Geometric Solution to Probabilistic Admissible Region Based Track Initialization

Probabilistic Admissible Region (PAR) is a technique to initialize the probability density function (pdf) of the states of a Resident Space Object (RSO). It combines apriori information about some of the orbital elements and a single partial-state observation to initialize the pdf of the RSO. A unified, geometrical solution to Probabilistic Admissible Region, G-PAR, is proposed. The proposed scheme gives a closed-form, clearly explainable solution for PAR particle mapping for the first time. It is shown that the G-PAR can be posed as a Bayesian measurement update of the very diffuse pdf of the states given by the postulated statistics. The effectiveness of the proposed G-PAR will be shown on diverse combinations of sensors and apriori knowledge. Its unique advantages in resolving the data association problem inherent in initializing the pdf of the objects when tracking multiple objects will also be presented.