CN111102993A - Initial alignment method for shaking base of rotary modulation type strapdown inertial navigation system - Google Patents

Initial alignment method for shaking base of rotary modulation type strapdown inertial navigation system Download PDF

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CN111102993A
CN111102993A CN201911407932.7A CN201911407932A CN111102993A CN 111102993 A CN111102993 A CN 111102993A CN 201911407932 A CN201911407932 A CN 201911407932A CN 111102993 A CN111102993 A CN 111102993A
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coordinate system
carrier
earth
component
carrier coordinate
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王怀鹏
蔡远文
辛朝军
杨晨
史美玲
黄梦盈
赵龙
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Space Engineering University
Peoples Liberation Army Strategic Support Force Aerospace Engineering University
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Space Engineering University
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    • G—PHYSICS
    • G01—MEASURING; TESTING
    • G01C—MEASURING DISTANCES, LEVELS OR BEARINGS; SURVEYING; NAVIGATION; GYROSCOPIC INSTRUMENTS; PHOTOGRAMMETRY OR VIDEOGRAMMETRY
    • G01C25/00—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass
    • G01C25/005—Manufacturing, calibrating, cleaning, or repairing instruments or devices referred to in the other groups of this subclass initial alignment, calibration or starting-up of inertial devices

Abstract

The invention relates to an initial alignment method of a rotary modulation type strapdown inertial navigation system under a shaking base. Establishing an error model of a rotary modulation type strapdown inertial navigation system by using a specific force equation; error compensation of constant drift of the inertial element is realized based on a rotation modulation technology; the components of the tracking gravity vector under a navigation coordinate system and a carrier coordinate system are adopted to realize coarse alignment under the shaking base; the invention belongs to the field of inertial navigation, and can be used for rapid positioning and orientation before launching of a carrier rocket during rapid emergency launching.

Description

Initial alignment method for shaking base of rotary modulation type strapdown inertial navigation system
Technical Field
The invention belongs to the field of inertial navigation, and can be used for quick positioning and orientation before launching of a carrier rocket during quick emergency launching.
Technical Field
The initial alignment technology is the first step of real-time navigation and positioning of the strapdown inertial navigation system, the subsequent navigation can be accurate only by ensuring the high accuracy of the initial alignment, and the initial alignment can be divided into two processes of coarse alignment and fine alignment. The rough alignment is mainly a process of determining the initial moment attitude of a carrier by a double-vector attitude determination method, namely two non-collinear vectors in space, and when the carrier is in a static condition, a gravity vector and an earth rotation angular velocity vector are generally adopted; when the carrier is in a base shaking condition, the rotational angular velocity vector of the earth is greatly interfered, and initial attitude determination alignment cannot be carried out. The Qinyangyuan of northwest industrial university and the like provide a coarse alignment method of a solidification coordinate system in the document strapdown inertial navigation coarse alignment research based on information on a swinging base, the method utilizes a method for tracking a gravity vector, namely components of the gravity vector under a terrestrial coordinate system and a carrier coordinate system at different moments to realize double-vector attitude determination, and the method can effectively shield the influence of shaking on the coarse alignment. The fine alignment is mainly realized by utilizing a Kalman filtering technology and establishing an error equation to estimate an azimuth misalignment angle and a horizontal misalignment angle, and on the basis, volumetric Kalman filtering, extended Kalman filtering, evanescent factor Kalman filtering and the like are developed.
The former document uses coarse alignment of a solidification coordinate system and a fine alignment method of Kalman filtering in SINS initial alignment method research under a shaking base, such as the pigment and the like, to solve the initial alignment problem of the shaking base, but the constant drift of the inertial element is not compensated, so that the output accuracy of the inertial element is not high, and the alignment error is large. Aiming at the problem that the constant drift of an inertial element influences the alignment precision, an initial alignment algorithm of a rotary modulation type strapdown inertial navigation system on a shaking base is provided.
Disclosure of Invention
The technical problem to be solved by the invention is as follows: the initial alignment algorithm of the shaking base of the rotary modulation type strapdown inertial navigation system is provided, and accurate initial alignment of the rotary modulation type strapdown inertial navigation system under the condition of shaking the base is realized. The method can compensate the constant drift of the inertial element through a rotation modulation technology, can realize the coarse alignment process of the shaking base through a method of solidifying a coordinate system, and finally realizes the fine alignment by utilizing a Kalman filtering method, thereby providing a brand new algorithm for the initial alignment of the rotation modulation type strapdown inertial navigation system under the shaking base.
The technical solution of the invention is as follows: establishing a rotary modulation type strapdown inertial navigation system error equation, realizing the compensation of constant drift of an inertial element through a rotary modulation technology, realizing coarse alignment under the condition of shaking a base by using a method of a solidification coordinate system, and finally estimating a misalignment angle by adopting a Kalman filtering technology to finish fine alignment. The method specifically comprises the following steps:
(1) a rotation modulation technology and a rotation modulation type strapdown inertial navigation error model:
the basic principle of continuous rotation modulation is as follows:
if the inertia element rotates around the Z axis at a constant angular velocity omega under the drive of the rotating table, the output of the gyroscope at any time t is an expression (1), and the component converted into a carrier coordinate system is an expression (2)
Figure BDA0002349158250000021
Figure BDA0002349158250000022
ωs-the output of the gyroscope;
ωn-a component of the earth rotation angular velocity in the navigation coordinate system;
ωZ-the component of the rotation of the turntable at angular velocity in the inertial element coordinate system;
εc-is a constant drift of the gyroscope;
εr-random drift of the gyroscope;
Figure BDA0002349158250000023
-a transformation matrix from the carrier coordinate system to the inertial element coordinate system;
Figure BDA0002349158250000024
-is a transformation matrix from the navigation coordinate system to the carrier coordinate system;
Figure BDA0002349158250000031
-a transformation matrix from the inertial element coordinate system to the carrier coordinate system.
