CN112013872A - Static base self-alignment method based on characteristic value decomposition - Google Patents

Static base self-alignment method based on characteristic value decomposition Download PDF

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CN112013872A
CN112013872A CN202010810168.4A CN202010810168A CN112013872A CN 112013872 A CN112013872 A CN 112013872A CN 202010810168 A CN202010810168 A CN 202010810168A CN 112013872 A CN112013872 A CN 112013872A
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alignment
static base
alignment method
angular velocity
earth
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张亚
高伟
李敬春
刘超
于飞
王国臣
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Harbin Institute of Technology
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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 discloses a static base self-alignment method based on characteristic value decomposition. In order to improve the noise suppression capability, the problem of non-latitude alignment of a static base is converted into the problem of Wahba attitude determination, firstly, a corresponding model is established by utilizing self-accelerometer and gyroscope information to replace latitude information to realize estimation of the spin angular velocity vector of a ground ball under a navigation system; secondly, constructing a target function in the least square sense by using a plurality of measurement vectors; and finally, obtaining a least square solution of the target function, namely an attitude quaternion by using a quaternion method of characteristic value decomposition, and finishing the alignment process. The invention solves the problem of high-precision alignment of ships under the condition of unknown latitude.

Description

Static base self-alignment method based on characteristic value decomposition
Technical Field
The invention relates to the technical field of strapdown inertial navigation, in particular to a static base self-alignment method based on characteristic value decomposition.
Background
An inertial navigation system is an autonomous navigation system based on the principle of inertia. The strapdown inertial navigation system directly and fixedly connects the gyroscope and the accelerometer to the carrier to measure angular motion and linear motion information of the carrier, and calculates speed, position, attitude and heading information of the carrier relative to the earth through integral operation. The initial alignment is a key technology of the strapdown inertial navigation system, the accuracy of the alignment directly affects the accuracy of the navigation system, and the time for completing the alignment directly affects the quick response capability of the system.
Aiming at the simpler application condition of static base alignment, the traditional static base alignment algorithm is relatively mature in research, and the theoretical alignment accuracy of the algorithm is close to the limit value of the error of the device. Although the conventional inertia kinematic base alignment method can be used for the static base alignment, the alignment time is long, and the alignment error increases with time, so that the alignment accuracy is not as good as that of the conventional static base analytic alignment method. In addition, the analytic alignment directly determines an initial attitude matrix by using the spatial relationship between the angular velocity of rotation of the earth and the gravity acceleration vector, has the advantages of simple principle, high alignment speed, satisfaction of the initial alignment requirement under any attitude condition and the like, and has the defect that the alignment precision is easily influenced by noise of a device.
The traditional static base alignment technology can be generally divided into three types, namely analytic alignment, compass alignment and Kalman filtering combination alignment based on optimal estimation, and local latitude information needs to be input externally when initial alignment is carried out, so that the autonomy and the safety of the strapdown attitude and heading reference system are reduced. In addition, the compass alignment and kalman filter combined alignment mainly aims at the situation that the initial attitude angle is a small angle, for example, the fine alignment process, and the initial alignment task under any heading angle condition cannot be completed due to the limitation of application conditions. In addition, the compass alignment and kalman filter combined alignment process usually takes a long time and is difficult to adapt to the requirement of fast alignment of the static base. Aiming at the initial alignment of the static base under the condition that the GPS positioning information cannot be obtained from the tunnel, the mountainous jungle, the seabed and the like, the traditional initial alignment technology of the static base cannot complete the alignment task, and the application of the strapdown attitude and heading reference system in the complex environment is further limited.
Aiming at the problems, the invention designs a static base self-alignment method based on eigenvalue decomposition, which makes full use of measurement information to convert the attitude determination problem into a least square solution problem based on multiple vectors and has better noise suppression capability. The method can be used for high-precision alignment under the condition that the ship latitude is unknown, and the environmental adaptability of alignment is improved.
Disclosure of Invention
The invention aims to provide a high-precision transfer alignment method under the condition of unknown latitude.
The technical scheme for realizing the purpose of the invention is as follows: a ship large azimuth misalignment angle transfer alignment method based on cubature Kalman filtering comprises the following steps:
the method comprises the following steps: the estimation of the angular velocity vector of the earth is completed by utilizing the measurement information of an accelerometer and a gyroscope, the attitude and coordinate transformation are represented by using a unit quaternion, and the angular velocity vector of the earth and the gravity acceleration vector need to be normalized at the same time;
