Efficient Monte Carlo Filtering for Discretely Observed Jumping Processes

This paper addresses a tracking problem in which the unobserved process is characterised by a collection of random jump times and associated random parameters. We construct a scheme for obtaining particle approximations to the posterior distributions of interest in the framework of sequential Monte Carlo (SMC) samplers [1]. We describe efficient sampling schemes and demonstrate that two existing schemes can be interpreted as particular cases of the proposed method. Results are provided which illustrate the performance improvements possible with our approach.