## Info

7.7 J Angular Separation Match Technique

The angular separation match technique matches angular distances between observations with angular distances between catalog stars. For this technique to work, the estimated GC frame must be sufficiently undistorted. That is, the spacecraft motion must be sufficiently well modeled such that

holds for enough observations, where O, and 02 are unit vectors for two stars in the true CC frame and Oj and 0'2 are the corresponding unit vectors in the estimate CC frame, ¡i is an error allowance for the inaccuracies of observation and the distortion of the estimated CC frame.

In addition, the number of candidates, or catalog stars which could possibly be identified with an observation, must be manageable. Because candidates are chosen for their proximity to the observation, the initial attitude estimates must be sufficiently accurate so that the number of catalog stars within the candidate search window is not so large as to impose storage or processing time problems; i.e., d{ 6\S)<e (7-124)

holds for sufficiently few catalog stars, where t is the radius of the candidate search window. Experience with the SAS-3 spacecraft suggests that an average of two or three candidates per observation is satisfactory. However, if this number exceeds five to ten, ambiguities and misidentifications may lead to an insufficient number of correct unambiguous identifications.

The simplest angular separation match is a pairwise match between just two observations. This is done by picking two observations with unit vectors Oj and 02 in the estimated CC frame. The candidate catalog stars for O', are those that meet the requirement d(6'„S)<c

The candidates for 02 are similarly selected. A match exists and O', and 02 are associated with S, and S2, respectively, provided that

If this condition is met by more than one pair of catalog stars, the match is ambiguous.

Polygon matches can help resolve ambiguities and generally increase the reliability of the star identification. This technique consists of selecting a set of N observations (N >2). Each pair of observations can be matched with catalog stars as above. The polygon match is considered successful when each pairwise distance match is successful and when the catalog star associated with each observation is the same for all pairwise distance matches involving that observation. An alternative approach is to form m vectors containing the distances between all pairs of observations, where /w=(Jr)= N (N— l)/2. For example, for N = 4, the m vector for observations 1, 2, 3, and 4 would be

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