CN114370867A - Attitude optimization method of high-dynamic star sensor - Google Patents
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Abstract
The invention relates to a method for optimizing the attitude of a high-dynamic star sensor, which comprises the following steps: a. analyzing the change relation of the attitude of the high-dynamic star sensor along with time when the high-dynamic star sensor works; b. analyzing the change relation of the attitude of the high-dynamic star sensor along with time when the high-dynamic star sensor works, and modeling the high-dynamic star sensor into a nonlinear control system; c. initializing parameters in the modeled nonlinear control system; d. predicting a state vector in the nonlinear control system and a square root of a state error covariance matrix; e. correcting the predicted state vector in the nonlinear control system and the square root of the state error covariance matrix; f. and d, repeating the step d and the step e by taking the corrected state vector and the state error covariance matrix as initial values so as to realize iterative filtering of the measured attitude of the high-dynamic star sensor. The attitude measurement method can effectively improve the attitude measurement precision of the high-dynamic star sensor and realize the attitude optimization of the high-dynamic star sensor.
Description
Technical Field
The invention relates to an attitude optimization method of a high-dynamic star sensor.
Background
The star sensor is an attitude measuring instrument taking fixed stars as measuring objects, has the characteristics of light weight, small volume, low power consumption, high precision, strong anti-interference performance, capability of autonomous navigation without depending on other systems and the like, and is widely applied to attitude measurement of various space vehicles at present. The attitude measurement principle of the star sensor is as follows: firstly, imaging a fixed star by using an optical lens and an image sensor, obtaining the position and brightness information of the star point on the image sensor through star point extraction and mass center positioning, then finding the corresponding fixed star of the star point in a star table through star map identification, finally obtaining the three-axis attitude of the star sensor through attitude calculation according to the identification result, and providing attitude data for a carrier control system to realize the navigation of a carrier. Generally, the star sensor works in the stage of stable flight of a carrier, when the star sensor works in high-dynamic fields such as initial track entering of the carrier, maneuvering, large-angle attitude adjustment and the like, a star point moves in a photosensitive area of an image sensor within exposure time, and finally a section of track image is formed on a target surface of the sensor, so that the accuracy of star point centroid positioning is reduced, and the attitude measurement accuracy of the star sensor is influenced. Therefore, how to improve the attitude measurement accuracy of the high-dynamic star sensor is an urgent problem to be solved in the current star sensor research.
At present, many research institutions at home and abroad have proposed methods for improving the attitude measurement accuracy of the high-dynamic star sensor, and the methods are mainly divided into two types: one is a method based on extended kalman filtering: although the method solves the problem of attitude filtering of the high-dynamic star sensor, truncation errors are caused after expanded high-order terms are ignored, and the accuracy of attitude filtering is influenced; another class is unscented kalman filter based approaches: the method adopts the unscented transformation to ensure higher attitude filtering precision, but is easily influenced by system parameters to cause filtering divergence and has poorer robustness.
Disclosure of Invention
In view of the above, it is necessary to provide a method for optimizing the attitude of a high dynamic star sensor.
The invention provides a method for optimizing the attitude of a high-dynamic star sensor, which comprises the following steps: a. analyzing the change relation of the attitude of the high-dynamic star sensor along with time when the high-dynamic star sensor works; b. modeling the posture of the high-dynamic star sensor into a nonlinear control system by analyzing the change relation of the posture of the high-dynamic star sensor along with time when the high-dynamic star sensor works; c. initializing parameters in the modeled nonlinear control system; d. predicting a state vector in the nonlinear control system and a square root of a state error covariance matrix by square root cubature Kalman filtering; e. correcting the predicted state vector in the nonlinear control system and the square root of a state error covariance matrix by utilizing square root cubature Kalman filtering; f. and d, repeating the step d and the step e by taking the corrected state vector and the state error covariance matrix as initial values to realize iterative filtering of the measured attitude of the high-dynamic star sensor, thereby finishing the attitude optimization of the high-dynamic star sensor.
Specifically, the method further comprises the steps of:
and verifying the filtering effect through experiments.