The component of the constant drift in the carrier system can be expressed as
Figure BDA0002349158250000032
εc-is a constant drift of the gyroscope;
εb-is the component of the constant drift of the gyroscope under the carrier system;
Figure BDA0002349158250000033
-a transformation matrix from the inertial element coordinate system to the carrier coordinate system;
x, y, z-represent coordinate axes.
An error model of a rotary modulation type strapdown inertial navigation system:
in the case of a carrier with only shaking and no displacement, neglecting the horizontal cross-coupling term, the following error model can be obtained:
Figure BDA0002349158250000034
Figure BDA0002349158250000035
Figure BDA0002349158250000036
Figure BDA0002349158250000037
Figure BDA0002349158250000038
Figure BDA0002349158250000039
because the initial alignment time is short, the acceleration error and the gyro drift can be assumed to be random constants, that is, the inertial device model is:
Figure BDA00023491582500000310
Figure BDA00023491582500000311
for a rotation modulation type strapdown inertial navigation system
Figure BDA00023491582500000312
Figure BDA0002349158250000041
δVN-a north direction velocity error;
δVE-east-direction velocity error;
Figure BDA0002349158250000042
-a north misalignment angle;
Figure BDA0002349158250000043
-an east misalignment angle;
Figure BDA0002349158250000044
-an azimuthal misalignment angle;
ωie-rotational angular velocity of the earth;
g-local gravitational acceleration;
l-local geographic latitude;
r-is the radius of the earth;
Figure BDA0002349158250000045
-a random constant bias for the accelerometer;
ε -is the random constant drift of the gyroscope;
x, y, z-respectively denote the inertial element coordinate axes.
(2) Coarse alignment based on a solidification coordinate system
Under the condition of shaking the base, the output information of the gyroscope can be influenced, and the output of the accelerometer is hardly influenced, so the coarse alignment method of the solidification coordinate system mainly obtains an alignment matrix by a double-vector attitude determination method according to the components of the gravity vectors under a carrier coordinate system and a navigation coordinate system at different moments, and the specific method comprises the following steps:
according to the chain rule can be obtained
Figure BDA0002349158250000046
Figure BDA0002349158250000047
Figure BDA0002349158250000048
Figure BDA0002349158250000049
Figure BDA00023491582500000410
-a transformation matrix from the carrier coordinate system to the navigation coordinate system;
Figure BDA0002349158250000051
-a transformation matrix from a terrestrial coordinate system to a navigational coordinate system;
Figure BDA0002349158250000052
-is a transformation matrix from the solidified inertial earth coordinate system to the earth coordinate system;
Figure BDA0002349158250000053
-a transformation matrix from a solidification inertia carrier coordinate system to a solidification inertia earth coordinate system;
Figure BDA0002349158250000054
-a transformation matrix from the carrier coordinate system to the solidified inertial carrier coordinate system;
l-is the local geographic latitude;
ωie-is the rotational angular velocity of the earth;
Δ t-is the time interval;
Figure BDA0002349158250000055
-a transformation matrix from the carrier coordinate system to the solidified inertial carrier coordinate system;
Figure BDA0002349158250000056
-the component of the gyroscope output in the solidification inertial carrier coordinate system;
x-represents the cross product calculation of the matrix.
Wherein
Figure BDA0002349158250000057
The carrier rotation angular rate measured by a gyroscope in a carrier coordinate system.
Figure BDA0002349158250000058
The following can be obtained by a method of equivalent rotation vector:
while
Figure BDA0002349158250000059
Is measured by a gyroscope and is a time-varying quantity whose equivalent rotation vector can be approximately expressed as T in the case of a time interval
Figure BDA00023491582500000510
Figure BDA00023491582500000511
Figure BDA00023491582500000512
Figure BDA00023491582500000513
-is the equivalent rotation vector over the sampling interval T time;
Δθ1is within 0 to T/2
Figure BDA00023491582500000514
Integrating the result;
Δθ2within a time of T/2 to T
Figure BDA00023491582500000515
Integrating the result;
Figure BDA00023491582500000516
-a transformation matrix from the carrier coordinate system to the solidified inertial carrier coordinate system;
x-represents the cross product calculation of the matrix.
Figure BDA00023491582500000517
The method is a conversion matrix from a carrier coordinate system at an initial moment to a terrestrial coordinate system, the matrix is a constant value, and can be obtained by adopting a double-vector attitude determination method, but the output error of a gyroscope is larger due to the shaking of a base in the traditional double-vector attitude determination method, so that a tracking gravity vector is adopted, namely, components of gravity acceleration at different moments under the carrier coordinate system at the initial moment and the terrestrial coordinate system at the initial moment are selected as double vectors for attitude determination, and the method can effectively shield the influence of angular shaking on the initial alignment precision;
according to the definition of the inertial navigation coordinate system
Figure BDA0002349158250000061
Figure BDA0002349158250000062
g is the earth gravity acceleration;
gn-is the component of the gravitational acceleration in the navigation coordinate system;
Figure BDA0002349158250000063
-is the component of the gravitational acceleration in earth coordinates;
Figure BDA0002349158250000064
-is a transformation matrix from the navigation coordinate system to the terrestrial coordinate system;
Figure BDA0002349158250000065
-a transformation matrix for the earth coordinate system to the solidified inertia earth coordinate system;
l-is the local geographic latitude;
ωie-is the rotational angular velocity of the earth;
Δ t-is the time interval.
