Robust Bayesian Particle Filter for Space Object Tracking Under Severe Uncertainty

Abstract

This paper introduces a robust Bayesian particle filter that can handle epistemic uncertainty in the measurements, dynamics, and initial conditions. The robust filter returns robust bounds on the output quantity of interest, rather than a crisp value. Particles are generated with an importance sampling technique and propagated only one time during the estimation process. The proposal distribution is constructed by running a parallel unscented Kalman filter to drive particles in regions of high expected likelihood and achieve a high effective sample size. The bounds are then computed by an inexpensive tuning of the importance weights via numerical optimization. A Branch & Bound algorithm over simplexes with a Lipschitz bounding function is employed to achieve guaranteed convergence to the lower and upper bounds in a finite number of steps. The filter is applied to the robust computation of the collision probability of SENTINEL 2B with a FENGYUN 1C debris in different operational instances, all characterized by a mix of aleatory and epistemic uncertainty on initial conditions and observation likelihoods.