PhD Seminar Series: “Non-Gaussian Orbit Determination for Near-Earth and Cislunar Space Domain Awareness”

Abstract: 

Utilization of the space environment is changing at a rapid pace. The emergence of large constellations operating in low-Earth orbit, the decommissioning of satellites that are left in orbit, and the expansion of consistent operations into the cislunar domain produce new challenges in space domain awareness that must be addressed using limited sensor resources. A key element of space domain awareness is formulating and maintaining up-to-date information on the state (e.g., position and velocity) of objects in the domain. One way to achieve this awareness is to overcome any lack of knowledge through the deployment and acquisition of an ever-increasing amount of information. Space domain awareness is – almost by definition – a topic in which it is impossible to dominate the problem through more information; instead, it becomes necessary to embrace uncertainty and advance the state-of-the-art in an alternative manner.

In this talk, a new approach to Bayesian estimation for nonlinear, non-Gaussian systems is devel- oped and applied to the space object tracking problem. Tracking algorithms are broadly separated into two stages: prediction and inference. The prediction stage forecasts uncertainty forward in time using the system dynamics to provide an understanding of where a space object might be. The inference stage fuses new information with the predicted uncertainty using Bayes’ rule to produce an updated uncertainty. Previous work has focused primarily on the propagation of uncertainty in the presence of nonlinear dynamics, and it has been shown that Gaussian mixture representations are better able to approximate the underlying probability distribution for space object tracking. This work leverages the findings from uncertainty propagation to produce approximate Bayesian inference via a homotopic approach that operates on Gaussian mixture representations of the un- certainty. The new approach formulates a progression of partial updates, and a limiting procedure is used to solve for ordinary differential equations that govern the update stage. This so-called “parameter flow” approach is shown to improve upon existing techniques for processing nonlin- ear measurements. The new method is demonstrated on illustrative problems, including examples relevant for near-Earth space domain awareness and cislunar space domain awareness.