The component of the gravity acceleration g under the carrier coordinate system can be obtained by an accelerometer, and the component of the gravity acceleration g under the carrier coordinate system can be obtained by converting the gravity acceleration g into the component under the solidification inertia carrier coordinate system
Figure BDA0002349158250000066
In the formula
Figure BDA0002349158250000067
-is the component of the accelerometer output in the solidification inertia carrier coordinate system;
fb-is the component of the accelerometer output in the carrier coordinate system;
Figure BDA0002349158250000068
-a transformation matrix from the carrier coordinate system to the solidified inertia carrier coordinate system.
According to the specific force equation, when the linear interference of the carrier is neglected, the method can obtain
Figure BDA0002349158250000069
Figure BDA00023491582500000610
-is the component of the accelerometer output in the solidification inertia carrier coordinate system;
Figure BDA0002349158250000071
-is the component of the gravitational acceleration in earth coordinates;
Figure BDA0002349158250000072
-a transformation matrix for the solidification inertia earth coordinate system to the solidification inertia carrier coordinate system.
Taking different moments, t1Time of dayAnd t2After the time, cross-multiplication and transposition item-shifting combination is performed to obtain the formula (25). Can realize the pair through the complaint method
Figure BDA0002349158250000073
In the actual initial alignment process of the strapdown inertial navigation, measurement data are obtained through inertial elements, noise interference is inevitable in the measurement process, and in order to effectively shield noise and not lose information, the measurement data are respectively aligned
Figure BDA0002349158250000074
And
Figure BDA0002349158250000075
at time [0, t]Integration and taking two different times, t, in the same way1Time t and2at the moment of time, the time of day,
Figure BDA0002349158250000076
the matrix can be solved as follows
Figure BDA0002349158250000077
Figure BDA0002349158250000078
Figure BDA0002349158250000079
Figure BDA00023491582500000710
Figure BDA00023491582500000711
Figure BDA00023491582500000712
-outputting the component integration result for the accelerometer in the solidified inertial carrier coordinate system；
Figure BDA00023491582500000713
-is the component integral result of the gravitational acceleration under the solidification inertia earth coordinate system;
g is the earth gravity acceleration;
Δ t-is the time interval;
ωie-is the rotational angular velocity of the earth;
l-is the local geographic latitude;
Figure BDA00023491582500000714
-is the component of the accelerometer output in the solidification inertia carrier coordinate system;
fb-is the component of the accelerometer output in the carrier coordinate system;
Figure BDA0002349158250000081
-a transformation matrix from the carrier coordinate system to the solidified inertia carrier coordinate system.
(3) Fine alignment based on Kalman filtering technology
Fine alignment method based on Kalman filtering
And (3) obtaining a larger error of an initial attitude angle through coarse alignment, and estimating a horizontal misalignment angle and a square misalignment angle by using a Kalman filtering technology.
The discrete kalman filtering process is as follows:
Figure BDA0002349158250000082
Figure BDA0002349158250000083
Figure BDA0002349158250000084
Figure BDA0002349158250000085
Pk＝(I-KkHk)Pk/k-1(34)
Figure BDA0002349158250000086
-a state one-step prediction;
Figure BDA0002349158250000087
-state estimation;
Kk-a filter gain;
Pk/k-1-one-step prediction of mean square error;
Pk-estimating the mean square error;
Hk-an observation matrix;
Zk-an observation vector;
Φk,k-1-transferring the matrix in one step;
Γk-1-a system noise driving matrix.
An error state equation of initial alignment of the rotary modulation type strapdown inertial navigation system:
Figure BDA0002349158250000088
Figure BDA0002349158250000089
Figure BDA00023491582500000810
Figure BDA0002349158250000091
Figure BDA0002349158250000092
δVN-a north direction velocity error;
δVE-east-direction velocity error;
Figure BDA0002349158250000093
-a north misalignment angle;
Figure BDA0002349158250000094
-an east misalignment angle;
Figure BDA0002349158250000095
-an azimuthal misalignment angle;
ωie-rotational angular velocity of the earth;
g-local gravitational acceleration;
l-local geographic latitude;
r-is the radius of the earth;
Figure BDA0002349158250000096
-a random constant bias for the accelerometer;
ε -is the random constant drift of the gyroscope;
x, y, z-respectively represent the coordinate axes of the inertia element;
Cij-is
Figure BDA0002349158250000097
The corresponding element in (1);
w-white Gaussian noise that is N (0, Q).
Selecting two horizontal velocity errors as observed quantities, and then the observation equation is as follows:
Z＝HX+V (40)
x is a state vector;
z-is an observation vector;
h is a system observation matrix;
V-System Observation noise.