Specifically, the step a specifically includes:
quaternion q ═ q for star sensor posture0 q1 q2 q3]TTo describe, let w ═ wx wy wz]TThe angular velocity vector of the high-dynamic star sensor is obtained, and the change of the attitude along with time meets the following conditions:
solving the differential equation in the formula (1) to obtain q (t) which changes with time and satisfies:
q(t)＝eW·t (2)
let Δ t be tk-tk-1Obtaining q (t) according to the formula (2)k) And q (t)k-1) In betweenThe relationship is as follows:
q(tk)＝eW·Δtq(tk-1) (3)
due to the fact that
Is an orthorhombic and symmetrical matrix, so e in formula (3)W·ΔtExpressed as:
specifically, the step b specifically includes:
the state equation and the measurement equation of the nonlinear control system are as follows:
wherein: x is a state vector of the system and represents the attitude of the high-dynamic star sensor; z is a measurement vector of the system and represents a measurement value of the attitude of the high-dynamic star sensor; w represents gaussian noise with mean 0 and covariance matrix Q; v represents gaussian noise with mean 0 and covariance matrix R; phi is ak-1Is a state transfer function of the system, hkIs a measurement function of the system;
according to the formula (3) and the formula (4), the state transfer function phi of the systemk-1Expressed as:
in addition, because the state vector and the measurement vector of the system are the postures of the high-dynamic star sensor, the measurement function h of the systemk(xk)＝xk。
Specifically, the step c comprises:
estimation of system state vector
Square root of sum state error covariance matrix C0And (3) initializing:
where ' E ' represents the mathematical expectation, the function chol represents the decomposition of the matrix using Cholesky's method.
Specifically, the step d includes:
using estimates of state vectors
Square root of sum state error covariance matrix C0And calculating volume points of the state vector:
wherein a represents the matrix [ I4×4,-I4×4]；
Propagating the volume points through the state transfer function and computing the predicted state vector:
the square root of the predicted state error covariance matrix is calculated:
wherein the content of the first and second substances,
the function Tria represents triangularization calculation on the matrix.
Specifically, the step e includes:
calculate volume points of the predicted state vector:
the volume points are propagated through the measurement function and the predicted measurement vector is calculated:
the square root of the innovation covariance matrix is calculated:
Czz,k|k-1＝Tria([zk|k-1,CR,k]) (13)
wherein the content of the first and second substances,
calculating a cross covariance matrix of the state vector and the measurement vector:
Pxz,k|k-1＝xk|k-1(zk|k-1)T (14)
wherein the content of the first and second substances,
calculating a gain matrix, modifying the square root of the predicted state vector and the state error covariance matrix:
specifically, the step f includes:
after obtaining the corrected state vector
Square root of sum state error covariance matrix CkAnd then, repeating the step d and the step f by taking the initial value as the initial value, namely performing iterative filtering on the attitude z measured by the high-dynamic star sensorA wave.
The method carries out system modeling on the high-dynamic star sensor, and predicts and corrects the attitude of the high-dynamic star sensor by square root cubature Kalman filtering on the basis. The method is easy to realize, and the attitude measurement precision of the high-dynamic star sensor is effectively improved.
Drawings
FIG. 1 is a flow chart of a method for optimizing the attitude of a high dynamic star sensor according to the present invention;
fig. 2 is an attitude quaternion representation diagram of the high-dynamic star sensor before and after filtering according to the embodiment of the invention.
Detailed Description
The present invention will be described in further detail with reference to the accompanying drawings and specific embodiments.
Referring to fig. 1, a flow chart of the operation of the attitude optimization method of the high dynamic star sensor according to the preferred embodiment of the invention is shown.
And step S1, analyzing the change relation of the posture of the high-dynamic star sensor along with the time when the high-dynamic star sensor works. Specifically, the method comprises the following steps:
in the present embodiment, the attitude of the star sensor is represented by a quaternion q ═ q0 q1 q2 q3]TA description will be given. Let w be [ w ]xwy wz]TThe angular velocity vector of the high-dynamic star sensor is obtained, and the change of the attitude along with time meets the following conditions:
solving the differential equation in the formula (1) to obtain q (t) which changes with time and satisfies:
q(t)＝eW·t (2)
let Δ t be tk-tk-1Obtaining q (t) according to the formula (2)k) And q (t)k-1) The relationship between them is:
q(tk)＝eW·Δtq(tk-1) (3)
due to the fact that
Is an orthorhombic and symmetrical matrix, so e in formula (3)W·ΔtExpressed as:
and step S2, modeling the high-dynamic star sensor into a nonlinear control system by analyzing the change relation of the posture of the high-dynamic star sensor along with time when the high-dynamic star sensor works. Specifically, the method comprises the following steps:
as can be seen from the formula (3) and the formula (4), when the star sensor operates under the high dynamic condition, the attitude of the star sensor changes nonlinearly with time, so that the high dynamic star sensor is modeled into a nonlinear control system, and the present embodiment lists the state equation and the measurement equation of the nonlinear control system:
wherein: x is a state vector of the system and represents the attitude of the high-dynamic star sensor; z is a measurement vector of the system and represents a measurement value of the attitude of the high-dynamic star sensor; w represents gaussian noise with mean 0 and covariance matrix Q; v represents gaussian noise with mean 0 and covariance matrix R; phi is ak-1Is a state transfer function of the system, hkAs a function of the measurements of the system.