step two: constructing a target function in the least square sense by using multiple measurement vectors to inhibit noise interference of the device;
step three: and solving the attitude quaternion by using a characteristic value decomposition method.
In step one, the estimation model of the earth rotation angular velocity vector is as follows:
unit quaternion
Figure BDA0002630678540000021
And to the rotational angular velocity of the earth
Figure BDA0002630678540000022
And gravity acceleration vector
Figure BDA0002630678540000023
And (3) carrying out normalization treatment:
Figure BDA0002630678540000024
Figure BDA0002630678540000025
and normalizing the output values of the triaxial accelerometer and the triaxial gyroscope:
Figure BDA0002630678540000026
Figure BDA0002630678540000027
projection of normalized earth rotation angular velocity vector under navigation coordinate system
Figure BDA0002630678540000028
Only the y-axis and z-axis components are non-zero. Therefore, the temperature of the molten metal is controlled,
Figure BDA0002630678540000029
can be written as:
Figure BDA00026306785400000210
the horizontal attitude angle can be determined using accelerometer information under static base conditions:
Figure BDA00026306785400000211
using accelerometer output information, the horizontal plane and z of a navigational coordinate system can be determinednAxial direction (perpendicular to the horizontal plane, meeting the right hand coordinate system criteria). Based on the horizontal plane, an intermediate transformation orthogonal coordinate system can be determined
Figure BDA00026306785400000212
Of the series
Figure BDA00026306785400000213
Z of axes and navigation coordinate systemnThe axes are coincident but the heading angles differ by an angle ψ as shown in figure 2.
Earth rotation angular velocity vector measured by three-axis gyroscope
Figure BDA00026306785400000214
The transformation from the carrier system to the navigation coordinate system can be written as:
Figure BDA00026306785400000215
the angular velocity vector of the earth rotation can be obtained
Figure BDA00026306785400000216
Projection components of the y-axis and z-axis under the navigation coordinate system.
Figure BDA00026306785400000217
Figure BDA00026306785400000218
The local latitude L can be determined by the above formula. So far, the constraint relation between the intermediate conversion orthogonal coordinate system determined by the accelerometer and the gyro measurement information and the navigation coordinate system is utilized to obtain the earth rotation angular velocity vector in the navigation coordinate system
Figure BDA00026306785400000219
Figure BDA00026306785400000220
In the second step, a target function under the least square meaning is constructed by using a plurality of measurement vectors as follows:
Figure BDA0002630678540000031
wherein a (k) is a measurement weight coefficient, b (k) and r (k) respectively represent a measured value and a theoretical value of the same group of vectors, and A represents a coordinate system transformation matrix.
Firstly, the gravity acceleration vector is converted from a navigation coordinate system to a carrier coordinate system to obtain
Figure BDA0002630678540000032
Note the book
Figure BDA0002630678540000033
Then there are algorithms according to quaternion
Figure BDA0002630678540000034
Figure BDA0002630678540000035
In addition, the first and second substrates are,
Figure BDA0002630678540000036
and
Figure BDA0002630678540000037
respectively satisfy
Figure BDA0002630678540000038
Figure BDA0002630678540000039
Wherein, [ v ]i×]Representing a vector vi(i＝1,2)。
In the same way, examine
Figure BDA00026306785400000310
And
Figure BDA00026306785400000311
is finished to obtain
Figure BDA00026306785400000312
Combining the above two formulas
Figure BDA00026306785400000313
Note the book
Figure BDA00026306785400000314
Thus, it is possible to provide
Figure BDA00026306785400000315
Due to unit quaternion
Figure BDA00026306785400000316
Need to satisfy constraints
Figure BDA00026306785400000317
Thus, an objective function can be obtained
Satisfy constraints
Figure BDA00026306785400000318
Figure BDA00026306785400000319
To this end, the attitude quaternion
Figure BDA00026306785400000320
By seeking an objective function
Figure BDA00026306785400000321
Is determined.
In the third step, the objective function in the second step is solved by using eigenvalue decomposition:
note the book
Figure BDA0002630678540000041
Then the objective function
Figure BDA0002630678540000042
Is finished to obtain
Figure BDA0002630678540000043
Satisfy constraints
Figure BDA0002630678540000044
Wherein
Figure BDA0002630678540000045
And satisfy K ═ KT
According to the quaternion method optimization idea, introducing a Lagrange multiplier lambda to obtain:
Figure BDA0002630678540000046
therefore, the temperature of the molten metal is controlled,
Figure BDA0002630678540000047
should be located at the minimum value of
Figure BDA0002630678540000048
To (3). Then pair the upper two sides
Figure BDA0002630678540000049
Derived and arranged to obtain
Figure BDA00026306785400000410
Solution of the equation
Figure BDA00026306785400000411
Is a normalized eigenvector of K, and λ is its corresponding eigenvalue. After the above formula is substituted back to obtain
Figure BDA00026306785400000412
Compared with the prior art, the invention has the beneficial effects that:
according to the method, under the condition that the latitude is unknown, the attitude determination problem is converted into the least square solving problem based on multiple vectors by information, noise interference can be effectively inhibited, the estimation of the rotational angular velocity vector of the earth is realized by utilizing the measurement information of an accelerometer and a gyroscope of the static base without depending on the external latitude, and the static base fast alignment method based on characteristic value decomposition is provided on the basis, so that the self alignment of the static base under the latitude-free condition is met.
Drawings
FIG. 1 is a basic flow diagram of the present invention;
FIG. 2 is a horizontal alignment error comparison;
FIG. 3 is a comparison of heading alignment errors for attitude (0, 45);
FIG. 4 is a heading alignment error comparison of 0-360.
Detailed Description
The invention is further described below with reference to the accompanying drawings.
