On the two-filter approximations of marginal smoothing distributions in general state space models

TL;DR

This paper rigorously analyzes the two-filter algorithms used for approximating smoothing distributions in general state space models, extending existing results to these combined forward and backward filtering approaches.

Contribution

It provides a theoretical extension of existing results to the two-filter smoothing algorithms in state space models.

Findings

The analysis confirms the validity of two-filter approximations for smoothing distributions.

The paper extends theoretical understanding of combined forward-backward filtering methods.

Results support the use of two-filter algorithms in practical state estimation tasks.

Abstract

A prevalent problem in general state space models is the approximation of the smoothing distribution of a state conditional on the observations from the past, the present, and the future. The aim of this paper is to provide a rigorous analysis of such approximations of smoothed distributions provided by the two-filter algorithms. We extend the results available for the approximation of smoothing distributions to these two-filter approaches which combine a forward filter approximating the filtering distributions with a backward information filter approximating a quantity proportional to the posterior distribution of the state given future observations.