In order to verify the effect of the method, the geographical position of the carrier is 45.7 degrees of north latitude, and the rotation modulation rotating speed is 10 degrees/s at 129.7 degrees of east longitude; the constant deviation of the accelerometer is 1 x 10-4g, random deviation of 0.5X 10-4g; the constant drift of the gyroscope is 0.02 degree/h, the random drift is 0.01 degree/h, and the installation error is Kgx＝Kgy＝Kgz＝10×10-6Error of scale factor Kgxy＝Kgxz＝Kgyx＝Kgyz＝Kgzx＝Kgzy＝1.5×10-6rad; the attitude angle change due to the shake is:
course angle:
Figure BDA0002349158250000101
pitch angle:
Figure BDA0002349158250000102
transverse roll angle:
Figure BDA0002349158250000103
the simulation results are shown in fig. 2, fig. 3 and fig. 4, wherein fig. 2 is the comparison of the output error of the inertia element after rotation modulation and without rotation modulation, wherein the dotted line of gray is the result of rotation modulation, and the solid line of black is the result of non-rotation modulation. It can be obviously seen that after rotation modulation, the constant drift shows periodic variation around zero, and because the experimental scheme is rotation around the Z axis, the error of the Z axis cannot be compensated, so that the comparison result has no obvious variation. The periodically varying error is further compensated by integration, filtering and the like in the subsequent initial alignment process and approaches to zero, and the constant error is difficult to compensate.
Fig. 3 is an initial attitude angle obtained after coarse alignment of the solidification coordinate system using the output of the inertial element after non-rotational modulation and rotational modulation as input. Wherein the dotted line is the result of coarse alignment after the rotational modulation technique is utilized, the dotted line shows the result of coarse alignment without any processing, and the solid line shows the theoretical result. It can be seen from the figure that the course angle and roll angle results are not changed obviously, and the pitch angle results are obvious. The effect is not significant because the results of the Z-axis of the inertial element are not modulated, but instead the course angle and roll angle are related to the Z-axis data during the course of the settlement. However, it can be clearly seen from the pitch angle result that the result after rotation modulation is closer to the theoretical result, which shows that the initial alignment precision can be improved by adopting the rotation modulation technology.
FIG. 4 is a view showing that the initial attitude angle obtained by coarse alignment is subjected to Kalman filtering and then the misalignment angle is estimated, and it can be seen that the misalignment angle is mostly 1 × 10-4The degree of the left and right fluctuation meets the requirement of precision alignment on precision.
Compared with the prior art, the scheme of the invention has the main advantages that: aiming at the problem that the initial alignment precision of the strapdown inertial navigation system is low due to constant drift of an inertial element, the initial alignment method of the strapdown inertial navigation system based on the rotation modulation technology under the condition of shaking the base is provided, so that the constant drift of the inertial element is compensated, the problem of high-precision initial alignment of the shaking base can be solved, and a brand new technical approach is provided for high-precision alignment of the strapdown inertial navigation system under the condition of shaking the base.
Drawings
FIG. 1 is a diagram of an overall initial alignment design;
FIG. 2 is a flowchart of a solidification coordinate system algorithm;
FIG. 3 is an error diagram of an inertial component;
FIG. 4 is a simulation result of coarse alignment of a solidification coordinate system;
FIG. 5 is a Kalman filtering fine alignment simulation result.
Detailed description of the preferred embodiments
According to the embodiment of the invention, as shown in fig. 1, firstly, a rotation modulation technology is utilized to carry out error compensation on constant drift of an inertial element, the output of a compensated high-precision inertial element is used as the input of a strapdown inertial navigation system, then, a method of solidifying a coordinate system is utilized to realize coarse alignment under the condition of shaking a base, and finally, a Kalman filtering technology is utilized to realize estimation of a misalignment angle so as to complete an initial alignment process.
(1) Error compensation of constant drift of the inertial element is realized by utilizing a rotation modulation technology, an error equation of a rotation modulation type strapdown inertial navigation system is established, and error analysis is carried out on the system;
the basic principle of continuous rotation modulation is as follows:
if the inertia element rotates around the Z axis at a constant angular velocity omega under the drive of the rotating table, the output of the gyroscope at any time t is an expression (1), and the component converted into a carrier coordinate system is an expression (2)
Figure BDA0002349158250000111
Figure BDA0002349158250000121
ωs-the output of the gyroscope;
ωn-a component of the earth rotation angular velocity in the navigation coordinate system;
ωZ-the component of the rotation of the turntable at angular velocity in the inertial element coordinate system;
εc-is a constant drift of the gyroscope;
εr-random drift of the gyroscope;
Figure BDA0002349158250000122
-a transformation matrix from the carrier coordinate system to the inertial element coordinate system;
Figure BDA0002349158250000123
-is a transformation matrix from the navigation coordinate system to the carrier coordinate system;
Figure BDA0002349158250000124
as coordinates of inertial elementsTo the transformation matrix of the carrier coordinate system.
The component of the constant drift in the carrier system can be expressed as
Figure BDA0002349158250000125
εc-is a constant drift of the gyroscope;
εb-is the component of the constant drift of the gyroscope under the carrier system;
Figure BDA0002349158250000126
-a transformation matrix from the inertial element coordinate system to the carrier coordinate system;
x, y, z-represent coordinate axes.
An error model of a rotary modulation type strapdown inertial navigation system:
in the case of a carrier with only shaking and no displacement, neglecting the horizontal cross-coupling term, the following error model can be obtained:
Figure BDA0002349158250000127
Figure BDA0002349158250000128
Figure BDA0002349158250000129
Figure BDA00023491582500001210
Figure BDA0002349158250000131
Figure BDA0002349158250000132
because the initial alignment time is short, the acceleration error and the gyro drift can be assumed to be random constants, that is, the inertial device model is:
Figure BDA0002349158250000133
Figure BDA0002349158250000134
for a rotation modulation type strapdown inertial navigation system
Figure BDA0002349158250000135
Figure BDA0002349158250000136
δVN-a north direction velocity error;
δVE-east-direction velocity error;
Figure BDA0002349158250000137
-a north misalignment angle;
Figure BDA0002349158250000138
-an east misalignment angle;
Figure BDA0002349158250000139
-an azimuthal misalignment angle;
ωie-rotational angular velocity of the earth;
g-local gravitational acceleration;
l-local geographic latitude;
r-is the radius of the earth;
Figure BDA00023491582500001310
-a random constant bias for the accelerometer;
ε -is the random constant drift of the gyroscope;
x, y, z-respectively denote the inertial element coordinate axes.
