CN112013873A - Static base rapid alignment method based on gradient descent optimization - Google Patents

Static base rapid alignment method based on gradient descent optimization Download PDF

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CN112013873A
CN112013873A CN202010810178.8A CN202010810178A CN112013873A CN 112013873 A CN112013873 A CN 112013873A CN 202010810178 A CN202010810178 A CN 202010810178A CN 112013873 A CN112013873 A CN 112013873A
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alignment
gradient descent
descent optimization
static base
quaternion
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高伟
张亚
刘超
王国臣
李敬春
于飞
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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 gradient descent optimization. Firstly, establishing a corresponding model by utilizing self-accelerometer and gyroscope information to replace latitude information to realize estimation calculation of the spin angular velocity vector of the earth under a navigation system; secondly, 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, and a target function in the least square sense is constructed by using multiple measurement vectors; and finally, obtaining a least square solution of the target function by using batch gradient descent optimization, so that the target function can be updated by fully utilizing all previous measurement information after each attitude quaternion is updated, and the target function is only related to the latest attitude quaternion, thereby accelerating the alignment convergence speed. The invention solves the problem of fast high-precision alignment of ships under the condition of unknown latitude.

Description

Static base rapid alignment method based on gradient descent optimization
Technical Field
The invention relates to the technical field of strapdown inertial navigation, in particular to a static base rapid alignment method based on gradient descent optimization.
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 rapid alignment method based on gradient descent optimization, and the least square solution of a target function is determined by using batch gradient descent optimization, so that the target function can be updated by fully utilizing all previous measurement information after each attitude quaternion is updated, the target function is only related to the latest attitude quaternion, and the alignment convergence speed is accelerated; meanwhile, the noise interference of the device can be effectively inhibited by constructing the objective function by utilizing all the measurement information. The method can be used for carrying out quick high-precision alignment under the condition that the latitude of the ship is unknown, and the environmental adaptability of alignment is improved.
Disclosure of Invention
The invention aims to provide a rapid 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 static base rapid alignment method based on gradient descent optimization comprises the following steps:
the method comprises the following steps: the estimation of the angular velocity vector of the earth rotation is completed by utilizing self-accelerometer and gyroscope measurement information: representing the posture and coordinate transformation by using a unit quaternion, and simultaneously carrying out normalization processing on the rotation angular velocity and the gravity acceleration vector of the earth;
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: a least squares solution of the attitude quaternion is obtained by a batch gradient descent method.
In step one, the estimation model of the earth rotation angular velocity vector is as follows:
unit quaternion
Figure BDA0002630680020000021
And to the rotational angular velocity of the earth
Figure BDA0002630680020000022
And gravity acceleration vector
Figure BDA0002630680020000023
And (3) carrying out normalization treatment:
Figure BDA0002630680020000024
Figure BDA0002630680020000025
and normalizing the output values of the triaxial accelerometer and the triaxial gyroscope:
Figure BDA0002630680020000026
Figure BDA0002630680020000027
projection of normalized earth rotation angular velocity vector under navigation coordinate system
Figure BDA0002630680020000028
Only the y-axis and z-axis components are non-zero. Therefore, the temperature of the molten metal is controlled,
Figure BDA0002630680020000029
can be written as:
Figure BDA00026306800200000210
the horizontal attitude angle can be determined using accelerometer information under static base conditions:
Figure BDA00026306800200000211
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).
Earth rotation angular velocity vector measured by three-axis gyroscope
Figure BDA00026306800200000212
Obtaining the earth rotation angular velocity vector after converting the carrier system into the navigation coordinate system
Figure BDA00026306800200000213
Figure BDA00026306800200000214
Projection components of the y-axis and z-axis in the navigation coordinate system:
Figure BDA00026306800200000215
Figure BDA00026306800200000216
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 BDA0002630680020000031
Figure BDA0002630680020000032
In the second step, an objective function is constructed by using the batch gradient descent optimization idea:
Figure BDA0002630680020000033
Figure BDA0002630680020000034
in the formula rnAnd rbCorresponding physical vectors under the navigation reference system and the carrier system respectively, which are assumed to contain the quaternion for determining the attitude
Figure BDA0002630680020000035
The required information.
Further, the optimal value of the attitude quaternion in the least square sense can be obtained by utilizing gradient descent optimization:
Figure BDA0002630680020000036
Figure BDA0002630680020000037
wherein, lambda is the gradient iteration step length,
Figure BDA0002630680020000038
the matrix of the Jacobian is obtained,
Figure BDA0002630680020000039
and is
Figure BDA00026306800200000310
Gradient of gradient
Figure BDA00026306800200000311
All the previous measurement information is used for each update, so that the method has strong inhibition capability on interference such as white noise of a device. It should be noted that it is preferable to provide,
