Application of Girsanov Theorem to Particle Filtering of Discretely Observed Continuous-Time Non-Linear Systems

摘要

This article considers the application of particle filtering tocontinuous-discrete optimal filtering problems, where the system model is astochastic differential equation, and noisy measurements of the system areobtained at discrete instances of time. It is shown how the Girsanov theoremcan be used for evaluating the likelihood ratios needed in importance sampling.It is also shown how the methodology can be applied to a class of models, wherethe driving noise process is lower in the dimensionality than the state andthus the laws of state and noise are not absolutely continuous.Rao-Blackwellization of conditionally Gaussian models and unknown staticparameter models is also considered.