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

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

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Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics. / Karvonen, Toni; Bonnabel, Silvere; Särkkä, Simo; Moulines, Eric.

Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018. Vol. 2018-December Institute of Electrical and Electronics Engineers, 2019. p. 7176-7181 8619726 (Proceedings of the IEEE Conference on Decision & Control).

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

Harvard

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, Institute of Electrical and Electronics Engineers, pp. 7176-7181, IEEE Conference on Decision and Control, Miami, United States, 17/12/2018. https://doi.org/10.1109/CDC.2018.8619726

APA

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). [8619726] (Proceedings of the IEEE Conference on Decision & Control). Institute of Electrical and Electronics Engineers. https://doi.org/10.1109/CDC.2018.8619726

Vancouver

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. Institute of Electrical and Electronics Engineers. 2019. p. 7176-7181. 8619726. (Proceedings of the IEEE Conference on Decision & Control). https://doi.org/10.1109/CDC.2018.8619726

Author

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

Bibtex - Download

@inproceedings{3a176e54976143f3ba9e7d96b9d7bb12,
title = "Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics",
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.",
keywords = "Differential equations, Mathematical model, Covariance matrices, Kalman filters, Riccati equations, Upper bound, Numerical models, Convergence, Stochastic stability, Equation",
author = "Toni Karvonen and Silvere Bonnabel and Simo S{\"a}rkk{\"a} and Eric Moulines",
year = "2019",
month = "1",
day = "18",
doi = "10.1109/CDC.2018.8619726",
language = "English",
volume = "2018-December",
series = "Proceedings of the IEEE Conference on Decision & Control",
publisher = "Institute of Electrical and Electronics Engineers",
pages = "7176--7181",
booktitle = "Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018",
address = "United States",

}

RIS - Download

TY - GEN

T1 - Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics

AU - Karvonen, Toni

AU - Bonnabel, Silvere

AU - Särkkä, Simo

AU - Moulines, Eric

PY - 2019/1/18

Y1 - 2019/1/18

N2 - 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.

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

KW - Kalman filters

KW - Riccati equations

KW - Upper bound

KW - Numerical models

KW - Convergence

KW - Stochastic stability

KW - Equation

UR - http://www.scopus.com/inward/record.url?scp=85062175916&partnerID=8YFLogxK

U2 - 10.1109/CDC.2018.8619726

DO - 10.1109/CDC.2018.8619726

M3 - Conference contribution

VL - 2018-December

T3 - Proceedings of the IEEE Conference on Decision & Control

SP - 7176

EP - 7181

BT - Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018

PB - Institute of Electrical and Electronics Engineers

ER -

ID: 30436140