Figure BDA00026306800200000312
is updated in dependence on the initial value
Figure BDA00026306800200000313
And selecting an iteration step length lambda.
In the third step, the objective function in the second step is solved by using batch gradient descent optimization:
firstly, will fall intoNormalized navigation system down gravity acceleration vector
Figure BDA00026306800200000314
Conversion to a carrier system to obtain
Figure BDA00026306800200000315
Figure BDA00026306800200000316
The difference value between the theoretical value and the actual measured value of the gravity acceleration vector under the carrier system is
Figure BDA00026306800200000317
Further, remember
Figure BDA00026306800200000318
To represent
Figure BDA00026306800200000319
To pair
Figure BDA00026306800200000320
The Jacobian matrix of
Figure BDA0002630680020000041
In the same way, the normalized earth rotation angular velocity vector theoretical value under the carrier system is obtained
Figure BDA0002630680020000042
Figure BDA0002630680020000043
Figure BDA0002630680020000044
The difference value between the theoretical value and the actual measurement value of the earth rotation angular velocity vector under the carrier system is as follows:
Figure BDA0002630680020000045
Figure BDA0002630680020000046
determining an attitude quaternion by combining the information of the gravity acceleration vector and the earth rotation angular velocity vector, and establishing a unified equation as follows:
Figure BDA0002630680020000047
while obtaining a jacobian matrix
Figure BDA0002630680020000048
Figure BDA0002630680020000049
In practice, device noise of the accelerometer and gyroscope can affect alignment performance. In order to overcome the influence brought by device noise, the following objective function is constructed based on batch gradient descent optimization:
Figure BDA00026306800200000410
where k denotes the current moment of the alignment process.
Determining the attitude quaternion by utilizing gradient descent optimization, wherein the iteration process is as follows:
Figure BDA0002630680020000051
Figure BDA0002630680020000052
wherein λ iskRepresents the iteration step size, at setting λkAnd time-varying parameter values gradually reduced along with the iteration process are selected, so that the convergence speed is accelerated, and the precision is improved. Because errors such as device errors exist, quaternion normalization is required in the iteration process to ensure
Figure BDA0002630680020000053
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 a multi-vector-based least square solving problem through information, noise interference can be effectively inhibited, the estimation of the rotational angular velocity vector of the earth is realized by using self accelerometer and gyroscope measurement information without depending on the external latitude, and a static base rapid alignment method based on gradient descent optimization is provided on the basis. The attitude quaternion can utilize the latest quaternion and all the previous measurement information to update the target function every time when being updated, thereby being beneficial to accelerating the convergence speed and further realizing the autonomy and rapidity of the alignment of the static base under the condition of no latitude.
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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 BDA0002630680020000054
Zero offset of the accelerometer: 1X 10-4g
The accelerometer measures noise:
Figure BDA0002630680020000055
sampling frequency: 100Hz
Initial value
Figure BDA0002630680020000056
Iteration step λ ═ β Δ t
Where β represents a parameter of the system dynamics and Δ t represents the system sampling period.
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 rapid alignment method (GDSA) based on gradient descent optimization proposed by the present invention 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 alignment convergence process of the GDFA method based on gradient descent optimization is the same as that of OTRIAD2, and the error curves of the two are completely overlapped, which shows that the GDFA method has a faster alignment convergence speed.
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 fluctuation of the horizontal error of the GDSA is very small, the result of each alignment error is 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 GDSA horizontal attitude is respectively reduced by 12.31%. Meanwhile, the results in table 1 and table 2 show that the maximum horizontal attitude error of the GDSA method proposed by the present invention is the same as OTRIAD2 and ONTRIAD2, and is 0.0057 °.
TABLE 1 roll alignment error result (°)
Figure BDA0002630680020000061
TABLE 2 Pitch alignment error results
Figure BDA0002630680020000062
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 OTRIAD2, ONTRIAD2 and GDSA 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; the GDFA results were identical to OTRIAD2, with the curves also coinciding completely, with a maximum alignment error of 0.0618 °. Compared with the ONTRIAD1 method, the maximum error of the GDSA heading is reduced by 2.83%.
TABLE 3 course alignment error results
Figure BDA0002630680020000071
In addition, the maximum errors of the GDSA and the ONTRIAD2 in the existing weftless alignment method are 0.0618 degrees and 0.0619 degrees respectively, and the GDSA can be considered to be the same as the maximum error of the ONTRIAD2 after data averaging preprocessing. Further analysis of table 3 and fig. 4 reveals that, at 0 ° -180 ° of heading, the maximum error of both GDSA and ontridad 2 is 0.0875 °, when ontridad 2 is smaller than GDSA; and when the heading is 180-360 degrees, the maximum errors of the GDSA and the ONTRIAD2 are respectively 0.0875 degree and 0.0893 degree, and the maximum error of the GDSA heading is smaller than that of the ONTRIAD 2. This shows that the weftless alignment method GDSA 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 maximum alignment error of the GDSA in 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 GDSA roll, pitch and heading 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 maximum error of GDSA heading is smaller than ONTRIAD2 when the heading is 180-360 degrees.

