MCMC for On-line Filtering: The Particle Path Filter |
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| Abstract | We propose a novel Monte Carlo (MC) method for on-line filtering of
dynamical state-space 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 time-series 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 state-of-the-art 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 | State-space models, Markov Chain Monte Carlo, particle filters, path sampling, mean first passage-time |
| Type | Journal paper [Submitted] |
| Year | 2006 |
| Address | Richard Petersens Plads, Building 321, DK-2800 Kgs. Lyngby |
| Electronic version(s) | [pdf] |
| BibTeX data | [bibtex] |
| IMM Group(s) | Intelligent Signal Processing |