A Recursive Newton Method for Smoothing in Nonlinear State Space Models

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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.

Original languageEnglish
Title of host publication31st European Signal Processing Conference, EUSIPCO 2023 - Proceedings
PublisherEuropean Signal Processing Conference (EUSIPCO)
Pages1758-1762
Number of pages5
ISBN (Electronic)978-9-4645-9360-0
DOIs
Publication statusPublished - 2023
MoE publication typeA4 Conference publication
EventEuropean Signal Processing Conference - Helsinki, Finland
Duration: 4 Sept 20238 Sept 2023
Conference number: 31
https://eusipco2023.org/

Publication series

NameEuropean Signal Processing Conference
ISSN (Print)2219-5491

Conference

ConferenceEuropean Signal Processing Conference
Abbreviated titleEUSIPCO
Country/TerritoryFinland
CityHelsinki
Period04/09/202308/09/2023
Internet address

Keywords

  • iterated Kalman filter and smoother
  • line search
  • Newton's method
  • state-space model
  • trust region

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