Claims (4)

1. A static base rapid alignment method based on gradient descent optimization is characterized by comprising the following steps:
the method comprises the following steps: the estimation of the angular velocity vector of the earth rotation is completed by utilizing self-accelerometer and gyroscope measurement information: representing the posture and coordinate transformation by using a unit quaternion, and simultaneously carrying out normalization processing on the rotation angular velocity and the gravity acceleration vector of the earth;
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: a least squares solution of the attitude quaternion is obtained by a batch gradient descent method.
2. The method for fast aligning the static base based on the gradient descent optimization as claimed in claim 1, wherein the projection components of the earth rotation angular velocity vector in the y-axis and the z-axis of the navigation coordinate system are as follows:
Figure FDA0002630680010000011
Figure FDA0002630680010000012
speed vector of self-rotation angle of earth under navigation coordinate system
Figure FDA0002630680010000013
Figure FDA0002630680010000014
3. The method for fast aligning the static base based on the gradient descent optimization according to claim 1, characterized in that an objective function is constructed by using a batch gradient descent optimization idea:
Figure FDA0002630680010000015
Figure FDA0002630680010000016
in the formula rnAnd rbCorresponding physical vectors under the navigation reference system and the carrier system respectively, which are assumed to contain the quaternion for determining the attitude
Figure FDA00026306800100000111
The required information.
4. The method for fast alignment of a static base based on gradient descent optimization according to claim 1, wherein the following objective function is constructed based on the batch gradient descent optimization by using the batch gradient descent optimization solution:
Figure FDA0002630680010000017
where k denotes the current moment of the alignment process.
Determining the attitude quaternion by utilizing gradient descent optimization, wherein the iteration process is as follows:
Figure FDA0002630680010000018
Figure FDA0002630680010000019
wherein λ iskRepresents the iteration step size, at setting λkAnd time-varying parameter values gradually reduced along with the iteration process are selected, so that the convergence speed is accelerated, and the precision is improved. Because errors such as device errors exist, quaternion normalization is required in the iteration process, and the quaternion normalization is guaranteedCertificate (certificate)
Figure FDA00026306800100000110
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