According to the formula (3) and the formula (4), the state transfer function phi of the systemk-1Expressed as:
in addition, because the state vector and the measurement vector of the system are the postures of the high-dynamic star sensor, the measurement function h of the systemk(xk)＝xk。
And step S3, initializing parameters in the nonlinear control system. Specifically, the method comprises the following steps:
estimation of system state vector
Square root of sum state error covariance matrix C0And (3) initializing:
where ' E ' represents the mathematical expectation, the function chol represents the decomposition of the matrix using Cholesky's method.
Step S4, using square root cubature kalman filtering, predicting a state vector in the nonlinear control system and a square root of a state error covariance matrix. Specifically, the method comprises the following steps:
using estimates of state vectors
Square root of sum state error covariance matrix C0And calculating volume points of the state vector:
wherein a represents the matrix [ I4×4,-I4×4]。
Propagating the volume points through the state transfer function and computing the predicted state vector:
the square root of the predicted state error covariance matrix is calculated:
wherein the content of the first and second substances,
the function Tria represents triangularization calculation on the matrix.
Step S5, using square root cubature kalman filtering, correcting the state vector predicted in the nonlinear control system and the square root of the state error covariance matrix. Specifically, the method comprises the following steps:
calculate volume points of the predicted state vector:
the volume points are propagated through the measurement function and the predicted measurement vector is calculated:
the square root of the innovation covariance matrix is calculated:
Czz,k|k-1＝Tria([zk|k-1,CR,k]) (13)
wherein the content of the first and second substances,
calculating a cross covariance matrix of the state vector and the measurement vector:
Pxz,k|k-1＝xk|k-1(zk|k-1)T (14)
wherein the content of the first and second substances,
calculating a gain matrix, modifying the square root of the predicted state vector and the state error covariance matrix:
and S6, repeating the step S4 and the step S5 by taking the corrected state vector and the state error covariance matrix as initial values to realize iterative filtering of the attitude measured by the high-dynamic star sensor, and verifying the filtering effect through experiments. Specifically, the method comprises the following steps:
after obtaining the corrected state vector
Square root of sum state error covariance matrix CkAnd then, repeating the steps S4 and S5 by taking the initial value as the initial value, so that the attitude z measured by the high-dynamic star sensor can be subjected to iterative filtering.
In addition, the method verifies that the attitude measured by the high-dynamic star sensor has errors as shown in fig. 2, and the errors are obviously reduced after the method is used for processing, so that the method has a good filtering effect on the attitude of the high-dynamic star sensor.
According to the method, the high-dynamic star sensor is modeled into a nonlinear control system and is processed by square root cubature Kalman filtering, and therefore the attitude measurement precision of the high-dynamic star sensor is effectively improved.
Although the present invention has been described with reference to the presently preferred embodiments, it will be understood by those skilled in the art that the foregoing description is illustrative only and is not intended to limit the scope of the invention, as claimed.
Claims (8)
1. A method for optimizing the attitude of a high-dynamic star sensor is characterized by comprising the following steps:
a. analyzing the change relation of the attitude of the high-dynamic star sensor along with time when the high-dynamic star sensor works;
b. modeling the posture of the high-dynamic star sensor into a nonlinear control system by analyzing the change relation of the posture of the high-dynamic star sensor along with time when the high-dynamic star sensor works;
c. initializing parameters in the modeled nonlinear control system;
d. predicting a state vector in the nonlinear control system and a square root of a state error covariance matrix by square root cubature Kalman filtering;
e. correcting the predicted state vector in the nonlinear control system and the square root of a state error covariance matrix by utilizing square root cubature Kalman filtering;
f. and d, repeating the step d and the step e by taking the corrected state vector and the state error covariance matrix as initial values to realize iterative filtering of the measured attitude of the high-dynamic star sensor, thereby finishing the attitude optimization of the high-dynamic star sensor.
