On the Relationship Between Iterated Statistical Linearization and Quasi-Newton Methods

TL;DR

This paper explores the connections between statistical linearization-based filtering algorithms like IUKF and quasi-Newton methods, revealing their mathematical equivalences and differences to deepen understanding of their properties.

Contribution

It demonstrates that IUKF and IPLF can be viewed as quasi-Newton algorithms, providing a new perspective on their theoretical foundations.

Findings

IUKF and IPLF can be expressed as quasi-Newton algorithms.

The IPLF/IUKF update is approximately identical to QN-IEKF with an extra correction.

This analysis offers a richer understanding of iterated filtering algorithms.

Abstract

This letter investigates relationships between iterated filtering algorithms based on statistical linearization, such as the iterated unscented Kalman filter (IUKF), and filtering algorithms based on quasi-Newton (QN) methods, such as the QN iterated extended Kalman filter (QN-IEKF). Firstly, it is shown that the IUKF and the iterated posterior linearization filter (IPLF) can be viewed as QN algorithms, by finding a Hessian correction in the QN-IEKF such that the IPLF iterate updates are identical to that of the QN-IEKF. Secondly, it is shown that the IPLF/IUKF update can be rewritten such that it is approximately identical to the QN-IEKF, albeit for an additional correction term. This enables a richer understanding of the properties of iterated filtering algorithms based on statistical linearization.