On the Relationship Between Iterated Statistical Linearization and Quasi-Newton Methods
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.
Keywords
Cite
@article{arxiv.2309.07636,
title = {On the Relationship Between Iterated Statistical Linearization and Quasi-Newton Methods},
author = {Anton Kullberg and Martin A. Skoglund and Isaac Skog and Gustaf Hendeby},
journal= {arXiv preprint arXiv:2309.07636},
year = {2023}
}
Comments
4 pages, Accepted to IEEE Signal Processing Letters