ON LAPLACE'S ORBIT DETERMINATION METHOD: SOME MODIFICATIONS

Three modifications towards enhancing the accuracy and performance of Laplace's method of orbit determination are presented. In the main procedure of the algorithm, an eighth order polynomial needs to be solved for each iteration as the middle range gets corrected. Also an initial guess is required to start the iteration and the correct root should be chosen with care. The first modification presented in this work completely eliminates the polynomial root solving procedure and the trivial initial guess of zero can be used to start the iteration. In the second modification, the first and second time derivatives of the middle range is approximated by the other ranges so all three ranges (if three observations) can be determined by solving just one system of equation which is the basis of the next algorithm improvement based on which the singularity associated with Laplace's method for the coplanar cases will be removed. To handle the coplanar scenarios, at least four observations would be required. Also multiple observations can be used with the modified algorithm to increase the accuracy. All multiple ranges can be determined at the same time while the original Laplace's method estimates just one unknown range at a time.

ON LAPLACE'S ORBIT DETERMINATION METHOD: SOME MODIFICATIONS Conference Paper