Non-linear Bayesian orbit determination based on the generalized admissible region

In this paper, we propose a non-linear Bayesian estimation technique where, for a set of observations, the physical limits of the knowledge of the observed object are represented not as likelihood functions but as probability density functions (pdfs). When the codimension of the observations are high, a direct numerical implementation of Bayes' theorem is practical. The pdfs are mapped analytically in time by means of a special solution to the Fokker-Planck equations for deterministic systems. This approach requires no a priori information, enables direct comparison of observations with any probabilistic data, and is robust to outlier observations.