  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
extend the twisted particle filtering methodology, establish accessible
theoretical results which convey its rationale, and provide a demonstration of
its practical performance within particle Markov chain Monte Carlo for
estimating static model parameters. We derive twisted particle filters that
incorporate systematic or multinomial resampling and information from
historical particle states, 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 and we apply such approximations to two examples: a range and
bearing tracking problem and an indoor positioning problem with Bluetooth
signal strength measurements. We demonstrate improvements over standard
algorithms in terms of variance of marginal likelihood estimates and Markov
chain autocorrelation for given CPU time, and improved tracking performance
using estimated parameters.
