On Propagating Uncertainties for Estimation and Association using Validated Interval Simulation

Abstract

We present a new uncertainty propagation algorithm based on interval arithmetic. The goal is to explore the benefits of a set-based approach for estimation and data association using validated simulation. The presented algorithm capitalises on the measures of a dynamical system to improve its estimation and reduce uncertainties on its trajectory. Our approach also contributes to data association by computing the precision required for a measure to belong to a given track with confidence levels. Mainly interested in space surveillance, we illustrate the contributions of this new algorithm with several scenarios of orbit determination and satellite tracking and their numerical simulations.