A New Representation of Uncertainty for Data Fusion in SSA Detection and Tracking Problems

A key challenge in the design of a Resident Space Object (RSO) detection and tracking algorithm is the scarcity of available information on the various sources of uncertainty in the underlying estimation problem, such as the orbital mechanics or the data sources producing the observations. Some of these uncertain components lack statistical description, such as the Two-Line Elements (TLEs), so that their description as a random variable and their exploitation in a standard Bayesian filtering algorithm remains largely unexplored. This paper exploits uncertain variables and outer probability measures (o.p.m.s), a generalization of the concepts of random variables and probability distributions, in order to propose a representation of all the uncertain components of a typical RSO tracking problem that matches the information available to a space analyst, and fuse them into a coherent Bayesian estimation filter. This algorithm is then illustrated on a scenario where the kinematic state of a Low-Earth Orbit (LEO) satellite is estimated, using realistically simulated radar observations and real TLEs queried from the U.S. Strategic Command (USSTRATCOM)'S catalog.