Possibilistic admissible region using outer probability measure theory

The admissible region method provides a reliable orbit initialization framework for space objects with extremely limited observations. In general, the uncertainty of the admissible region is either ignored or treated as a probability distribution. However, the probabilistic characterization requires that one possess exact knowledge of the distribution of all random errors, e.g., the observation process, the constraint parameters, and the observer related information, which may not be available in realistic scenarios. In this paper, we explore the use of Outer Probability Measure (OPM) theory to achieve a more truthful characterization of the uncertainty of the admissible region, dubbed the Possibilistic Admissible Region (PAR+). Considering that the uncertainty of the constraints is epistemic and modeled by possibility functions, a rigorous possibilistic uncertainty representation is achieved without the need of known random statistics of the system. To wit, the method presented herein can be appropriately interpreted as initializing our inference of a dynamical system with a so-called uninformative prior. The developed PAR+ models the uncertainty of the admissible region as an OPM represented by a collection of particles. It provides a method for space object tracking in the presence of assumed ignorance and unknown randomness (i.e. uninformative prior). The PAR+ for the commonly used angles-only and radar measurements are developed and illustrated using simulated scenarios.