CN115630254A - On-orbit calibration method for parameter micro-variation in high-precision star sensor optical system - Google Patents
On-orbit calibration method for parameter micro-variation in high-precision star sensor optical system Download PDFInfo
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Abstract
The invention relates to an on-orbit calibration method for parameter micro-variation in a high-precision star sensor optical system, and belongs to the technical field of high-precision on-orbit calibration of spacecrafts. Firstly, taking the internal parameters of the optical system calibrated on the ground as the internal parameter values of the initial optical system, combining the relationship of each coordinate system with the angular distance model of the star point of the star sensor to list the relationship that the included angle of the direction vector in the coordinate system of the star sensor camera is equal to the included angle of the navigation star in the celestial coordinate system, then establishing a calibration model for indicating the micro-variation of the internal parameters of the optical system of the star sensor required to be used according to the characteristic that the angular distance of the observation star and the angular distance of the navigation star are not changed after the environment is changed, and finally calibrating the micro-variation of the internal parameters of the optical system by using the filtering method of the extended Kalman filtering algorithm (EKF). After the calibration of the micro-variation is finished, the initial optical system internal parameter value is added to obtain the optical system internal parameter after the environmental change.
Description
Technical Field
The invention relates to the technical field of high-precision on-orbit calibration of spacecrafts, in particular to an on-orbit calibration method for micro-variation of parameters in an optical system of a high-precision star sensor, which is a method for calibrating the parameters in the optical system with higher precision in an on-orbit mode in the operation process of the star sensor.
Background
The star sensor is a high-precision optical navigation device which takes a fixed star as a reference object and a spacecraft space attitude measurement as a working object, completes resolving by detecting the fixed star on an celestial sphere and combining high-precision fixed star astronomical coordinates and parameters (focal length and principal point) in an optical system of the star sensor, has autonomous navigation capability, and is widely applied in the aerospace field. The star sensor is an optical device, and an optical system of the star sensor is used for imaging a fixed star to obtain an observation star map of the fixed star. The method comprises the steps of obtaining image coordinates of a fixed star through star map preprocessing and centroid extraction, matching star points in an observation star map with star points in a navigation star table by using a star map recognition algorithm, and realizing three-axis attitude resolution of a star sensor optical system coordinate system in an celestial coordinate system by combining image coordinates of known high-precision star celestial sphere coordinates and centroid and parameters in a star sensor optical system. In the working process of the star sensor, accurate optical system internal parameters are one of necessary conditions for ensuring high-precision attitude measurement.
Before the star sensor is put into service, the calibration of internal parameters of the optical system needs to be completed on the ground, however, the optical system of the star sensor is influenced by environmental conditions such as vibration, heat radiation and the like in the transmitting and using processes, so that the optical system of the star sensor is enlarged in aberration and deformed in structure, and the internal parameters of the optical system in the actual using process are slightly changed compared with the ground calibration. The micro-variation of the internal parameters can change various calibration parameters of the star sensor, reduce the attitude measurement precision of the star sensor, and particularly cause direct influence on the attitude measurement due to the change of the main point position. Therefore, the micro-variation of the parameters in the optical system of the star sensor becomes one of the main factors limiting the precision measurement of the star sensor. In the traditional on-orbit calibration method, the internal parameters of the optical system are used as calibration objects, the model is rough, the micro-variation of the internal parameters of the optical system is generally used as random errors to be processed, and the precision of the calibration result needs to be improved. Therefore, in the working process of the star sensor, the on-orbit high-precision calibration of the micro-variation of the internal parameter is needed, and the calibration compensation is carried out on the star sensor so as to ensure the attitude measurement precision.
Disclosure of Invention
The invention aims to provide an on-orbit calibration method for the micro-variation of parameters in a high-precision star sensor optical system, which solves the problem that the micro-variation of the star sensor in-orbit calibration in the prior art cannot be processed. The invention realizes the calibration of the micro-variation of the parameters in the optical system of the star sensor, and is mainly used for the main point position and the actual imaging focal length. The method takes the internal parameters of the optical system calibrated on the ground as initial values, and adds the initial internal parameters of the optical system after calibrating the micro-variation of the internal parameters of the optical system to obtain the changed internal parameters of the optical system. Compared with the traditional method for directly calibrating the internal parameters of the optical system, the method can enable the internal parameters of the optical system of the star sensor to be calibrated more accurately and efficiently, and particularly has higher calibration precision on the principal point, thereby improving the attitude calculation precision of the star sensor.
