 0, t and t1The integral of (a) is calculated,
Figure BDA00026382737100000412
is t0Take 0, t and t2Integral of (1);
Figure BDA00026382737100000413
is composed of
Figure BDA00026382737100000414
Middle t0Take 0, t and t1The integral of (a) is calculated,
Figure BDA00026382737100000415
is t0Take 0, t and t2Integral of, t1＝1/2*t2And tau is a variable of the integral expression.
On the basis of the technical scheme, the method is as follows
Figure BDA00026382737100000416
And
Figure BDA00026382737100000417
obtaining an initial attitude transformation matrix of the IMU
Figure BDA00026382737100000418
The method specifically comprises the following steps:
according to the formula
Figure BDA00026382737100000419
Obtaining an initial time earth inertia coordinate system E'I0Attitude transformation matrix to B system
Figure BDA00026382737100000420
According to the formula
Figure BDA00026382737100000421
Calculating to obtain an initial attitude transformation matrix of the IMU
Figure BDA00026382737100000422
On the basis of the technical scheme, the utilization
Figure BDA0002638273710000051
And fBThe method for calculating reverse pure inertial navigation to obtain the pure inertial navigation speed at each moment comprises the following steps:
according to the formula
Figure BDA0002638273710000052
Calculating to obtain the pure inertial navigation speed v at each momentN，
Wherein, the superscript represents the differentiation of the parameter, the section of No. book represents the parameter which needs to be inverted in the reverse solving process,
Figure BDA0002638273710000053
is composed of
Figure BDA0002638273710000054
The process is carried out in a reverse manner,
Figure BDA0002638273710000055
is v isNThe process of (1) is carried out in a reverse manner,
Figure BDA0002638273710000056
in the form of a matrix of positions,
Figure BDA0002638273710000057
l is the latitude of the current moment, and lambda is the longitude of the current moment;
Figure BDA0002638273710000058
the projection of the earth rotation angular velocity in an E system of an earth coordinate system after the earth rotation angular velocity is inverted and the projection of the earth rotation angular velocity in an N system of a northeast geographical coordinate system
Figure BDA0002638273710000059
Is the angular velocity of N relative to E,
Figure BDA00026382737100000510
h is the height, R is the radius of the earth,
Figure BDA00026382737100000511
and
Figure BDA00026382737100000512
is the pure inertial velocity
Figure BDA00026382737100000513
X, Y and a component in the Z direction, g, under NN＝[0 0 -g]TG is the local gravitational acceleration; h is the height of the glass substrate,
Figure BDA00026382737100000514
is the pure inertial velocity vNThe Z-direction component of (a).
On the basis of the technical scheme, fitting the pure inertial navigation speed to obtain a fitting inertial navigation speed specifically comprises:
pure inertial navigation velocity v for each momentNPerforming quadratic fitting to obtain a basic fitting equation as follows:
Figure BDA00026382737100000515
wherein a, b and c are fitting coefficients.
On the basis of the technical scheme, the obtaining of the shaking speed at each moment according to the pure inertial navigation speed and the fitting inertial navigation speed specifically comprises:
according to the formula
Figure BDA0002638273710000061
Calculating the shaking speed at each time
Figure BDA0002638273710000062
On the basis of the technical scheme, the corrected posture conversion matrix is obtained according to the shaking speed
Figure BDA0002638273710000063
The method specifically comprises the following steps:
according to the formula
Figure BDA0002638273710000064
Is calculated to obtain
Figure BDA0002638273710000065
Wherein the content of the first and second substances,
Figure BDA0002638273710000066
according to
Figure BDA0002638273710000067
And
Figure BDA0002638273710000068
is corrected
Figure BDA0002638273710000069
According to the formula
Figure BDA00026382737100000610
To obtain
Figure BDA00026382737100000611
According to the formula
Figure BDA00026382737100000612
To obtain
Figure BDA00026382737100000613
Compared with the prior art, the invention has the advantages that: a shaking base self-alignment method based on speed fitting is a moving base self-alignment method independent of an external speed reference, navigation resolving is carried out by using original data output by inertial navigation after coarse alignment is completed, inertial navigation self errors and shaking speeds are separated through fitting, moving base alignment is carried out by using the separated shaking speeds, and alignment errors caused by the fact that the speed is assumed to be zero in traditional inertial system alignment are effectively solved. And no extra speed auxiliary equipment is needed, and engineering application can be conveniently carried out.
