Unified Linearization-based Nonlinear Filtering

TL;DR

This paper unifies various recursive nonlinear filtering algorithms into a single general framework, enhancing understanding of their similarities, differences, and performance in nonlinear localization tasks.

Contribution

It introduces a unified linearization-based algorithm that encompasses standard, iterated, and dynamically iterated nonlinear filters, clarifying their relationships.

Findings

Unified framework reveals similarities between filter classes

Numerical example compares accuracy of different filters

Insights into pros and cons of each filter class

Abstract

This letter shows that the following three classes of recursive state estimation filters: standard filters, such as the extended Kalman filter; iterated filters, such as the iterated unscented Kalman filter; and dynamically iterated filters, such as the dynamically iterated posterior linearization filters; can be unified in terms of a general algorithm. The general algorithm highlights the strong similarities between specific filtering algorithms in the three filter classes and facilitates an in-depth understanding of the pros and cons of the different filter classes and algorithms. We end with a numerical example showing the estimation accuracy differences between the three classes of filters when applied to a nonlinear localization problem.