Hybrid System Diagnosis with Parameter Estimation Using Particle Filters

Particle filtering algorithms are a commonly used approach to state estimation and diagnosis in a variety of systems, particularly those with a combination of discrete and continuous state variables. When applied in dynamic or unknown environments, these algorithms need to be able to estimate the parameters of the model at the same time as they track it. In this paper we look at how particle filtering algorithms can adapt to dynamic environments or uncertainty in two different kinds of hybrid system: discrete time systems such as are commonly used in Kalman filters and most particle filtering algorithms, and the continuous-time models for which the continuoustime particle filter has recently been developed. We show that it is possible to estimate the values of unobservable continuous system parameters such as the rate at which a pipe leaks. We also show that it is possible in some cases to estimate and adjust the parameters of the process that governs the discrete behaviour of the system.