Fundamental limits on orbit uncertainty

The orbital environment of Resident Space Objects (RSO) is highly structured and deterministic in general, with stochastic effects only arising due to mis-modeling and to some variability in the physical environment in which they orbit. Due to this RSO can be well modeled as following Hamiltonian Dynamics, and thus their state space can be expressed as motion on a symplectic manifold, including their uncertainty distributions. There has been recent progress in understanding the fundamental dynamics of phase flows in symplectic systems, with the preeminent advance being “Gromov's Non-Squeezing Theorem,” which can be shown to be similar to the famous Heisenberg Uncertainty Principle in quantum mechanics. This paper applies this concept to probability distribution functions and discusses the resulting implications for their dynamics and measurement updates.