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arXiv · 2309.07636

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

Anton Kullberg·Martin A. Skoglund·Isaac Skog·Gustaf Hendeby
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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.

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Anton Kullberg, Martin A. Skoglund, Isaac Skog, Gustaf Hendeby. 2023-09-14. On the Relationship Between Iterated Statistical Linearization and Quasi-Newton Methods. https://arxiv.org/abs/2309.07636

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