Kalman-Bucy filtering technique has widely been proved useful in trajectory determination of a satellite, launching rocket, since a precise trajectory information necessary for injection control to achieve a predetermined orbit is readily obtainable in real time by that filtering technique. In applying the filtering technique to an actual trajectory determination, however, several semi-empirical practices are often used in order to eliminate convergence difficulties primarily related with probable non-positive definite character of sequentially obtained variance-covariance matrices. By applying a method of pnimipal component analysis in this paper to investigate the reason and elimination of the difficulties, it is shown that the difficulties are associated rather with mathematical expression of the pursued trajectory than round- off errror due to finite digit calculation, and the difficulties are, to some extent, eliminated by choosing a proper caordinate system. The real-time tracking programme presently used at Kagoshima Space Center for a satellite launching purpose is reviewed with respect to the results of this analysis, and it is shown that a practically optimum filter with no convergence difficulties even for 6～10 digits computation can be used in the real time program by improving a small part of the program.
オンライン軌道推定におけるKalman Filterの応用について
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