# Research Article Particle smoothing in continuous time: A fast approach via density estimation

## Abstract

We consider the particle smoothing problem for state-space models where the transition density is not available in closed form, in particular for continuous-time, nonlinear models expressed via stochastic differential equations (SDEs). Conventional forward-backward and two-filter smoothers for the particle filter require a closed-form transition density, with the linear-Gaussian Euler-Maruyama discretization usually applied to the SDEs to achieve this. We develop a pair of variants using kernel density approximations to relieve the dependence, and in doing so enable use of faster and more accurate discretization schemes such as Runge-Kutta. In addition, the new methods admit arbitrary proposal distributions, providing an avenue to deal with degeneracy issues. Experimental results on a functional magnetic resonance imaging (fMRI) deconvolution task demonstrate comparable accuracy and significantly improved runtime over conventional techniques.

## Reference

L.M. Murray and A. Storkey (2011). Particle smoothing in continuous time: A fast approach via density estimation. IEEE Transactions on Signal Processing. 59:1017--1026. doi:10.1109/TSP.2010.2096418.

## BibTeX

@Article{Murray2011b,
title = {Particle smoothing in continuous time: A fast approach via density estimation},
author = {Lawrence Matthew Murray and Amos Storkey},
journal = {IEEE Transactions on Signal Processing},
year = {2011},
volume = {59},
pages = {1017--1026},
doi = {10.1109/TSP.2010.2096418},}