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In order to more clearly illustrate the technical solutions in the embodiments of the present application, the drawings needed to be used in the description of the embodiments are briefly introduced below, and it is obvious that the drawings in the following description are only some embodiments of the present application, and it is obvious for those skilled in the art to obtain other drawings based on these drawings without creative efforts.
FIG. 1 is a flow chart of a method for shaking base self-alignment based on velocity fitting according to an embodiment of the present invention.
Detailed Description
In order to make the objects, technical solutions and advantages of the embodiments of the present application clearer, the technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application, and it is obvious that the described embodiments are some embodiments of the present application, but not all embodiments. All other embodiments, which can be derived by a person skilled in the art from the embodiments given herein without making any creative effort, shall fall within the protection scope of the present application.
Embodiments of the present invention will be described in further detail below with reference to the accompanying drawings. FIG. 1 is a flow chart of a method for shaking base self-alignment based on velocity fitting according to an embodiment of the present invention.
As shown in FIG. 1, the invention provides a shaking base self-alignment method based on speed fitting, which comprises the following steps:
s1: collecting the ratio of an inertial measurement unit IMU in a system B of a body coordinate systemForce fBAnd collecting the projection of the angular velocity of the body coordinate system B relative to the earth center inertial coordinate system I under the B system
Figure BDA0002638273710000071
In this embodiment, the gyroscope output body coordinate system B of the IMU is projected under the system B relative to the angular velocity of the inertial coordinate system I of the earth center
Figure BDA0002638273710000072
The accelerometer of the IMU outputs a specific force f under a body coordinate system B systemBThe geocentric inertial coordinate system: the origin is located at the center of the earth, and the directions of the coordinate axes are unchanged in the inertial space.
S2: according to fBAnd
Figure BDA0002638273710000073
obtaining a posture transformation matrix from a B system of the IMU to an N system of a northeast geographic coordinate system
Figure BDA0002638273710000074
In this embodiment, the step S2 specifically includes:
s21: obtaining an initial time earth inertia coordinate system E'I0Attitude transformation matrix to N system
Figure BDA0002638273710000075
The step S21 specifically includes:
according to the formula
Figure BDA0002638273710000081
Determining
Figure BDA0002638273710000082
Wherein L is0To align the start t0Latitude, omega of moment strapdown inertial unitIEIs the rotational angular velocity of the earth.
S22: according to
Figure BDA0002638273710000083
And fBObtaining a strapdown inertial navigation inertial coordinate system B of a system B at the current time relative to the initial timeI0Of the rotation matrix
Figure BDA0002638273710000084
And an initial moment strapdown inertial navigation inertial coordinate system BI0Specific speed of
Figure BDA0002638273710000085
S22: the method specifically comprises the following steps:
s221: according to
Figure BDA0002638273710000086
Updating through strapdown inertial navigation attitude
Figure BDA0002638273710000087
Calculating a strapdown inertial navigation inertial coordinate system B of the system B at the current time relative to the initial timeI0Of the rotation matrix
Figure BDA0002638273710000088
Wherein the content of the first and second substances,
Figure BDA0002638273710000089
i is an identity matrix;
s222: according to the formula
Figure BDA00026382737100000810
Calculating to obtain an initial moment strapdown inertial navigation inertial coordinate system BI0Specific speed of
Figure BDA00026382737100000811
τ is a variable of the integral expression.
In the present embodiment, the specific velocity is an integral of a specific force, which is one unit of acceleration, and the integral is a velocity, and the integral thereof is a specific velocity.
