Knowledge area(s)

Stochastic hybrid systems Bayesian filtering Particle filtering State dependent switching Jump-nonlinear systems Non-Markov jumps Maneuvering target tracking Exact Bayesian and particle filtering of stochastic hybrid systems Problem area In literature on Bayesian filtering of stochastic hybrid systems most studies are limited to Markov jump systems. The main exceptions are approximate Bayesian filters for semi-Markov jump linear systems. These studies showed that nonlinear filtering becomes much more challenging under non-Markov jumps. This challenge however does not apply to particle filtering of stochastic hybrid systems. In practice, non-Markov jumps rather are the rule, not the exception. For example, on an airport, the probability at which a taxiing aircraft makes a maneuver depends heavily on its position; e.g. when taxiing near a crossing on the airport, the probability of starting a turn is relatively high, whereas outside these areas this probability may be very small. A similar difference applies to the probability of an aircraft making a turn when it is flying near a waypoint versus flying halfway two waypoints. Similar non-Markov jump behavior also applies to other traffic modalities, and to any other intelligently controlled system. Nevertheless in target tracking, particle filtering studies have continued to focus on Markov jump systems Description of work This report considers filtering of stochastic hybrid systems that go beyond the well known Markov jump system. First the non-Markovian jump system studied in this report is formally defined. Next the exact Bayesian filter recursion for this system is developed and the implication of going beyond Markov jumps is shown. Subsequently a novel particle filter for jump nonlinear systems is developed which is referred to a