(2) The output of the high-precision inertia element after rotation modulation is used as input, and high-precision coarse alignment under the condition of shaking the base is realized through a coarse alignment method of a solidification coordinate system;
under the condition of shaking the base, the output information of the gyroscope can be influenced, and the output of the accelerometer is hardly influenced, so the coarse alignment method of the solidification coordinate system mainly obtains an alignment matrix by a double-vector attitude determination method according to the components of the gravity vectors under a carrier coordinate system and a navigation coordinate system at different moments, and the specific method comprises the following steps:
according to the chain rule can be obtained
Figure BDA0002349158250000141
Figure BDA0002349158250000142
Figure BDA0002349158250000143
Figure BDA0002349158250000144
Figure BDA0002349158250000145
-a transformation matrix from the carrier coordinate system to the navigation coordinate system;
Figure BDA0002349158250000146
-a transformation matrix from a terrestrial coordinate system to a navigational coordinate system;
Figure BDA0002349158250000147
-is a transformation matrix from the solidified inertial earth coordinate system to the earth coordinate system;
Figure BDA0002349158250000148
-a transformation matrix from a solidification inertia carrier coordinate system to a solidification inertia earth coordinate system;
Figure BDA0002349158250000149
-a transformation matrix from the carrier coordinate system to the solidified inertial carrier coordinate system;
l-is the local geographic latitude;
ωie-is the rotational angular velocity of the earth;
Δ t-is the time interval;
Figure BDA00023491582500001410
-a transformation matrix from the carrier coordinate system to the solidified inertial carrier coordinate system;
Figure BDA00023491582500001411
-the component of the gyroscope output in the solidification inertial carrier coordinate system;
x-represents the cross product calculation of the matrix.
Wherein
Figure BDA00023491582500001412
The carrier rotation angular rate measured by a gyroscope in a carrier coordinate system.
Figure BDA00023491582500001413
The following can be obtained by a method of equivalent rotation vector:
while
Figure BDA00023491582500001414
Is measured by a gyroscope and is a time-varying quantity inThe equivalent rotation vector for a time interval of T can be approximately expressed as
Figure BDA00023491582500001415
Figure BDA0002349158250000151
Figure BDA0002349158250000152
Figure BDA0002349158250000153
-is the equivalent rotation vector over the sampling interval T time;
Δθ1is within 0 to T/2
Figure BDA0002349158250000154
Integrating the result;
Δθ2within a time of T/2 to T
Figure BDA0002349158250000155
Integrating the result;
Figure BDA0002349158250000156
-a transformation matrix from the carrier coordinate system to the solidified inertial carrier coordinate system;
x-represents the cross product calculation of the matrix.
Figure BDA0002349158250000157
The method is a conversion matrix from a carrier coordinate system to a terrestrial coordinate system at an initial moment, the matrix is a constant value, and a double-vector attitude determination method can be adopted for solving the matrix, but the output error of a gyroscope is larger due to the shaking of a base in the traditional double-vector attitude determination method, so that a tracking gravity vector is adopted, namely, the carrier coordinate system of the gravity acceleration at the initial moment at different moments is selectedThe components under the earth coordinate system at the system and the initial moment are used as double vectors for attitude determination, and the method can effectively shield the influence of angular oscillation on the initial alignment precision;
according to the definition of the inertial navigation coordinate system
Figure BDA0002349158250000158
Figure BDA0002349158250000159
g is the earth gravity acceleration;
gn-is the component of the gravitational acceleration in the navigation coordinate system;
Figure BDA00023491582500001510
-is the component of the gravitational acceleration in earth coordinates;
Figure BDA00023491582500001511
-is a transformation matrix from the navigation coordinate system to the terrestrial coordinate system;
Figure BDA00023491582500001512
-a transformation matrix for the earth coordinate system to the solidified inertia earth coordinate system;
l-is the local geographic latitude;
ωie-is the rotational angular velocity of the earth;
Δ t-is the time interval.
The component of the gravity acceleration g under the carrier coordinate system can be obtained by an accelerometer, and the component of the gravity acceleration g under the carrier coordinate system can be obtained by converting the gravity acceleration g into the component under the solidification inertia carrier coordinate system
Figure BDA0002349158250000161
In the formula
Figure BDA0002349158250000162
-is the component of the accelerometer output in the solidification inertia carrier coordinate system;
fb-is the component of the accelerometer output in the carrier coordinate system;
Figure BDA0002349158250000163
-a transformation matrix from the carrier coordinate system to the solidified inertia carrier coordinate system.
According to the specific force equation, when the linear interference of the carrier is neglected, the method can obtain
Figure BDA0002349158250000164
Figure BDA0002349158250000165
-is the component of the accelerometer output in the solidification inertia carrier coordinate system;
Figure BDA0002349158250000166
-is the component of the gravitational acceleration in earth coordinates;
Figure BDA0002349158250000167
-a transformation matrix for the solidification inertia earth coordinate system to the solidification inertia carrier coordinate system.
