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

TL;DR

This paper extends twisted particle filters for non-linear state-space models, providing theoretical insights and demonstrating improved efficiency and accuracy in parameter estimation and tracking tasks.

Contribution

It introduces new twisted particle filtering algorithms incorporating resampling and historical data, with theoretical analysis and practical demonstrations.

Findings

Reduced variance in marginal likelihood estimates

Improved Markov chain autocorrelation

Enhanced tracking performance with estimated parameters

Abstract

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.