S23: based on
Figure BDA00026382737100000812
And
Figure BDA00026382737100000813
obtaining an initial moment strapdown inertial navigation inertial coordinate system BI0To initial time earth inertia coordinate system E'I0Attitude transformation matrix of
Figure BDA00026382737100000814
Preferably, step S23 specifically includes:
s231: according to the formula
Figure BDA00026382737100000815
Calculating to obtain an initial time earth inertia coordinate system E'I0Specific speed of
Figure BDA00026382737100000816
Wherein f isNIs a specific force under the N series,
Figure BDA00026382737100000817
is composed of
Figure BDA00026382737100000818
The transpose of (a) is performed,
Figure BDA00026382737100000819
s232: strapdown inertial navigation inertial coordinate system B based on initial timeI0Specific speed of
Figure BDA0002638273710000091
And an initial time earth inertia coordinate system E'I0Specific speed of
Figure BDA0002638273710000092
According to the formula
Figure BDA0002638273710000093
Calculate to obtain the initialInertial coordinate system B of strap-down inertial navigation at starting timeI0To initial time earth inertia coordinate system E'I0Attitude transformation matrix of
Figure BDA0002638273710000094
Wherein the content of the first and second substances,
Figure BDA0002638273710000095
is composed of
Figure BDA0002638273710000096
Middle t0Take 0, t and t1The integral of (a) is calculated,
Figure BDA0002638273710000097
is t0Take 0, t and t2Integral of (1);
Figure BDA0002638273710000098
is composed of
Figure BDA0002638273710000099
Middle t0Take 0, t and t1The integral of (a) is calculated,
Figure BDA00026382737100000910
is t0Take 0, t and t2Integral of, t1＝1/2*t2And tau is a variable of the integral expression.
In the present embodiment, t2And taking the current time t.
S24: according to
Figure BDA00026382737100000911
And
Figure BDA00026382737100000912
obtaining an initial attitude transformation matrix of the IMU
Figure BDA00026382737100000913
Step S24, specifically including the steps of:
s241: according to the formula
Figure BDA00026382737100000914
Obtaining an initial time earth inertia coordinate system E'I0Attitude transformation matrix to B system
Figure BDA00026382737100000915
S242: according to the formula
Figure BDA00026382737100000916
Calculating to obtain an initial attitude transformation matrix of the IMU
Figure BDA00026382737100000917
S3: by using
Figure BDA00026382737100000918
And fBAnd (4) performing reverse pure inertial navigation resolving to obtain the pure inertial navigation speed of the IMU at each moment.
Preferably, step S3 specifically includes the following steps:
inertial navigation is well known in the art, and the specific differential equation is as follows, superscript · denotes the differential of the parameter:
according to the formula
Figure BDA0002638273710000101
Calculating to obtain the pure inertial navigation speed v at each momentN，
Figure BDA0002638273710000102
Is composed of
Figure BDA0002638273710000103
The value of the sampling instant of (c).
Wherein, the equation of either the equation or the equation of the equation is used to calculate the inverse value,
Figure BDA0002638273710000104
is composed of
Figure BDA0002638273710000105
The process is carried out in a reverse manner,
Figure BDA0002638273710000106
is v isNThe process of (1) is carried out in a reverse manner,
Figure BDA0002638273710000107
in the form of a matrix of positions,
Figure BDA0002638273710000108
l is the latitude of the current moment, and lambda is the longitude of the current moment;
Figure BDA0002638273710000109
the projection of the earth under the E system of the earth coordinate system after the inversion of the rotational angular velocity of the earth,
Figure BDA00026382737100001010
is the angular velocity of N relative to E,
Figure BDA00026382737100001017
h is the height, R is the radius of the earth,
Figure BDA00026382737100001011
and
Figure BDA00026382737100001012
is the pure inertial velocity
Figure BDA00026382737100001013
X, Y and a component in the Z direction, g, under NN＝[0 0 -g]TG is the local gravitational acceleration; h is the height of the glass substrate,
Figure BDA00026382737100001014
is the pure inertial velocity vNThe projection of the earth rotation angular velocity under the N system of the northeast geographic coordinate system
Figure BDA00026382737100001015
S4: and fitting the pure inertial navigation speed to obtain a fitting inertial navigation speed.
Preferably, step S4 specifically includes: pure inertial navigation velocity v for each momentNPerforming quadratic fitting to obtain a basic fitting equation as follows:
Figure BDA00026382737100001016
wherein a, b and c are fitting coefficients.
