An Introduction to Twisted Particle Filters and Parameter Estimation in Non-linear State-space Models

Twisted particle filters are a class of sequential Monte Carlo methods recently introduced by Whiteley and Lee to improve the efficiency of marginal likelihood estimation in state-space models. The purpose of this article is to provide an accessible introduction to twisted particle filtering methodology, explain its rationale and extend it in a number of ways. We provide a derivation of the algorithms to incorporate systematic or multinomial resampling and a transparent proof which identifies the optimal algorithm for marginal likelihood estimation. We demonstrate how to approximate the optimal algorithm for nonlinear state-space models with Gaussian noise. Numerical results for an indoor positioning problem with bluetooth signal strength measurements demonstrate the performance of the algorithm in the context of estimating the static model parameters via particle Markov chain Monte Carlo, showing improvements over standard algorithms in terms of variance of marginal likelihood estimates and Markov chain autocorrelation for given CPU time.