A Recursive Newton Method for Smoothing in Nonlinear State Space Models

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Journal Title
Journal ISSN
Volume Title
Conference article in proceedings
Date
2023
Major/Subject
Mcode
Degree programme
Language
en
Pages
5
1758-1762
Series
31st European Signal Processing Conference, EUSIPCO 2023 - Proceedings, European Signal Processing Conference
Abstract
In this paper, we use the optimization formulation of nonlinear Kalman filtering and smoothing problems to develop second-order variants of iterated Kalman smoother (IKS) methods. We show that Newton's method corresponds to a recursion over affine smoothing problems on a modified state-space model augmented by a pseudo measurement. The first and second derivatives required in this approach can be efficiently computed with widely available automatic differentiation tools. Furthermore, we show how to incorporate line-search and trust-region strategies into the proposed second-order IKS algorithm in order to regularize updates between iterations. Finally, we provide numerical examples to demonstrate the method's efficiency in terms of runtime compared to its batch counterpart.
Description
Funding Information: This work was funded by the Academy of Finland* and the Finnish Center for Artificial Intelligence (FCAI)†. Publisher Copyright: © 2023 European Signal Processing Conference, EUSIPCO. All rights reserved.
Keywords
iterated Kalman filter and smoother, line search, Newton's method, state-space model, trust region
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Citation
Yaghoobi , F , Abdulsamad , H & Särkkä , S 2023 , A Recursive Newton Method for Smoothing in Nonlinear State Space Models . in 31st European Signal Processing Conference, EUSIPCO 2023 - Proceedings . European Signal Processing Conference , European Signal Processing Conference (EUSIPCO) , pp. 1758-1762 , European Signal Processing Conference , Helsinki , Finland , 04/09/2023 . https://doi.org/10.23919/EUSIPCO58844.2023.10290119