Taking different moments, t1Time t and2at the moment, cross-multiplication, transposition and item shifting combination are carried out to obtain an equation (25), and the method can realize the aim of cross-multiplication, transposition and item shifting
Figure BDA0002349158250000168
However, in the actual initial alignment process of the strapdown inertial navigation, the measurement data are obtained through the inertial element, noise interference is inevitable in the measurement process, and in order to effectively shield noise and avoid losing signalsThen are respectively paired
Figure BDA0002349158250000169
And
Figure BDA00023491582500001610
at time [0, t]Integration and taking two different times, t, in the same way1Time t and2at the moment of time, the time of day,
Figure BDA00023491582500001611
the matrix can be solved as follows
Figure BDA00023491582500001612
Figure BDA00023491582500001613
Figure BDA00023491582500001614
Figure BDA00023491582500001615
Figure BDA0002349158250000171
Figure BDA0002349158250000172
-outputting a component integration result for the accelerometer in a solidification inertial carrier coordinate system;
Figure BDA0002349158250000173
-is the component integral result of the gravitational acceleration under the solidification inertia earth coordinate system;
g is the earth gravity acceleration;
Δ t-is the time interval;
ωie-is the rotational angular velocity of the earth;
l-is the local geographic latitude;
Figure BDA0002349158250000174
-is the component of the accelerometer output in the solidification inertia carrier coordinate system;
fb-is the component of the accelerometer output in the carrier coordinate system;
Figure BDA0002349158250000175
-a transformation matrix from the carrier coordinate system to the solidified inertia carrier coordinate system.
(3) And finally, performing Kalman filtering by using the attitude angle obtained by the coarse alignment to obtain an estimated value of the misalignment angle, and correcting the attitude angle to finish the fine alignment based on the Kalman filtering.
And (3) obtaining a larger error of an initial attitude angle through coarse alignment, and estimating a horizontal misalignment angle and a square misalignment angle by using a Kalman filtering technology.
The discrete kalman filtering process is as follows:
Figure BDA0002349158250000176
Figure BDA0002349158250000177
Figure BDA0002349158250000178
Figure BDA0002349158250000179
Pk＝(I-KkHk)Pk/k-1(34)
Figure BDA00023491582500001710
-a state one-step prediction;
Figure BDA00023491582500001711
-state estimation;
Kk-a filter gain;
Pk/k-1-one-step prediction of mean square error;
Pk-estimating the mean square error;
Hk-an observation matrix;
Zk-an observation vector;
Φk,k-1-transferring the matrix in one step;
Γk-1-a system noise driving matrix.
An error state equation of initial alignment of the rotary modulation type strapdown inertial navigation system:
Figure BDA0002349158250000181
Figure BDA0002349158250000182
Figure BDA0002349158250000183
Figure BDA0002349158250000184
Figure BDA0002349158250000185
δVN-a north direction velocity error;
δVE-east-direction velocity error;
Figure BDA0002349158250000186
-a north misalignment angle;
Figure BDA0002349158250000187
-an east misalignment angle;
Figure BDA0002349158250000188
-an azimuthal misalignment angle;
ωie-rotational angular velocity of the earth;
g-local gravitational acceleration;
l-local geographic latitude;
r-is the radius of the earth;
Figure BDA0002349158250000191
-a random constant bias for the accelerometer;
ε -is the random constant drift of the gyroscope;
x, y, z-respectively represent the coordinate axes of the inertia element;
Cij-is
Figure BDA0002349158250000192
The corresponding element in (1);
w-white Gaussian noise that is N (0, Q).
Selecting two horizontal velocity errors as observed quantities, and then the observation equation is as follows:
Z＝HX+V (40)
x is a state vector;
z-is an observation vector;
h is a system observation matrix;
V-System Observation noise.
According to the typical simulation experiment result, the initial alignment method provided by the invention can modulate the constant drift into a periodic error, and then realize compensation through a subsequent filtering means. Simulation results show that the method can effectively improve the precision of the rough alignment pitch angle, the result obtained by the rough alignment is utilized to carry out fine alignment, and the error of the obtained estimated misalignment angle meets the precision requirement.
Those skilled in the art will appreciate that the details of the present invention not described in detail herein are well within the skill of those in the art.

Claims (4)

1. A method for initially aligning a rotary modulation type strapdown inertial navigation system under a shaking base is characterized by comprising the following steps of:
(1) error compensation of constant drift of the inertial element is realized by utilizing a rotation modulation technology, an error equation of a rotation modulation type strapdown inertial navigation system is established, and error analysis is carried out on the system;
(2) the output of the high-precision inertia element after rotation modulation is used as initial alignment input, and high-precision initial attitude information under the condition of shaking the base is obtained by a coarse alignment method of a solidification coordinate system;
(3) and finally, performing Kalman filtering by using the attitude angle obtained by the coarse alignment to obtain an estimated value of the misalignment angle, and correcting the attitude angle to complete the initial alignment of the rotary modulation type strapdown inertial navigation system under the condition of shaking the base.