The above object of the present invention is achieved by the following technical solutions:
the in-orbit calibration method for the parameter micro-variation in the high-precision star sensor optical system comprises the following steps:
firstly, performing ground calibration, wherein the internal parameters of the optical system calibrated on the ground are used as the internal parameter values of the initial optical system;
secondly, obtaining an image of a fixed star through an optical lens in the in-orbit working process of the star sensor, then preprocessing the star map, extracting the mass center and obtaining the position of the mass center of the fixed star in the image;
thirdly, after the position of the fixed star in the image is obtained, carrying out star map identification on the shot star map and the navigation star chart, and obtaining the navigation star in the celestial coordinate system and the observation star in the image coordinate system through matching of the star map identification;
step four, calibrating the parameter micro-variation in the optical system:
navigation star V in celestial coordinate system i ＝(X i ，Y i ，Z i )，V j ＝(X j ，Y j ，Z j ) As shown in formula (1); the projection point coordinate of the star i in the image coordinate system is (u) i ，v i ) Then the observation star is S i ＝(u i ，v i )，S j ＝(u j ，v j ) (ii) a Using the observation star to use the main point of the parameters in the standard optical system and the position of the focal length in the coordinate system of the back-stepping camera to obtain a direction vector W i And W j As in formula (2); wherein (u) 0 ，v 0 ) Denotes the coordinates of the principal point, f denotes the focal length, α i ，α j And delta i ，δ j Respectively represent right ascension and declination;
obtaining W in the star sensor camera coordinate system according to the principle that the star angular distance is not changed under coordinate conversion i And W j The included angle of the direction vector and the navigation star V in the celestial coordinate system i And V j Are equal and are represented by formula (3):
V i T V j ＝W i T W j (3)
substituting the formula (2) into the formula (3) to obtain the angular distance between fixed stars, as shown in the formula (4);
wherein, the first and the second end of the pipe are connected with each other,
setting the parameter change in the optical system after the environment change as
Such as (6)
Wherein, δ u 0 ，δv 0 δ f is the micro-variation of the parameters in the optical system;
after the environment is changed, the position of the star point in the image is changed into
Wherein, δ u i ，δv i ，δu j ，δv j The star position variation in the image is obtained;
the star-to-angle distance after the environment change is
The star point position and the parameters in the optical system change simultaneously, and the observation star angular distance and the navigation star angular distance are unchanged;
wherein, the first and the second end of the pipe are connected with each other,
can be obtained by the following formula (8),
the formula (10) adopts multi-element Taylor expansion, and high-order small terms are removed;
wherein, the first and the second end of the pipe are connected with each other,
wherein the content of the first and second substances,
written according to equation (10)
When n identified navigation stars exist in a shot star map, the method comprises the following steps:
M＝A*[δu 0 δv 0 δf] T (16)
wherein, the first and the second end of the pipe are connected with each other,
step five: calculating the star map by using the extended Kalman filtering algorithm to the shot star map, and calculating the delta u 0 ，δv 0 δ f, which is the micro-variation of the principal point coordinate and the focal length, is calibrated specifically as follows:
taking the formula (15) as a measurement equation, and calibrating by using extended Kalman filtering because the equation is a nonlinear equation; the state equation is:
x k ＝I 3×3 ·x k-1 (18)
x k ＝[δu 0 δv 0 δf] T (19)
wherein x k Micro-variation parameter delta u for principal point and focal length to be calibrated 0 ，δv 0 δ f, as in formula (19); k-1 and k represent the k-1 and k images, respectively, I 3×3 As an identity matrix, the measurement equation is:
z k ＝h(x k )+n c (20)
wherein z is k The two star-angular distances are respectively the star-angular distances obtained by calculating the position vectors in the celestial coordinate system and the star points after the change and the initial internal parameter values are subjected to back projection calculation to obtain the star-angular distances; h (x) k ) Is A [ delta u ] 0 δv 0 δf] T Simplified representation of (1), n c Is a measurement error caused by noise, the sidereal covariance P obtained from ground calibration 0 And parameter x 0 The initial estimation of (1) begins, processing the calibration frame by frame; for the kth star image, the EKF prediction equation is:
wherein
The covariance is estimated a priori at time k, Q is the covariance matrix of the system process, and the EKF update equation is:
where R is the covariance matrix of the observed noise, H k Is a jacobian matrix.
