A Recursive Newton Method for Smoothing in Nonlinear State Space Models

Fatemeh Yaghoobi; Hany Abdulsamad; Simo Särkkä

doi:10.23919/EUSIPCO58844.2023.10290119

A Recursive Newton Method for Smoothing in Nonlinear State Space Models

Fatemeh Yaghoobi, Hany Abdulsamad, Simo Särkkä

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

1 Citation (Scopus)

41 Downloads (Pure)

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 language	English
Title of host publication	31st European Signal Processing Conference, EUSIPCO 2023 - Proceedings
Publisher	European Signal Processing Conference (EUSIPCO)
Pages	1758-1762
Number of pages	5
ISBN (Electronic)	978-9-4645-9360-0
DOIs	https://doi.org/10.23919/EUSIPCO58844.2023.10290119
Publication status	Published - 2023
MoE publication type	A4 Conference publication
Event	European Signal Processing Conference - Helsinki, Finland Duration: 4 Sept 2023 → 8 Sept 2023 Conference number: 31 https://eusipco2023.org/

Publication series

Name	European Signal Processing Conference
ISSN (Print)	2219-5491

Conference

Conference	European Signal Processing Conference
Abbreviated title	EUSIPCO
Country/Territory	Finland
City	Helsinki
Period	04/09/2023 → 08/09/2023
Internet address	https://eusipco2023.org/

Keywords

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

Access to Document

10.23919/EUSIPCO58844.2023.10290119

0001758Accepted author manuscript, 242 KB

Cite this

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title = "A Recursive Newton Method for Smoothing in Nonlinear State Space Models",

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.",

keywords = "iterated Kalman filter and smoother, line search, Newton's method, state-space model, trust region",

author = "Fatemeh Yaghoobi and Hany Abdulsamad and Simo S{\"a}rkk{\"a}",

note = "Funding Information: This work was funded by the Academy of Finland* and the Finnish Center for Artificial Intelligence (FCAI)†. Publisher Copyright: {\textcopyright} 2023 European Signal Processing Conference, EUSIPCO. All rights reserved.; European Signal Processing Conference, EUSIPCO ; Conference date: 04-09-2023 Through 08-09-2023",

year = "2023",

doi = "10.23919/EUSIPCO58844.2023.10290119",

language = "English",

series = "European Signal Processing Conference",

publisher = "European Signal Processing Conference (EUSIPCO)",

pages = "1758--1762",

booktitle = "31st European Signal Processing Conference, EUSIPCO 2023 - Proceedings",

url = "https://eusipco2023.org/",

}

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

A Recursive Newton Method for Smoothing in Nonlinear State Space Models. / Yaghoobi, Fatemeh ; Abdulsamad, Hany ; Särkkä, Simo.
31st European Signal Processing Conference, EUSIPCO 2023 - Proceedings. European Signal Processing Conference (EUSIPCO), 2023. p. 1758-1762 (European Signal Processing Conference).

Research output: Chapter in Book/Report/Conference proceeding › Conference article in proceedings › Scientific › peer-review

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T1 - A Recursive Newton Method for Smoothing in Nonlinear State Space Models

AU - Yaghoobi, Fatemeh

AU - Abdulsamad, Hany

AU - Särkkä, Simo

N1 - Conference code: 31

PY - 2023

Y1 - 2023

N2 - 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.

AB - 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.

KW - iterated Kalman filter and smoother

KW - line search

KW - Newton's method

KW - state-space model

KW - trust region

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U2 - 10.23919/EUSIPCO58844.2023.10290119

DO - 10.23919/EUSIPCO58844.2023.10290119

M3 - Conference article in proceedings

AN - SCOPUS:85178344205

T3 - European Signal Processing Conference

SP - 1758

EP - 1762

BT - 31st European Signal Processing Conference, EUSIPCO 2023 - Proceedings

PB - European Signal Processing Conference (EUSIPCO)

T2 - European Signal Processing Conference

Y2 - 4 September 2023 through 8 September 2023

ER -

A Recursive Newton Method for Smoothing in Nonlinear State Space Models

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

-: Finnish Center for Artificial Intelligence

Cite this

A Recursive Newton Method for Smoothing in Nonlinear State Space Models

Abstract

Publication series

Conference

Keywords

Access to Document

Other files and links

Fingerprint

Projects

-: Finnish Center for Artificial Intelligence

Cite this