MCMC for Online Filtering: The Particle Path Filter 

Abstract  We propose a novel Monte Carlo (MC) method for online filtering of
dynamical statespace models called the particle path filter (PPF).
The main new feature of the method is the use of a proposal
distribution that exploits two key feature of Markovian systems: The
decomposability of the posterior probability of the latent variables
and the exponential decaying time correlations of the variables.
With this proposal distribution, the whole {\em path of variables
affecting the present} is sampled. This should be contrasted with
two extremes: Traditional Markov chain MC (MCMC) for filtering draws
samples from the latent variables across the whole timeseries and
particle filters (PFs) only drawing samples at the current time
step. In both cases knowledge about the correlations is ignored
leading to slow convergence of the Markov chain. We test and compare
the PPF with stateoftheart PFs for two generic 1d dynamical
systems with two attractive fix points emphasizing the importance of
using correlation time information. For filtering of systems with
very short correlation times PFs outperform PPF in terms of the
required particles to reach a given accuracy. For systems with long
correlations PPF outperforms PFs with orders of magnitude. 
Keywords  Statespace models, Markov Chain Monte Carlo, particle filters, path sampling, mean first passagetime 
Type  Journal paper [Submitted] 
Year  2006 
Address  Richard Petersens Plads, Building 321, DK2800 Kgs. Lyngby 
Electronic version(s)  [pdf] 
BibTeX data  [bibtex] 
IMM Group(s)  Intelligent Signal Processing 