The invention has the beneficial effects that: the method of the invention is adopted to calibrate the star sensor optical system internal parameter micro-variation and the initial optical system internal parameter value obtained after ground calibration, thus obtaining the current star sensor optical system internal parameter value after environment change, and the precision of the star sensor optical system internal parameter calibrated by the micro-variation technology is higher than that of the star angle distance calibration method based on the traditional method, especially in the precision of the principal point, and further improving the precision of the star sensor attitude information. Compared with the traditional on-orbit calibration model, the precision of the internal parameters of the star sensor optical system calibrated by the micro-variation on-orbit calibration method is high, the attitude precision is greatly improved compared with the traditional on-orbit calibration model, the attitude residual error is reduced, and the attitude calculation precision of the star sensor is improved.
Drawings
The accompanying drawings, which are included to provide a further understanding of the invention and are incorporated in and constitute a part of this application, illustrate embodiment(s) of the invention and together with the description serve to explain the invention and do not constitute a limitation of the invention.
FIG. 1 is a diagram of the relationship between the camera coordinate system and the physical image coordinate system according to the present invention;
FIG. 2 is a diagram of a relationship between a pixel coordinate system and a physical image coordinate system according to the present invention;
FIG. 3 is a star point angular distance model diagram of the star sensor of the present invention;
FIG. 4 is an in-orbit working schematic diagram of the star sensor of the present invention;
FIG. 5 is a schematic view of the process of calibrating the internal parameters of the optical system of the star sensor according to the present invention;
FIG. 6 is a simulation calibration result obtained by the method of the present invention;
FIG. 7 is a pose residual obtained using the method of the present invention;
FIG. 8 is a simulation calibration result obtained by using a conventional on-track calibration method;
fig. 9 shows the attitude residuals obtained by the conventional on-orbit calibration method.
Detailed Description
The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings, and it is obvious that the described embodiments are only a part of the embodiments of the present invention, and not all of the embodiments. All other embodiments, which can be obtained by a person skilled in the art without making any creative effort based on the embodiments in the present invention, belong to the protection scope of the present invention. In order to make the aforementioned objects, features and advantages of the present invention more comprehensible, the present invention is described in detail with reference to the accompanying drawings and the detailed description thereof.
Referring to fig. 1 to 5, the in-orbit calibration method for the micro-variation of the internal parameter of the high-precision star sensor optical system of the invention firstly uses the internal parameter of the optical system calibrated on the ground as the initial internal parameter value of the optical system, lists the relationship that the included angle of the direction vector in the coordinate system of the star sensor camera is equal to the included angle of the navigation star in the celestial coordinate system according to the combination of the relationship of each coordinate system and the angular distance model of the star point of the star sensor, then establishes the calibration model for the micro-variation of the internal parameter of the star sensor optical system required to be used according to the characteristic that the star angular distance and the navigation star angular distance are unchanged after the environment is changed, and finally calibrates the micro-variation of the internal parameter of the optical system by using the filtering method of the extended kalman filtering algorithm (EKF). After the calibration of the micro-variation is finished, the initial optical system internal parameter value is added to obtain the optical system internal parameter after the environmental change.
