Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics

Toni Karvonen; Silvere Bonnabel; Simo Särkkä; Eric Moulines

doi:10.1109/CDC.2018.8619726

Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics

Toni Karvonen, Silvere Bonnabel, Simo Särkkä, Eric Moulines

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

5 Citations (Scopus)

284 Downloads (Pure)

Abstract

We consider a broad class of Kalman-Bucy filter extensions for continuous-time systems with non-linear dynamics and linear measurements. This class contains, for example, the extended Kalman-Bucy filter, the unscented Kalman-Bucy filter, and most other numerical integration filters. We provide simple upper and lower bounds for the trace of the error covariance, as solved from a matrix Riccati equation, for this class of filters. The upper bounds require assuming that the state is fully observed. The bounds are applied to a simple simultaneous localisation and mapping problem and numerically demonstrated on a two-dimensional trigonometric toy model.

Original language	English
Title of host publication	Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018
Publisher	IEEE
Pages	7176-7181
Number of pages	6
Volume	2018-December
ISBN (Electronic)	9781538613955
DOIs	https://doi.org/10.1109/CDC.2018.8619726
Publication status	Published - 18 Jan 2019
MoE publication type	A4 Conference publication
Event	IEEE Conference on Decision and Control - Miami, United States Duration: 17 Dec 2018 → 19 Dec 2018 Conference number: 57

Publication series

Name	Proceedings of the IEEE Conference on Decision & Control
ISSN (Print)	0743-1546

Conference

Conference	IEEE Conference on Decision and Control
Abbreviated title	CDC
Country/Territory	United States
City	Miami
Period	17/12/2018 → 19/12/2018

Keywords

Differential equations
Mathematical model
Covariance matrices
Kalman filters
Riccati equations
Upper bound
Numerical models
Convergence
Stochastic stability
Equation

Access to Document

10.1109/CDC.2018.8619726

ELEC_Karvonen_etal_Bounds-on-the-Covariance_CDC2018Accepted author manuscript, 291 KB

Cite this

Karvonen, T., Bonnabel, S., Särkkä, S., & Moulines, E. (2019). Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics. In Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018 (Vol. 2018-December, pp. 7176-7181). Article 8619726 (Proceedings of the IEEE Conference on Decision & Control). IEEE. https://doi.org/10.1109/CDC.2018.8619726

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Karvonen, T, Bonnabel, S, Särkkä, S & Moulines, E 2019, Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics. in Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018. vol. 2018-December, 8619726, Proceedings of the IEEE Conference on Decision & Control, IEEE, pp. 7176-7181, IEEE Conference on Decision and Control, Miami, Florida, United States, 17/12/2018. https://doi.org/10.1109/CDC.2018.8619726

Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics. / Karvonen, Toni; Bonnabel, Silvere; Särkkä, Simo et al.
Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018. Vol. 2018-December IEEE, 2019. p. 7176-7181 8619726 (Proceedings of the IEEE Conference on Decision & Control).

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

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AB - We consider a broad class of Kalman-Bucy filter extensions for continuous-time systems with non-linear dynamics and linear measurements. This class contains, for example, the extended Kalman-Bucy filter, the unscented Kalman-Bucy filter, and most other numerical integration filters. We provide simple upper and lower bounds for the trace of the error covariance, as solved from a matrix Riccati equation, for this class of filters. The upper bounds require assuming that the state is fully observed. The bounds are applied to a simple simultaneous localisation and mapping problem and numerically demonstrated on a two-dimensional trigonometric toy model.

KW - Differential equations

KW - Mathematical model

KW - Covariance matrices

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KW - Riccati equations

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KW - Numerical models

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KW - Stochastic stability

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Karvonen T, Bonnabel S, Särkkä S, Moulines E. Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics. In Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018. Vol. 2018-December. IEEE. 2019. p. 7176-7181. 8619726. (Proceedings of the IEEE Conference on Decision & Control). doi: 10.1109/CDC.2018.8619726

Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics

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