In order to verify the effectiveness of the invention, a designed static base latitude-free self-alignment method based on characteristic value decomposition is simulated by utilizing Matlab.
The simulation parameters are set as follows:
gyro drift: 0.01 degree/h
Random top wandering
Figure BDA0002630678540000051
Zero offset of the accelerometer: 1X 10-4g
The accelerometer measures noise:
Figure BDA0002630678540000052
sampling frequency: 100Hz
Both gyro random walk and accelerometer measurement noise are treated as white noise. Under the condition of setting a horizontal attitude (0 degrees and 0 degrees), acquiring and collecting inertial device data under the condition of a static base at an interval of 15 degrees one by one from a course angle of 0 degree, and acquiring 24 groups of data in total. Setting the local latitude to be 45.7796 degrees (Harbin), setting the simulation time to be 20s, and taking the difference value of the alignment result at the 20s th alignment completion time and the set benchmark reference value as the alignment error of a single experiment.
And (3) simulation results:
the results of the simulation are shown in tables 1-3 and FIGS. 2-4, using the above simulation conditions.
Fig. 2 and fig. 3 respectively show the conventional latitude information dependent analytical alignment method (otaad 1), the conventional latitude information dependent analytical alignment method (otaad 2) after data averaging preprocessing, and the horizontal attitude and heading alignment error curves of the static base self-alignment method (EDSA) based on eigenvalue decomposition under the typical attitude conditions of the static base (0 °,0 °,45 °). Although OTRIAD is one of the current analytic alignment methods with the highest theoretical alignment precision, the alignment result is susceptible to device noise interference. As shown in fig. 2 and 3, the alignment error of the OTRIAD1 fluctuates around the theoretical error value due to the device noise, and the OTRIAD2 method after data averaging preprocessing can overcome the device noise interference and converge to the theoretical error value quickly. The EDSA method alignment result based on eigenvalue decomposition is closer to OTRIAD2, converging around the theoretical value (0.0057 °,0.0057 °,0.0856 °).
Table 1 and table 2 show the results of the alignment errors in the roll and pitch of each algorithm in 24 alignment experiments, respectively. As can be seen from the table, the error of the OTRIAD1 and the existing non-latitude alignment method of the static base (ONTRIAD1) is large, and the fluctuation is large, which indicates that the algorithm has the defect of weak noise suppression capability; the horizontal error fluctuation of the EDSA is small, the alignment error results of all times are the same (after only 4 effective digits are reserved, the standard deviation is close to 0), and the maximum errors of the rolling and the pitching are 0.0057 degrees and 0.0057 degrees respectively; compared with OTRIAD1 and the existing static base weftless alignment method (ONTRIAD2) after data average preprocessing, the maximum error of the EDSA horizontal attitude is respectively reduced by 12.31%. Meanwhile, the results in tables 1 and 2 show that the maximum horizontal attitude error of the EDSA method provided by the invention is the same as OTRIAD2 and ONTRIAD2, and is 0.0057 degrees.
TABLE 1 roll alignment error result (°)
Figure BDA0002630678540000053
TABLE 2 Pitch alignment error results
Figure BDA0002630678540000061
TABLE 3 course alignment error results
Figure BDA0002630678540000062
Table 3 shows the heading alignment error results of each algorithm in the 24 alignment experiments. Meanwhile, in order to better show the algorithm course alignment result, fig. 4 shows the course alignment error curves of otriod 2, ontriod 2 and EDSA in 24 experiments. Because the course alignment error is mainly influenced by the drift of the equivalent east gyro under the navigation system, when the course changes from 0 degree to 360 degrees, the drift of the equivalent east gyro changes along with the course, and further the course alignment error changes periodically. From the results of the graphs, OTRIAD2 was able to suppress device noise well, and the alignment results were close to the theoretical error values. Because the OTRIAD1 and ONTRIAD1 have weak noise suppression capability, the alignment result fluctuates above and below the OTRIAD2 result; although the EDSA has slight deviation in some experimental results due to the convergence speed, the overall alignment error is the same as OTRIAD 2. Compared with the ONTRIAD1 method, the maximum error of the EDSA heading is reduced by 2.83%.
In addition, the maximum errors of the EDSA and the ONTRIAD2 in the existing weftless alignment method are 0.0618 degrees and 0.0619 degrees respectively, and the EDSA can be considered to be the same as the maximum error of the EDSA in the ONTRIAD2 after data averaging preprocessing. Further analysis of Table 3 and FIG. 4 reveals that at 0-180 heading, the maximum error of both EDSA and ONTRIAD2 is 0.0875, while the maximum error of ONTRIAD2 is less than EDSA; and when the heading is 180-360 degrees, the maximum errors of the EDSA and the ONTRIAD2 are respectively 0.0875 degree and 0.0893 degree, and the maximum error of the EDSA heading is smaller than that of the ONTRIAD 2. This shows that the weftless alignment method EDSA proposed by the present invention is a useful complement to the existing weftless alignment method ONTRIAD2, and can select corresponding algorithms for alignment according to different heading range conditions.
Therefore, simulation results show that the EDSA alignment maximum error of the static base weftless alignment method provided by the invention is the same as OTRIAD2 subjected to data average preprocessing, and is close to the error limit value of a device; compared with the existing weftless alignment method ONTRIAD1, the maximum errors of the EDSA roll, pitch and course are respectively reduced by 12.31%, 12.31% and 2.83%, and the better noise suppression capability is shown. In addition, the method can be beneficially complemented with the weftless alignment method ONTRIAD2 after data averaging preprocessing, wherein the EDSA heading maximum error is smaller than ONTRIAD2 when the heading is 180-360 degrees.

