Continuous Time Particle Filtering

We present the continuous-time particle filter (CTPF) – an extension of the discrete-time particle filter for monitoring continuous-time dynamic systems. Our methods apply to hybrid systems containing both discrete and continuous variables. The dynamics of the discrete state system are governed by a Markov jump process. Observations of the discrete process are intermittent and irregular. Whenever the discrete process is observed, CTPF samples a trajectory of the underlying Markov jump process. This trajectory is then used to estimate the continuous variables using the system dynamics determined by the discrete state in the trajectory. We use the unscented Kalman-Bucy filter to handle nonlinearities and continuous time. We present results showing that CTPF is more stable in its performance than discrete-time particle filtering, even when the discrete-time algorithm is allowed to update many more times than CTPF. We also present a method for online learning of the Markov jump process model that governs the discrete states.