2. The method for initial alignment of a rotary modulation type strapdown inertial navigation system under a shaking base as claimed in claim 1, wherein: the error compensation of the constant drift of the inertial element is realized by utilizing the rotation modulation technology in the step (1), an error equation of a rotation modulation type strapdown inertial navigation system is established, the error analysis is carried out on the system, and the method is realized according to the following method:
the basic principle of continuous rotation modulation is as follows:
if the inertia element rotates around the Z axis at a constant angular velocity omega under the drive of the rotating table, the output of the gyroscope at any time t is an expression (1), and the component converted into a carrier coordinate system is an expression (2)
Figure FDA0002349158240000011
Figure FDA0002349158240000012
ωs-the output of the gyroscope;
ωn-a component of the earth rotation angular velocity in the navigation coordinate system;
ωZ-the component of the rotation of the turntable at angular velocity in the inertial element coordinate system;
εc-is a constant drift of the gyroscope;
εr-random drift of the gyroscope;
Figure FDA0002349158240000013
-a transformation matrix from the carrier coordinate system to the inertial element coordinate system;
Figure FDA0002349158240000014
-is a transformation matrix from the navigation coordinate system to the carrier coordinate system;
Figure FDA0002349158240000021
-a transformation matrix from the inertial element coordinate system to the carrier coordinate system;
the component of the constant drift in the carrier system can be expressed as
Figure FDA0002349158240000022
εc-is a constant drift of the gyroscope;
εb-is the component of the constant drift of the gyroscope under the carrier system;
Figure FDA0002349158240000023
-a transformation matrix from the inertial element coordinate system to the carrier coordinate system;
x, y, z-represent coordinate axis directions;
in the case of a carrier with only shaking and no displacement, neglecting the horizontal cross-coupling term, the following error model can be obtained:
Figure FDA0002349158240000024
Figure FDA0002349158240000025
Figure FDA0002349158240000026
Figure FDA0002349158240000027
Figure FDA0002349158240000028
Figure FDA0002349158240000029
because the initial alignment time is short, the acceleration error and the gyro drift can be assumed to be random constants, that is, the inertial device model is:
Figure FDA00023491582400000210
Figure FDA00023491582400000211
for a rotation modulation type strapdown inertial navigation system
Figure FDA00023491582400000212
Figure FDA00023491582400000213
δVN-a north direction velocity error;
δVE-east-direction velocity error;
Figure FDA0002349158240000034
-a north misalignment angle;
Figure FDA0002349158240000035
-an east misalignment angle;
Figure FDA0002349158240000036
-an azimuthal misalignment angle;
ωie-rotational angular velocity of the earth;
g-local gravitational acceleration;
l-local geographic latitude;
r-is the radius of the earth;
Figure FDA0002349158240000031
-a random constant bias for the accelerometer;
ε -is the random constant drift of the gyroscope;
x, y, z-respectively represent the coordinate axes of the inertia element;
e, N, U-represents the coordinate axes of the navigation coordinate system, namely the north, the sky and the east directions.
3. The method for initial alignment of a rotary modulation type strapdown inertial navigation system under a shaking base as claimed in claim 1, wherein: and (2) taking the output of the high-precision inertia element after rotation modulation as input, obtaining high-precision initial attitude information by a coarse alignment method of a solidification coordinate system, and realizing the method according to the following steps:
under the condition of shaking the base, the output information of the gyroscope can be influenced, and the output of the accelerometer is hardly influenced, so the coarse alignment method of the solidification coordinate system mainly obtains an alignment matrix by a double-vector attitude determination method according to the components of the gravity vectors under a carrier coordinate system and a navigation coordinate system at different moments, and the specific method comprises the following steps:
according to the chain rule can be obtained
Figure FDA0002349158240000032
Figure FDA0002349158240000033
Figure FDA0002349158240000041
Figure FDA0002349158240000042
Figure FDA0002349158240000043
-a transformation matrix from the carrier coordinate system to the navigation coordinate system;
Figure FDA0002349158240000044
-a transformation matrix from a terrestrial coordinate system to a navigational coordinate system;
Figure FDA0002349158240000045
-is a transformation matrix from the solidified inertial earth coordinate system to the earth coordinate system;
Figure FDA0002349158240000046
-a transformation matrix from a solidification inertia carrier coordinate system to a solidification inertia earth coordinate system;
Figure FDA0002349158240000047
-a transformation matrix from the carrier coordinate system to the solidified inertial carrier coordinate system;
l-is the local geographic latitude;
ωie-is the rotational angular velocity of the earth;
Δ t-is the time interval;
Figure FDA0002349158240000048
-a transformation matrix from the carrier coordinate system to the solidified inertial carrier coordinate system;
Figure FDA0002349158240000049
-the component of the gyroscope output in the solidification inertial carrier coordinate system;
x-cross product calculation of the representation matrix;
wherein
Figure FDA00023491582400000410
The carrier rotation angular rate measured by a gyroscope in a carrier coordinate system.
