Filtering When Object Custody is Ambiguous

Filtering involves predicting the future state of a space object in orbit about the earth given observations (e.g. angles-only or radar measurements) about its current and past states. The task is simplest when the identity of the object is known. A recently developed “Adapted STructural (AST)” coordinate system enables the task to be carried out in a computationally efficient manner. Propagation for a single state (or a small number of sigma points) can be carried out using Keplerian dynamics or using a numerically more expensive propagator to accommodate perturbation effects. In either case, the uncertainty can be represented in AST coordinates as Gaussian to a high level of accuracy. An Unscented Kalman Filter (UKF) has been developed in this situation; in particular, there is no need to use particle filters. However, when object custody is uncertain, i.e. when the latest observation might correspond to two or more objects in a catalog, the filtering task is more complicated. In this case we propose a mixture of Gaussians in AST coordinates to represent the state. The paper will demonstrate the feasibility of this approach.