On the optimal accuracy and double solution in the calculation of initial orbits

Abstract

It is shown, by simulated calculation, that the reference vector algorithm we proposed of calculating initial orbits is “quasi-optimal”, because its accuracy approaches the Cramér-Rao lower bound in the statistical theory of estimation and is proportional to the observing error. Double solution exists in the orbit calculation: the smaller the eccentricity and the closer the mean anomaly M 0 is to ±90°, the greater is the probability of getting the false solution. We propose an algorithm which gives two solutions, one of which must be the true one and it has a high accuracy.