Satellite-to-satellite orbit determination using minimum, discrete range and range-rate data only

An observer satellite in a known orbit makes discrete measurement of the range and range-rate of an unknown satellite. If, at every observation, both range and range-rate are measured simutaneously, then three such observations are theoretically sufficient to determine the orbit of the unknown satellite. Techniques for achieving orbit determination from this minimum data are of interest, and are considered here. It is investigated by solving a set of nonlinear algebraic equations with a modified Newton's method. The method is applied to four typical preliminary orbit determination problems. The effect of total observation time interval on the precision of this method is examined. Rules for constructing initial guesses that significantly reduce computation and improve the probability of convergence to the true solution are presented. It will be shown that the method exhibits fast convergence even with poor initial guesses. Numerical examples show that excellent precision of resulting solution can be obtained.