2. The method of claim 1, wherein the method further comprises the steps of:
and verifying the filtering effect through experiments.
3. The method according to claim 2, wherein the step a specifically comprises:
quaternion q ═ q for star sensor posture0 q1 q2 q3]TTo describe, let w ═ wx wy wz]TThe angular velocity vector of the high-dynamic star sensor is obtained, and the change of the attitude along with time meets the following conditions:
solving the differential equation in the formula (1) to obtain q (t) which changes with time and satisfies:
q(t)＝eW·t (2)
let Δ t be tk-tk-1Obtaining q (t) according to the formula (2)k) And q (t)k-1) The relationship between them is:
q(tk)＝eW·Δtq(tk-1) (3)
due to the fact that
Is an orthorhombic and symmetrical matrix, so e in formula (3)W·ΔtExpressed as:
4. the method according to claim 3, wherein said step b comprises in particular:
the state equation and the measurement equation of the nonlinear control system are as follows:
wherein: x is a state vector of the system and represents the attitude of the high-dynamic star sensor; z is a measurement vector of the system and represents a measurement value of the attitude of the high-dynamic star sensor; w represents gaussian noise with mean 0 and covariance matrix Q; v represents gaussian noise with mean 0 and covariance matrix R; phi is ak-1Is a state transfer function of the system, hkIs a measurement function of the system;
according to the formula (3) and the formula (4), the state transfer function phi of the systemk-1Expressed as:
in addition, because the state vector and the measurement vector of the system are the postures of the high-dynamic star sensor, the measurement function h of the systemk(xk)＝xk。
5. The method of claim 4, wherein said step c comprises:
estimation of system state vector
Square root of sum state error covariance matrix C0And (3) initializing:
where ' E ' represents the mathematical expectation, the function chol represents the decomposition of the matrix using Cholesky's method.
6. The method of claim 5, wherein step d comprises:
using estimates of state vectors
Square root of sum state error covariance matrix C0And calculating volume points of the state vector:
wherein a represents the matrix [ I4×4,-I4×4]；
Propagating the volume points through the state transfer function and computing the predicted state vector:
the square root of the predicted state error covariance matrix is calculated:
wherein the content of the first and second substances,
the function Tria represents triangularization calculation on the matrix.
7. The method of claim 6, wherein step e comprises:
calculate volume points of the predicted state vector:
the volume points are propagated through the measurement function and the predicted measurement vector is calculated:
the square root of the innovation covariance matrix is calculated:
Czz,k|k-1＝Tria([zk|k-1,CR,k]) (13)
wherein the content of the first and second substances,
calculating a cross covariance matrix of the state vector and the measurement vector:
Pxz,k|k-1＝xk|k-1(zk|k-1)T (14)
wherein the content of the first and second substances,
calculating a gain matrix, modifying the square root of the predicted state vector and the state error covariance matrix:
8. the method of claim 7, wherein step f comprises:
after obtaining the corrected state vector
Square root of sum state error covariance matrix CkAnd then, repeating the step d and the step f by taking the initial value as the initial value, and performing iterative filtering on the attitude z measured by the high-dynamic star sensor.
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| CN108344409A (en) * | 2017-12-26 | 2018-07-31 | 中国人民解放军国防科技大学 | Method for improving satellite attitude determination precision |
| CN109211276A (en) * | 2018-10-30 | 2019-01-15 | 东南大学 | SINS Initial Alignment Method based on GPR Yu improved SRCKF |
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| CN108344409A (en) * | 2017-12-26 | 2018-07-31 | 中国人民解放军国防科技大学 | Method for improving satellite attitude determination precision |
| CN109211276A (en) * | 2018-10-30 | 2019-01-15 | 东南大学 | SINS Initial Alignment Method based on GPR Yu improved SRCKF |
Non-Patent Citations (2)
| Title |
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| WANG JUN 等: "An attitude tracking method for star sensor under dynamic conditions", OPTOELECTRONICS LETTERS, vol. 15, no. 5, XP036899427, DOI: 10.1007/s11801-019-8197-z * |
| 王军: "高动态星敏感器关键技术研究", 中国博士学位论文全文数据库 工程科技Ⅱ辑, pages 5 * |
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