S5: obtaining the shaking speed of the IMU at each moment according to the pure inertial navigation speed and the fitting inertial navigation speed, and obtaining a corrected posture conversion matrix according to the shaking speed
Figure BDA0002638273710000111
Preferably, step S5 specifically includes:
according to the formula
Figure BDA0002638273710000112
Calculating the shaking speed at each time
Figure BDA0002638273710000113
According to the formula
Figure BDA0002638273710000114
Is calculated to obtain
Figure BDA0002638273710000115
Wherein the content of the first and second substances,
Figure BDA0002638273710000116
is an intermediate amount of
Figure BDA0002638273710000117
And
Figure BDA0002638273710000118
to sum, i.e.
Figure BDA0002638273710000119
According to
Figure BDA00026382737100001110
And
Figure BDA00026382737100001111
is corrected
Figure BDA00026382737100001112
According to the formula
Figure BDA00026382737100001113
To obtain
Figure BDA00026382737100001114
According to the formula
Figure BDA00026382737100001115
To obtain
Figure BDA00026382737100001116
In this embodiment, the method further includes the following steps according to the result of the alignment by using the moving base and the acquired IMU raw data: and carrying out pure inertial navigation calculation on the gyroscope output data and the accelerometer output data to obtain position and attitude information at each moment.
The specific calculation formula is as follows,
Figure BDA00026382737100001117
wherein the content of the first and second substances,
Figure BDA00026382737100001118
in the embodiment of the present invention, in order to verify the practical application effect of the above moving base alignment scheme, self-alignment test data is analyzed, the range of the alignment result is counted, and the quality of the result is determined accordingly, the influence of the embodiment of the present invention and the zero-speed-based scheme on the self-alignment result is analyzed by comparison, and the self-alignment result is shown in the following table:
TABLE 1 self-alignment results
Figure BDA00026382737100001119
Figure BDA0002638273710000121
As can be seen from the table above, the self-alignment precision is obviously improved after the scheme is implemented.
Aiming at the problem that zero-speed hypothesis alignment errors are large when the shaking base is self-aligned without external speed auxiliary information, the embodiment of the invention provides a shaking base self-alignment method based on speed fitting, which is a moving base self-alignment method independent of an external speed reference. According to the scheme, additional speed auxiliary equipment is not needed, and engineering application can be conveniently carried out.
It is noted that, in the present application, relational terms such as "first" and "second", and the like, are used solely to distinguish one entity or action from another entity or action without necessarily requiring or implying any actual such relationship or order between such entities or actions. Also, the terms "comprises," "comprising," or any other variation thereof, are intended to cover a non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements does not include only those elements but may include other elements not expressly listed or inherent to such process, method, article, or apparatus. Without further limitation, an element defined by the phrase "comprising an … …" does not exclude the presence of other identical elements in a process, method, article, or apparatus that comprises the element.
The above description is merely exemplary of the present application and is presented to enable those skilled in the art to understand and practice the present application. Various modifications to these embodiments will be readily apparent to those skilled in the art, and the generic principles defined herein may be applied to other embodiments without departing from the spirit or scope of the application. Thus, the present application is not intended to be limited to the embodiments shown herein but is to be accorded the widest scope consistent with the principles and novel features disclosed herein.