Figure FDA00023491582400000411
The following can be obtained by a method of equivalent rotation vector:
while
Figure FDA00023491582400000412
Is measured by a gyroscope and is a time-varying quantity whose equivalent rotation vector can be approximately expressed as T in the case of a time interval
Figure FDA00023491582400000413
Figure FDA00023491582400000414
Figure FDA00023491582400000415
Figure FDA00023491582400000416
-is the equivalent rotation vector over the sampling interval T time;
Δθ1is within 0 to T/2
Figure FDA00023491582400000417
Integrating the result;
Δθ2within a time of T/2 to T
Figure FDA00023491582400000418
Integrating the result;
Figure FDA0002349158240000051
-a transformation matrix from the carrier coordinate system to the solidified inertial carrier coordinate system;
x-cross product calculation of the representation matrix;
Figure FDA0002349158240000052
the method is a conversion matrix from a carrier coordinate system at an initial moment to a terrestrial coordinate system, the matrix is a constant value and can be obtained by adopting a double-vector attitude determination method, but the output error of a gyroscope is larger due to the shaking of a base in the traditional double-vector attitude determination method, so that a tracking gravity vector is adopted, namely, components of gravity acceleration at different moments under the carrier coordinate system at the initial moment and the terrestrial coordinate system at the initial moment are selected as double vectors for attitude determination, and the method can effectively shield angular shaking from the initial alignment precision(ii) an effect;
according to the definition of the inertial navigation coordinate system
Figure FDA0002349158240000053
Figure FDA0002349158240000054
g is the earth gravity acceleration;
gn-is the component of the gravitational acceleration in the navigation coordinate system;
Figure FDA0002349158240000055
-is the component of the gravitational acceleration in earth coordinates;
Figure FDA0002349158240000056
-is a transformation matrix from the navigation coordinate system to the terrestrial coordinate system;
Figure FDA0002349158240000057
-a transformation matrix for the earth coordinate system to the solidified inertia earth coordinate system;
l-is the local geographic latitude;
ωie-is the rotational angular velocity of the earth;
Δ t-is the time interval;
the component of the gravity acceleration g under the carrier coordinate system can be obtained by an accelerometer, and the component of the gravity acceleration g under the carrier coordinate system can be obtained by converting the gravity acceleration g into the component under the solidification inertia carrier coordinate system
Figure FDA0002349158240000058
In the formula
Figure FDA0002349158240000059
-is the component of the accelerometer output in the solidification inertia carrier coordinate system;
fb-is the component of the accelerometer output in the carrier coordinate system;
Figure FDA0002349158240000061
-a transformation matrix from the carrier coordinate system to the solidified inertial carrier coordinate system;
according to the specific force equation, when the linear interference of the carrier is neglected, the method can obtain
Figure FDA0002349158240000062
Figure FDA0002349158240000063
-is the component of the accelerometer output in the solidification inertia carrier coordinate system;
Figure FDA0002349158240000064
-is the component of the gravitational acceleration in earth coordinates;
Figure FDA0002349158240000065
-a transformation matrix from a solidification inertia earth coordinate system to a solidification inertia carrier coordinate system;
taking different moments, t1Time t and2at the moment, cross-multiplication, transposition and item shifting combination are carried out to obtain an equation (25), and the method can realize the aim of cross-multiplication, transposition and item shifting
Figure FDA0002349158240000066
However, in the actual initial alignment process of the strapdown inertial navigation, the measurement data are obtained through inertial elements, noise interference is inevitable in the measurement process, and in order to effectively shield noise and not lose information, the method is divided intoIdentification pair
Figure FDA0002349158240000067
And
Figure FDA0002349158240000068
at time [0, t]Integration and taking two different times, t, in the same way1Time t and2at the moment of time, the time of day,
Figure FDA0002349158240000069
the matrix can be solved as follows
Figure FDA00023491582400000610
Figure FDA00023491582400000611
Figure FDA00023491582400000612
Figure FDA00023491582400000613
Figure FDA00023491582400000614
Figure FDA00023491582400000615
-outputting a component integration result for the accelerometer in a solidification inertial carrier coordinate system;
Figure FDA00023491582400000616
-is the component integral result of the gravitational acceleration under the solidification inertia earth coordinate system;
g is the earth gravity acceleration;
Δ t-is the time interval;
ωie-is the rotational angular velocity of the earth;
l-is the local geographic latitude;
Figure FDA0002349158240000071
-is the component of the accelerometer output in the solidification inertia carrier coordinate system;
fb-is the component of the accelerometer output in the carrier coordinate system;
Figure FDA0002349158240000072
-a transformation matrix from the carrier coordinate system to the solidified inertia carrier coordinate system.
4. The method for initial alignment of a rotary modulation type strapdown inertial navigation system under a shaking base as claimed in claim 1, wherein: and (3) performing Kalman filtering by using the attitude angle obtained by the coarse alignment to obtain an estimated value of a misalignment angle, correcting the attitude angle to complete the fine alignment, and realizing the method according to the following steps:
fine alignment method based on Kalman filtering
And (3) obtaining a larger error of an initial attitude angle through coarse alignment, and estimating a horizontal misalignment angle and a square misalignment angle by using a Kalman filtering technology.
The discrete kalman filtering process is as follows:
Figure FDA0002349158240000073
Figure FDA0002349158240000074
Figure FDA0002349158240000075
Figure FDA0002349158240000076
Pk＝(I-KkHk)Pk/k-1(34)
Figure FDA0002349158240000077
-a state one-step prediction;
Figure FDA0002349158240000078
-state estimation;
Kk-a filter gain;
Pk/k-1-one-step prediction of mean square error;
Pk-estimating the mean square error;
Hk-an observation matrix;
Zk-an observation vector;
Φk,k-1-transferring the matrix in one step;
Γk-1-a system noise driving matrix;
an error state equation of initial alignment of the rotary modulation type strapdown inertial navigation system:
Figure FDA0002349158240000081
Figure FDA0002349158240000082
Figure FDA0002349158240000083
Figure FDA0002349158240000084
Figure FDA0002349158240000085
δVN-a north direction velocity error;
δVE-east-direction velocity error;
Figure FDA0002349158240000086
-a north misalignment angle;
Figure FDA0002349158240000087
-an east misalignment angle;
Figure FDA0002349158240000088
-an azimuthal misalignment angle;
ωie-rotational angular velocity of the earth;
g-local gravitational acceleration;
l-local geographic latitude;
r-is the radius of the earth;
Figure FDA0002349158240000089
-a random constant bias for the accelerometer;
ε -is the random constant drift of the gyroscope;
x, y, z-respectively represent the coordinate axes of the inertia element;
Cij-is
Figure FDA0002349158240000091
The corresponding element in (1);
w-white Gaussian noise of N (0, Q)
Selecting two horizontal velocity errors as observed quantities, and then the observation equation is as follows:
Z＝HX+V (40)
x is a state vector;
z-is an observation vector;
h is a system observation matrix;
V-System Observation noise.
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