identification algorithms f o r t he star trackers have been studied widely for ... closest reference star so-called align star which length with respect to the pivot star ...
Modified Grid Algorithm for Star Pattern Identification by Using Star Trackers Hyunjae Lee, Choong-Suk Oh and Hyochoong Bang Korea Advanced Institute of Science and Technology D e p a b e n t ofAerospace Engineering 373-1, Kusong-Dong, Yusong-Gu, Daejon, 305-701, Korea
Abstract - In this paper a star pattern identification algorithm is addressed. Proposed algorithm is associated in terms of pattern recognition. Each star has related with well-defined pattern that can he determined by the sumounding stars. One of the well-known types related the class is the grid algorithm. The proposed algorithm is based on the algorithm. To enhance the algorithm the modifying methods so called virtual grids and selection multi-reference stars are proposed. This method makes the grid algorithm more accurate and reliable. INTRODUCTION
Voyaging into the deep space or orbiting the earth, the spacecraft must have the accurate guidance information. The reliable guidance information enables the spacecraft to achieve the given mission reliably. Especially the loss of the guidance control information during voyage is big potential threatening. Emphasis to obtain the guidance information is addressed in this paper by establish a attitude determination algorithm by using star patterns. Stars are one of the most accurate references for attitude and position determination of the spacecraft, because the stars can be assumed fixed bodies in the inertial frame and the sizes of the stars a r e small to b e identified as seen from the solar system. Star identification algorithms f o r t he star trackers have been studied widely for spacecraft attitude determination and control. There are numerous strategies to identify the star patterns. Various identification methods are available, and some of them are actually implemented on-board spacecraft. An efficient identification technique so-called grid algorithm has been introduced to overcome the disadvantage of conventional angle matching method. This class of identification algorithms can be classified in terms of pattern recognition. This class has a database in which each star has well defined p attem determined b y the surrounding stars in the specified field of view. Measured star field by the star tracker is converted a specified pattern by various methods. The pattern can be identified by finding the best matching pattern in the star pattern database. T h e grid algorithm, one of the pattern recognition algorithms for star pattern, is known to he robust with respect to sensor noise. Also it requires less computer resources compared to other algorithms because of simplicity of the algorithm.
0-7803-8 142-4/03/$17.0002003 IEEE
A modified grid algorithm for more accurate and reliable identification is introduced in this paper. A promising star identification approach is to choose multireference stars with which specific patterns are to be identified. If there is noise in the CCD image detector, a reference star could b e mis-matched with the generated grid database. However, the possibility of misidentification can be reduced for the final star identification by selecting the multi-reference stars as addressed in this study. Another useful approach is to generate so-called virtual grids. The reference stars in the outside of the pattern radius are always eliminated in the original grid algorithm since they are located far from the selected reference star. I t may lead to mis-identification by eliminating the reference stars because sometimes they could he very useful information. The reference stars eliminated in the previous algorithm are employed in this study by t he grids generated virtually on the outside of the virtualCCDplane. T h e virtualgridcovers thearea beyond that defined by the pattem radius in the original grid algorithm. The general grid algorithm in the previous study is introduced briefly in this study. And then the modified method is applied to the original grid algorithm for performance enhancement. Simulation studies include how many reference stars and how many virtual grids are effective for star identification. Thus a guideline for selecting suitable parameters for efficient identification is established. Also, star identification probability versus position accuracy of the image in the CCD plane is presented. The simulation results show that it is more stable about the Gaussian noise in the CCD image detector compared to the original grid algorithm. Obviously, the grid algorithm is generally known to be robust compared to general angle matching technique. Finally the modified grid algorithm proposed in this study is believed to provide robust star identification performance over a wide range of sensor noise GRIDALGORKHM The grid algorithm is a pattern recognition algorithm for star fieldoffered by CCD plane of the star tracker. Main key ideas of the algorithm are to generate a specified pattem database and to construct a grid pattern from the measured star filed in the CCD plane. The specified pattem is designed by using grids. Searching
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the best matching pattern in the database, the measured grid pattern can be identified. In this section we briefly introduce the grid algorithm. A set constituted by the stars in the specified field of view is needed to be pattern. Each star in the set is called reference siar. The pattern is constructed in the following manner [See Ref.71. A t first, o n e can select a reference star so-calledpivot siar in the set. The pivot star can be a star to be identified by the given database. And then, part the sky of the surrounding sky within patiern radius ( rp) which center is pivot star position. The pattern radius can be determined by a function of the FOV and by a marginal value. Thus, translate the pivot star in the center of the FOV and related reference stars also translate with same length with pivot star. And then, one can select a closest reference star so-called align star which length with respect to the pivot star is marginally bigger than a buffer radius ( 5 ). Then, orient the align star to be aligned with a reference frame also related reference stars should be rotated with same angle. Finally make a grid of size g x g in the pattern. If a grid cell contains a reference staf, one can let the cell can he 1 otherwise 0 to generate a standard format for the pattern. Bits of the grid cell are pattem information of each star in the real sky. The database is constituted by the bits information about each star. The next work is t o determine which pattern i n the database is related closely,with the imaged pattern in the CCD plane o f t he star tracker. The imaged pattern also can be generated a standard format by using same manner in the previous paragraph. If there are so many shared or .matched cells between the imaged pattern and a pattern in the database, more formally the shared cells are greater than some threshold, it could be a candidate star to be identified. When there is only one candidate star, the candidate star can be treated as the matched star. But, if there are a lot of candidate stars through the cell matching process, the candidate star of containing the maximum matching cells can be assumed as the identified star.
IP, and
6;
I=f
(1)
is the angle between pivot star and ith reference
star. Thus, the length of the
pi is given by
IPr I I Pi I= cos e, A imaged star vector be expressed by
(p,)attached in the CCD plane can Pi=Pi-P,
(3) T h e x value of the imaged star vector is 0 with respect to the CCD body frame. p is right ascension and q is declination with respect to the inertial frame.
Y *'
Indial f m e
Fig.1 Coordinated definition of the inertial frame and CCD body frame. From the geometric relations shown in Fig.1, the star vector(S)isgivenby
s=[cosqcosy, cosqsiny, s i n q r (4) The direction cosine matrix to CCD body frame from inertial frame is given by
Database Generation The method of generating a set of patterns which constitute a database is introduced. The reference stars are known priori from a star catalog by which Bright Star Catalog (BSC) is used in this paper. BSC contains star briehtness. rieht ascension and declination with . respect to the inertial frame. There are about 91 10 stars. The coordinate of the star is defined in Fig.1. useful For convenience, we introduce itF shown Fig,l, this paper a unit star vector in the real sky with respect to the inertial frame, sr is the Pivot vector. And P is a star vector imaged in the CCD plane with respect to the CCD body frame. The length of the p is defined and I
length of the pivot star is identical with the focal length.
cospcosq -cospsinq
-siny,cos< cos y, -siny,sing
sins cosq
-
,,
notation
related by the 'oca' length(f). Moreover, Pr is pivot star vector in the imaged in the CCD and the
where we used C, C, (-$) rotational sequence. To obtain a set constituted by the stars in the specified field of view by using the catalog information, every stars in the catalog can be transformed such as Eqn.(4). The set with a pivot star is limited by a threshold angle. Thus, the related reference stars in the set are simply chosen by the inner product relationship such as --f
ei =cos-'((s~,s,))