Claims (4)

1. A static base self-alignment method based on eigenvalue decomposition is characterized by comprising the following steps:
the method comprises the following steps: the estimation of the angular velocity vector of the earth is completed by utilizing the measurement information of an accelerometer and a gyroscope, the attitude and coordinate transformation are represented by using a unit quaternion, and the angular velocity vector of the earth and the gravity acceleration vector need to be normalized at the same time;
step two: constructing a target function in the least square sense by using multiple measurement vectors to inhibit noise interference of the device;
step three: and solving the attitude quaternion by using a characteristic value decomposition method.
2. The eigenvalue decomposition based static base self-alignment method of claim 1, wherein the estimation model of the earth rotation angular velocity vector is as follows:
angular velocity vector of earth rotation
Figure FDA0002630678530000011
Projection components of the y-axis and z-axis under the navigation coordinate system.
Figure FDA0002630678530000012
Figure FDA0002630678530000013
Speed vector of self-rotation angle of earth under navigation coordinate system
Figure FDA0002630678530000014
Figure FDA0002630678530000015
3. The eigenvalue decomposition based static base self-alignment method of claim 1, where multiple measurement vectors are used to construct the objective function in the least squares sense as:
Figure FDA0002630678530000016
wherein a (k) is a measurement weight coefficient, b (k) and r (k) respectively represent a measured value and a theoretical value of the same group of vectors, and A represents a coordinate system transformation matrix.
4. The static base self-alignment method based on eigenvalue decomposition according to claim 1, wherein the following objective function is solved by eigenvalue decomposition:
note the book
Figure FDA0002630678530000017
Then object letterNumber of
Figure FDA0002630678530000018
Is finished to obtain
Figure FDA0002630678530000019
Satisfy constraints
Figure FDA00026306785300000110
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Publication number Priority date Publication date Assignee Title
US8915116B2 (en) * 2013-01-23 2014-12-23 Freescale Semiconductor, Inc. Systems and method for gyroscope calibration
CN106595711A (en) * 2016-12-21 2017-04-26 东南大学 Strapdown inertial navigation system coarse alignment method based on recursive quaternion
CN108592943A (en) * 2018-03-16 2018-09-28 东南大学 A kind of inertial system coarse alignment computational methods based on OPREQ methods

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Publication number Priority date Publication date Assignee Title
US8915116B2 (en) * 2013-01-23 2014-12-23 Freescale Semiconductor, Inc. Systems and method for gyroscope calibration
CN106595711A (en) * 2016-12-21 2017-04-26 东南大学 Strapdown inertial navigation system coarse alignment method based on recursive quaternion
CN108592943A (en) * 2018-03-16 2018-09-28 东南大学 A kind of inertial system coarse alignment computational methods based on OPREQ methods

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Application publication date: 20201201