Claims (10)

1. A shaking base self-alignment method based on speed fitting is characterized by comprising the following steps:
collecting specific force f of inertial measurement unit IMU in system B of body coordinate systemBAnd collecting the projection of the angular velocity of the B system relative to the I system of the earth center inertial coordinate system under the B system
Figure FDA0002638273700000011
According to fBAnd
Figure FDA0002638273700000012
obtaining a posture transformation matrix from a B system of the IMU to an N system of a northeast geographic coordinate system
Figure FDA0002638273700000013
By using
Figure FDA0002638273700000014
And fBPerforming reverse pure inertial navigation resolving to obtain pure inertial navigation speed of the IMU at each moment;
fitting the pure inertial navigation speed to obtain a fitting inertial navigation speed;
obtaining the shaking speed of the IMU at each moment according to the pure inertial navigation speed and the fitting inertial navigation speed, and obtaining a corrected posture conversion matrix according to the shaking speed
Figure FDA0002638273700000015
2. The method for shaking base self-alignment based on velocity fitting of claim 1, wherein according to fBAnd
Figure FDA0002638273700000016
obtaining an attitude transformation matrix from a B system to an N system of an IMU
Figure FDA0002638273700000017
The method specifically comprises the following steps:
obtaining an initial time earth inertia coordinate system E'I0Attitude transformation matrix to N system
Figure FDA0002638273700000018
According to
Figure FDA0002638273700000019
And fBObtaining a strapdown inertial navigation inertial coordinate system B of a system B at the current time relative to the initial timeI0Of the rotation matrix
Figure FDA00026382737000000110
And an initial moment strapdown inertial navigation inertial coordinate system BI0Specific speed of
Figure FDA00026382737000000111
Based on
Figure FDA00026382737000000112
And
Figure FDA00026382737000000113
obtaining an initial moment strapdown inertial navigation inertial coordinate system BI0Earth inertia to initial momentCoordinate system E'I0Attitude transformation matrix of
Figure FDA00026382737000000114
According to
Figure FDA00026382737000000115
And
Figure FDA00026382737000000116
obtaining an initial attitude transformation matrix of the IMU
Figure FDA00026382737000000117
3. The method for self-alignment of a rocking base based on velocity fitting according to claim 2, wherein the earth inertial coordinate system E 'at the initial moment is obtained'I0Attitude transformation matrix to N system
Figure FDA0002638273700000021
The method specifically comprises the following steps:
according to the formula
Figure FDA0002638273700000022
Determining
Figure FDA0002638273700000023
Wherein L is0To align the start t0Latitude, omega of moment strapdown inertial unitIEIs the rotational angular velocity of the earth.
4. The method for self-alignment of a rocking base based on velocity fitting of claim 2, wherein the method is based on
Figure FDA0002638273700000024
And fBObtaining strapdown inertial navigation of system B relative initial time of current timeInertial frame BI0Of the rotation matrix
Figure FDA0002638273700000025
And an initial moment strapdown inertial navigation inertial coordinate system BI0Specific speed of
Figure FDA0002638273700000026
The method specifically comprises the following steps:
according to
Figure FDA0002638273700000027
Updating through strapdown inertial navigation attitude
Figure FDA0002638273700000028
Calculating a strapdown inertial navigation inertial coordinate system B of the system B at the current time relative to the initial timeI0Of the rotation matrix
Figure FDA0002638273700000029
Wherein the content of the first and second substances,
Figure FDA00026382737000000210
i is an identity matrix;
according to the formula
Figure FDA00026382737000000211
Calculating to obtain an initial moment strapdown inertial navigation inertial coordinate system BI0Specific speed of
Figure FDA00026382737000000212
τ is a variable of the integral expression.
5. The method for self-alignment of a rocking base based on velocity fitting of claim 2, wherein the method is based on velocity fitting
Figure FDA00026382737000000213
And
Figure FDA00026382737000000214
obtaining an initial moment strapdown inertial navigation inertial coordinate system BI0To initial time earth inertia coordinate system E'I0Attitude transformation matrix of
Figure FDA00026382737000000215
The method specifically comprises the following steps:
according to the formula
Figure FDA00026382737000000216
Calculating to obtain an initial time earth inertia coordinate system E'I0Specific speed of
Figure FDA00026382737000000217
Wherein f isNIs a specific force under the N series,
Figure FDA00026382737000000218
is composed of
Figure FDA0002638273700000031
Transposing;
strapdown inertial navigation inertial coordinate system B based on initial timeI0Specific speed of
Figure FDA0002638273700000032
And an initial time earth inertia coordinate system E'I0Specific speed of
Figure FDA0002638273700000033
According to the formula
Figure FDA0002638273700000034
Calculating to obtain an initial moment strapdown inertial navigation inertial coordinate system BI0To initial time earth inertia coordinate system E'I0Attitude transformation matrix of
Figure FDA0002638273700000035
Wherein the content of the first and second substances,
Figure FDA0002638273700000036
is composed of
Figure FDA0002638273700000037
Middle t0Take 0, t and t1The integral of (a) is calculated,
Figure FDA0002638273700000038
is t0Take 0, t and t2Integral of (1);
Figure FDA0002638273700000039
is composed of
Figure FDA00026382737000000310
Middle t0Take 0, t and t1The integral of (a) is calculated,
Figure FDA00026382737000000311
is t0Take 0, t and t2Integral of, t1＝1/2*t2And tau is a variable of the integral expression.
