On the optimal accuracy and double solutions of initial orbit determination.

Details On the optimal accuracy and double solutions of initial orbit determination. On the optimal accuracy and double solutions of initial orbit determination.

Nov 1998

adsabs.harvard.edu/cgi-bin/nph-data_query?bibcode=1998acasn..39..337j&link_type=abstract

Acta Astron. Sin., Vol. 39, No. 4, p. 337 - 343

Statistics

1

Orbit Determination: Accuracy

Scientific paper

The optimal accuracy and quasi-optimal algorithm of determining the initial orbit solely with the short-arc measuring angle is investigated on the basis of the theory of optimal statistics. There exists the Cramer-Rao lower bound for the theoretical accuracy of general parameters' estimation. For initial orbit the Cramer-Rao lower bound has its optimal accuracy. For the case of small eccentricities, the authors find an important fact, i.e. there are double solutions in the initial orbit determination. To be precise, one is true and the other is false. When the eccentricity is smaller or M is closer to ±90, it will more probably be given by the false solution. In accordance with the double solutions, a method is derived in this paper. This method can yield two solutions simultaneously, and one of them is the true solution with high accuracy.

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