Referring to fig. 1 to 5, the in-orbit calibration method for the parameter micro-variation in the high-precision star sensor optical system comprises the following steps:
firstly, performing ground calibration, and taking the internal parameters of the optical system calibrated on the ground as the internal parameter values of the initial optical system;
secondly, obtaining an image of a fixed star through an optical lens in the in-orbit working process of the star sensor, then preprocessing the star map, extracting the mass center and obtaining the position of the mass center of the fixed star in the image;
step three, after the position of the fixed star in the image is obtained, star map recognition is carried out on the shot star map and the navigation star table; the triangular star map identification method is the most common method for star map identification, the most common method is to select the characteristic of angular distance in the identification process, the reference angular distance is obtained by the vector of the fixed star in the prepared navigation star table in the celestial coordinate system, the characteristic of the angular distance to be identified is obtained by combining the centroid coordinate of the image star point and the parameter value in the initial optical system, so that the star map identification is completed, and the navigation star in the celestial coordinate system and the observation star in the image coordinate system are obtained through the matching of the star map identification;
and step four, after the star map is identified and matched to obtain the positions of star points, calibrating the internal parameters of the optical system of the star sensor, and performing related calculation. The step relates to the core of the technology of the invention, namely the calibration of the parameter micro-variation in the optical system:
the invention mainly researches the calibration of parameter micro-variation in an optical system of the star sensor, and relates to three coordinate systems, wherein figure 1 is the relation between a camera coordinate system and a physical image coordinate system, and figure 2 is the relation between a pixel coordinate system and a physical image coordinate system.
O in FIG. 1 C -X C Y C Z C Is the camera coordinate system and o' -xy is the physical image coordinate system.
In FIG. 2, o' -xy is the physical image coordinate system, and o-uv is the pixel coordinate system.
The invention uses the angular distance mostly used in the present star sensor calibration method as the calibration reference, as shown in figure 3, the invention is a star point angular distance model of the star sensor, theta ij Is the angular distance between stars i, j.
Set navigation star V in celestial coordinate system i ＝(X i ，Y i ，Z i )，V j ＝(X j ，Y j ，Z j ) As in formula (1); the projection point coordinate of the fixed star i in the image coordinate system is (u) i ，v i ) Then the observation star is S i ＝(u i ，v i )，S j ＝(u j ，v j ) (ii) a Using the observation star to use the main point of the parameters in the standard optical system and the position of the focal length in the coordinate system of the back-stepping camera to obtain a direction vector W i And W j As shown in formula (2). Wherein (u) 0 ，v 0 ) Representing principal point coordinates, f focal length, alpha i ，α k And delta i ，δ j Respectively indicating the right ascension and the declination.
According to the principle that the star angular distance is not changed under coordinate conversion, W in the star sensor camera coordinate system can be deduced i And W j The included angle of the direction vector and the navigation star V in the celestial coordinate system i And V j Are equal and are represented by formula (3):
V i T V j ＝W i T W j (3)
substituting the formula 2 into the formula 3, and calculating the angular distance between fixed stars as the formula (4).
Wherein the content of the first and second substances,
the method of the invention is to calibrate the micro-variation of the star sensor after the environment changes, and set the internal parameters of the optical system after the environment changes, because the internal parameters of the optical system change after the environment changes, the star point position in the image also changes, and because the star point position and the internal parameters of the optical system change simultaneously, the observation star angular distance and the navigation star angular distance are unchanged.
Setting the parameter change in the optical system after the environment change as
As shown in formula (6).
Wherein, δ u 0 ，δv 0 And δ f is the micro variation of the parameters in the optical system.
After the environment is changed, the position of the star point in the image is changed into
Wherein, δ u i ，δv i ，δu j ，δv j The star position variation in the image is obtained;
the star-angle distance after the environment changes is
The star point position and the parameters in the optical system change simultaneously, and the observation star angular distance and the navigation star angular distance are unchanged.
Wherein, the first and the second end of the pipe are connected with each other,
can be obtained by the following formula (8),
the equation (10) adopts multivariate Taylor expansion, and high-order small terms are removed.
Wherein the content of the first and second substances,
wherein, the first and the second end of the pipe are connected with each other,
written according to equation (10)
When there are n identified navigation stars in a shot star map shot by people, there are:
M＝A*[δu 0 δv 0 δf] T (16)
wherein the content of the first and second substances,
step five: calculating the star map by using an Extended Kalman Filter (EKF) for the shot star map, and calculating delta u 0 ，δv 0 And delta f is the coordinate of the principal point and the micro-variation of the focal length.