6. The method for self-alignment of a rocking base based on velocity fitting of claim 2, wherein the method is based on
Figure FDA00026382737000000312
And
Figure FDA00026382737000000313
obtaining an initial attitude transformation matrix of the IMU
Figure FDA00026382737000000314
The method specifically comprises the following steps:
according to the formula
Figure FDA00026382737000000315
Obtaining an initial time earth inertia coordinate system E'I0Attitude transformation matrix to B system
Figure FDA00026382737000000316
According to the formula
Figure FDA00026382737000000317
Calculating to obtain an initial attitude transformation matrix of the IMU
Figure FDA00026382737000000318
7. The method for rocking base self-alignment based on velocity fitting of claim 1, wherein the using is performed by using a linear velocity model
Figure FDA00026382737000000319
And fBThe method for calculating reverse pure inertial navigation to obtain the pure inertial navigation speed at each moment comprises the following steps:
according to the formula
Figure FDA0002638273700000041
Calculating to obtain the pure inertial navigation speed v at each momentN，
Wherein, the superscript represents the differentiation of the parameter, the section of No. book represents the parameter which needs to be inverted in the reverse solving process,
Figure FDA0002638273700000042
is composed of
Figure FDA0002638273700000043
The process is carried out in a reverse manner,
Figure FDA0002638273700000044
Figure FDA0002638273700000045
is v isNThe process of (1) is carried out in a reverse manner,
Figure FDA0002638273700000046
Figure FDA0002638273700000047
in the form of a matrix of positions,
Figure FDA0002638273700000048
l is the latitude of the current moment, and lambda is the longitude of the current moment;
Figure FDA0002638273700000049
the projection of the earth rotation angular velocity in an E system of an earth coordinate system after the earth rotation angular velocity is inverted and the projection of the earth rotation angular velocity in an N system of a northeast geographical coordinate system
Figure FDA00026382737000000410
Figure FDA00026382737000000411
Is the angular velocity of N relative to E,
Figure FDA00026382737000000412
h is the height, R is the radius of the earth,
Figure FDA00026382737000000413
and
Figure FDA00026382737000000414
is the pure inertial velocity
Figure FDA00026382737000000415
X, Y and a component in the Z direction, g, under NN＝[0 0 -g]TG is the local gravitational acceleration; h is the height of the glass substrate,
Figure FDA00026382737000000416
is the pure inertial velocity vNThe Z-direction component of (a).
8. The method for self-alignment of a rocking base based on velocity fitting according to claim 1, wherein said fitting a pure inertial velocity to obtain a fitted inertial velocity comprises:
pure inertial navigation velocity v for each momentNPerforming quadratic fitting to obtain a basic fitting equation as follows:
Figure FDA00026382737000000417
wherein a, b and c are fitting coefficients.
9. The method for self-alignment of a shaking base based on velocity fitting according to claim 1, wherein the obtaining of the shaking velocity at each moment according to the pure inertial navigation velocity and the fitted inertial navigation velocity specifically comprises:
according to the formula
Figure FDA0002638273700000051
Calculating the shaking speed at each time
Figure FDA0002638273700000052
10. The method as claimed in claim 1, wherein the self-alignment of the rocking base based on velocity fitting is further characterized by obtaining a modified attitude transformation matrix according to the rocking velocity
Figure FDA0002638273700000053
The method specifically comprises the following steps:
according to the formula
Figure FDA0002638273700000054
Is calculated to obtain
Figure FDA0002638273700000055
Wherein the content of the first and second substances,
Figure FDA0002638273700000056
according to
Figure FDA0002638273700000057
And
Figure FDA0002638273700000058
is corrected
Figure FDA0002638273700000059
According to the formula
Figure FDA00026382737000000510
To obtain
Figure FDA00026382737000000511
According to the formula
Figure FDA00026382737000000512
To obtain
Figure FDA00026382737000000513
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