Parameter estimation in non-linear state-space models by automatic differentiation of non-linear kalman filters

Ajinkya Gorad; Zheng Zhao; Simo Särkkä

doi:10.1109/MLSP49062.2020.9231844

Parameter estimation in non-linear state-space models by automatic differentiation of non-linear kalman filters

Ajinkya Gorad, Zheng Zhao, Simo Särkkä

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

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Abstract

In this article, we propose automatic differentiation based methods for parameter estimation in non-linear state-space models. We use extended Kalman filter and cubature Kalman filters for approximating the negative log-likelihood (i.e., the energy function) of the parameter posterior distribution and compute the gradients and Hessians of this function by using automatic differentiation of the filter recursions. The proposed approach enables computing MAP estimates and forming Laplace approximations for the parameter posterior without a need for implementing complicated derivative recursions or manual computation of Jacobians. The methods are demonstrated in parameter estimation problems on a pendulum model and coordinated turn model.

Original language	English
Title of host publication	Proceedings of the 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing, MLSP 2020
Publisher	IEEE
Number of pages	6
ISBN (Electronic)	9781728166629
DOIs	https://doi.org/10.1109/MLSP49062.2020.9231844
Publication status	Published - Sep 2020
MoE publication type	A4 Article in a conference publication
Event	IEEE International Workshop on Machine Learning for Signal Processing - Aalto University, Espoo, Finland Duration: 21 Sep 2020 → 24 Sep 2020 Conference number: 30 https://ieeemlsp.cc

Publication series

Name	IEEE International Workshop on Machine Learning for Signal Processing
Publisher	IEEE
ISSN (Print)	2161-0363
ISSN (Electronic)	2161-0371

Workshop

Workshop	IEEE International Workshop on Machine Learning for Signal Processing
Abbreviated title	MLSP
Country/Territory	Finland
City	Espoo
Period	21/09/2020 → 24/09/2020
Internet address	https://ieeemlsp.cc

Keywords

Automatic differentiation
Cubature Kalman filter
Extended Kalman filter
Non -linear state space model
Parameter estimation

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10.1109/MLSP49062.2020.9231844

ELEC_Gorad_etal_Parameter-Estimation-in-Non-Linear_MLSP2020_acceptedauthormanuscriptAccepted author manuscript, 506 KB

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Gorad, A., Zhao, Z., & Särkkä, S. (2020). Parameter estimation in non-linear state-space models by automatic differentiation of non-linear kalman filters. In Proceedings of the 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing, MLSP 2020 [9231844] (IEEE International Workshop on Machine Learning for Signal Processing). IEEE. https://doi.org/10.1109/MLSP49062.2020.9231844

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abstract = "In this article, we propose automatic differentiation based methods for parameter estimation in non-linear state-space models. We use extended Kalman filter and cubature Kalman filters for approximating the negative log-likelihood (i.e., the energy function) of the parameter posterior distribution and compute the gradients and Hessians of this function by using automatic differentiation of the filter recursions. The proposed approach enables computing MAP estimates and forming Laplace approximations for the parameter posterior without a need for implementing complicated derivative recursions or manual computation of Jacobians. The methods are demonstrated in parameter estimation problems on a pendulum model and coordinated turn model. ",

keywords = "Automatic differentiation, Cubature Kalman filter, Extended Kalman filter, Non -linear state space model, Parameter estimation",

author = "Ajinkya Gorad and Zheng Zhao and Simo S{\"a}rkk{\"a}",

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doi = "10.1109/MLSP49062.2020.9231844",

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series = "IEEE International Workshop on Machine Learning for Signal Processing",

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booktitle = "Proceedings of the 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing, MLSP 2020",

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Gorad, A, Zhao, Z & Särkkä, S 2020, Parameter estimation in non-linear state-space models by automatic differentiation of non-linear kalman filters. in Proceedings of the 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing, MLSP 2020., 9231844, IEEE International Workshop on Machine Learning for Signal Processing, IEEE, IEEE International Workshop on Machine Learning for Signal Processing, Espoo, Finland, 21/09/2020. https://doi.org/10.1109/MLSP49062.2020.9231844

Parameter estimation in non-linear state-space models by automatic differentiation of non-linear kalman filters. / Gorad, Ajinkya; Zhao, Zheng; Särkkä, Simo.

Proceedings of the 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing, MLSP 2020. IEEE, 2020. 9231844 (IEEE International Workshop on Machine Learning for Signal Processing).

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

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N2 - In this article, we propose automatic differentiation based methods for parameter estimation in non-linear state-space models. We use extended Kalman filter and cubature Kalman filters for approximating the negative log-likelihood (i.e., the energy function) of the parameter posterior distribution and compute the gradients and Hessians of this function by using automatic differentiation of the filter recursions. The proposed approach enables computing MAP estimates and forming Laplace approximations for the parameter posterior without a need for implementing complicated derivative recursions or manual computation of Jacobians. The methods are demonstrated in parameter estimation problems on a pendulum model and coordinated turn model.

AB - In this article, we propose automatic differentiation based methods for parameter estimation in non-linear state-space models. We use extended Kalman filter and cubature Kalman filters for approximating the negative log-likelihood (i.e., the energy function) of the parameter posterior distribution and compute the gradients and Hessians of this function by using automatic differentiation of the filter recursions. The proposed approach enables computing MAP estimates and forming Laplace approximations for the parameter posterior without a need for implementing complicated derivative recursions or manual computation of Jacobians. The methods are demonstrated in parameter estimation problems on a pendulum model and coordinated turn model.

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KW - Non -linear state space model

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Gorad A, Zhao Z, Särkkä S. Parameter estimation in non-linear state-space models by automatic differentiation of non-linear kalman filters. In Proceedings of the 2020 IEEE 30th International Workshop on Machine Learning for Signal Processing, MLSP 2020. IEEE. 2020. 9231844. (IEEE International Workshop on Machine Learning for Signal Processing). doi: 10.1109/MLSP49062.2020.9231844

Parameter estimation in non-linear state-space models by automatic differentiation of non-linear kalman filters

Abstract

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Workshop

Keywords

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Parallel and distributed computing for Bayesian graphical models

Science-IT

Cite this

Parameter estimation in non-linear state-space models by automatic differentiation of non-linear kalman filters

Abstract

Publication series

Workshop

Keywords

Access to Document

OpenUrl availability

Other files and links

Fingerprint

Projects

Parallel and distributed computing for Bayesian graphical models

Equipment

Science-IT

Cite this