Equation (15) is used as a measurement equation, and since the equation is a non-linear equation, it is calibrated by Extended Kalman Filtering (EKF). The state equation is:
x k ＝I 3×3 ·x k-1 (18)
x k ＝[δu 0 δv 0 δf] T (19)
wherein x k Micro-variation parameter delta u for principal point and focal length to be calibrated 0 ，δv 0 δ f, as in formula (19). k-1 and k represent the k-1 and k images, respectively, I 3×3 As an identity matrix, the measurement equation is:
z k ＝h(x k )+n c (20)
wherein z is k And the two star-angular distances are respectively the star-angular distances obtained by performing back projection calculation on the star-angular distances obtained by calculating the position vectors in the celestial coordinate system, the changed star points and the initial internal parameter values. h (x) k ) Is A [ delta u ] 0 δv 0 δf] T Simplified representation of (a), n c Is a measurement error caused by noise, star covariance P scaled from the ground 0 And parameter x 0 The initial estimation of (1) begins, processing the calibration frame by frame; for the kth star image, the EKF prediction equation is:
wherein
The covariance is estimated a priori at time k, Q is the covariance matrix of the system process, and the EKF update equation is:
where R is the covariance matrix of the observed noise, H k Is a jacobian matrix.
The parameter value in the optical system of the star sensor after the environmental change can be obtained by utilizing the micro-variation of the internal parameter of the optical system of the star sensor calibrated by the method of the invention and the initial parameter value in the optical system obtained after the ground calibration. Therefore, the precision of the attitude information of the star sensor can be improved under the condition that the precision of the principal point parameter obtained by adopting the micro-variation technology for calibration is higher.
The embodiment is as follows:
in this embodiment, the evaluation standard for the in-orbit calibration method for the internal parameters of the star sensor optical system uses the attitude residual: calculating an attitude matrix and optical axis orientation by using star map simulation data used for calibration and a calibration result of parameters in an optical system, comparing the attitude matrix and the optical axis orientation calculated by using set standard parameters, calculating an included angle of two optical axis orientations obtained by each image, and finally evaluating an index to be a mean value of the included angles of the two optical axis orientations in the last 100 images, namely attitude residual error.
Simulating by adopting a simulated star map, wherein the value of the parameter in the optical system in the simulated data is set as f =16.04 0 ＝900，v 0 =500. Initial values of parameters in the optical system are set to f =16.00,u 0 ＝910，v 0 =510, i.e. the minor change in intrinsic parameter is: δ f = +0.04, δ u 0 ＝-10，δv 0 ＝-10。
Obtaining a simulation calibration result and a posture residual error by using the micro-variation on-orbit calibration method of the embodiment, as shown in fig. 6 and 7; the simulation calibration result and the attitude residual are obtained by using the conventional on-orbit calibration method, as shown in fig. 8 and 9.
The results of the calibration of the parameters in the optical system when the average number of the permanent stars per frame is 15.1 stars are shown in Table 1 and Table 2
Table 1: internal parameter micro-variation calibration experiment result
Table 2: comparative calibration experiment results
As can be seen from Table 2, compared with the conventional on-orbit calibration method, the precision of the internal parameters of the optical system calibrated by the on-orbit calibration method with the internal parameter micro-variation is improved, the attitude residual error is reduced, and the attitude calculation precision of the star sensor is improved.
The above description is only a preferred example of the present invention and is not intended to limit the present invention, and various modifications and changes may be made by those skilled in the art. Any modification, equivalent replacement, improvement and the like of the present invention shall be included in the protection scope of the present invention.
Claims (3)
1. An on-orbit calibration method for the parameter micro-variation in a high-precision star sensor optical system is characterized by comprising the following steps: the method comprises the following steps:
firstly, performing ground calibration, and taking the internal parameters of the optical system calibrated on the ground as the internal parameter values of the initial optical system;
secondly, obtaining an image of a fixed star through an optical lens in the in-orbit working process of the star sensor, then preprocessing the star map, extracting the mass center and obtaining the position of the mass center of the fixed star in the image;
thirdly, after the position of the fixed star in the image is obtained, carrying out star map identification on the shot star map and the navigation star chart, and obtaining the navigation star in the celestial coordinate system and the observation star in the image coordinate system through matching of the star map identification;
step four, calibrating the parameter micro-variation in the optical system:
navigation star V in celestial coordinate system i ＝(X i ,Y i ,Z i )，V j ＝(X j ,Y j ,Z j ) As shown in formula (1); the projection point coordinate of the star i in the image coordinate system is (u) i ,v i ) If the observation star is S i ＝(u i ,v i )，S j ＝(u j ,v h ) (ii) a Using the observation star to use the main point of the parameters in the standard optical system and the position of the focal length in the coordinate system of the back-stepping camera to obtain a direction vector W i And W j As in formula (2); wherein (u) 0 ,v 0 ) Representing principal point coordinates, f focal length, alpha i ，α j And delta i ，δ j Respectively represent right ascension and declination;
obtaining W in the star sensor camera coordinate system according to the principle that the star angular distance is not changed under coordinate conversion i And W j The included angle of the direction vector and the navigation star V in the celestial coordinate system i And V j Are equal and are represented by formula (3):
V i T V j ＝W i T W j (3)
substituting the formula (2) into the formula (3) to obtain the angular distance between fixed stars, as shown in the formula (4);
wherein the content of the first and second substances,
setting the parameter change in the optical system after the environment change as
Such as (6)
Wherein, δ u 0 ，δv 0 δ f is the micro-variation of the parameters in the optical system;
after the environment is changed, the position of the star point in the image is changed into
Wherein, δ u i ，δv i ，δu j ，δv j The star position variation in the image is obtained;
the star-to-angle distance after the environment change is
The position of the star point and the internal parameters of the optical system change simultaneously, and the observation star angular distance and the navigation star angular distance do not change;
wherein, the first and the second end of the pipe are connected with each other,
can be obtained from the formula (8),
the formula (10) adopts multivariate Taylor expansion to remove high-order small terms;
wherein the content of the first and second substances,
wherein the content of the first and second substances,
written according to equation (10)
When n identified navigation stars exist in a shot star map, the following steps are performed:
M＝A*[δu 0 δv 0 δf] T (16)
wherein the content of the first and second substances,
step five: calculating the star map by using the extended Kalman filtering algorithm to the shot star map, and calculating the delta u 0 ，δv 0 δ f is the micro of principal point coordinates and focal lengthAnd calibrating the variable quantity.
2. The on-orbit calibration method for the parameter micro-variation in the optical system of the high-precision star sensor according to claim 1, characterized in that: calculating the star map by using the extended Kalman filtering algorithm to the delta u 0 ，δv 0 δ f is the calibration of the micro-variation of the principal point coordinate and the focal length, and specifically comprises the following steps:
taking the formula (15) as a measurement equation, and calibrating by using extended Kalman filtering because the equation is a nonlinear equation; the state equation is:
x k ＝I 3×3 ·x k-1 (18)
x k ＝[δu 0 δv 0 δf] T (19)
wherein x k Micro-variation parameter delta u for principal point and focal length to be calibrated 0 ，δv 0 δ f, as in formula (19); k-1 and k represent the k-1 and k-th images, respectively, I 3×3 As an identity matrix, the measurement equation is:
z k ＝h(x k )+n c (20)
wherein z is k The two star-angular distances are respectively the star-angular distances obtained by calculating the position vectors in the celestial coordinate system, and the star-angular distances obtained by carrying out back projection calculation on the changed star points and the initial internal parameter values; h (x) k ) Is A [ delta u ] 0 δv 0 δf] T Simplified representation of (1), n c Is a measurement error caused by noise, the sidereal covariance P obtained from ground calibration 0 And parameter x 0 The initial estimation of (1) begins, processing the calibration frame by frame; for the kth star image, the EKF prediction equation is:
wherein
The covariance is estimated a priori at time k, Q is the covariance matrix of the system process, and the EKF update equation is:
where R is the covariance matrix of the observed noise, H k Is a jacobian matrix.
3. The on-orbit calibration method for the parameter micro-variation in the optical system of the high-precision star sensor according to claim 2, characterized in that: the precision of the star sensor optical system internal parameter calibrated by the micro-variation technology is higher than that based on the traditional star angular distance calibration method, especially in the precision of the principal point; and further improve the accuracy of the attitude information of the star sensor.
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|---|---|---|---|---|
| CN117011344A (en) * | 2023-10-07 | 2023-11-07 | 中国科学院光电技术研究所 | Method for correcting parameters in star sensor in two steps on-orbit |
| CN117011344B (en) * | 2023-10-07 | 2024-02-02 | 中国科学院光电技术研究所 | Method for correcting parameters in star sensor in two steps on-orbit |
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