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

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Conference article in proceedings › Scientific › vertaisarvioitu

5 Sitaatiot (Scopus)

287 Lataukset (Pure)

Abstrakti

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.

Alkuperäiskieli	Englanti
Otsikko	Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018
Kustantaja	IEEE
Sivut	7176-7181
Sivumäärä	6
Vuosikerta	2018-December
ISBN (elektroninen)	9781538613955
DOI - pysyväislinkit	https://doi.org/10.1109/CDC.2018.8619726
Tila	Julkaistu - 18 tammik. 2019
OKM-julkaisutyyppi	A4 Artikkeli konferenssijulkaisussa
Tapahtuma	IEEE CONFERENCE ON DECISION AND CONTROL - Miami, Yhdysvallat Kesto: 17 jouluk. 2018 → 19 jouluk. 2018 Konferenssinumero: 57

Julkaisusarja

Nimi	Proceedings of the IEEE Conference on Decision & Control
ISSN (painettu)	0743-1546

Conference

Conference	IEEE CONFERENCE ON DECISION AND CONTROL
Lyhennettä	CDC
Maa/Alue	Yhdysvallat
Kaupunki	Miami
Ajanjakso	17/12/2018 → 19/12/2018

Pääsy asiakirjaan

10.1109/CDC.2018.8619726

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

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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. teoksessa Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018 (Vuosikerta 2018-December, Sivut 7176-7181). Artikkeli 8619726 (Proceedings of the IEEE Conference on Decision & Control). IEEE. https://doi.org/10.1109/CDC.2018.8619726

@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 = jan,

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doi = "10.1109/CDC.2018.8619726",

language = "English",

volume = "2018-December",

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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. julkaisussa Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018. Vuosikerta 2018-December, 8619726, Proceedings of the IEEE Conference on Decision & Control, IEEE, Sivut 7176-7181, IEEE CONFERENCE ON DECISION AND CONTROL, Miami, Florida, Yhdysvallat, 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. Vuosikerta 2018-December IEEE, 2019. s. 7176-7181 8619726 (Proceedings of the IEEE Conference on Decision & Control).

Tutkimustuotos: Artikkeli kirjassa/konferenssijulkaisussa › Conference article in proceedings › Scientific › vertaisarvioitu

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

N1 - Conference code: 57

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

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U2 - 10.1109/CDC.2018.8619726

DO - 10.1109/CDC.2018.8619726

M3 - Conference article in proceedings

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 - IEEE

T2 - IEEE Conference on Decision and Control

Y2 - 17 December 2018 through 19 December 2018

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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. julkaisussa Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018. Vuosikerta 2018-December. IEEE. 2019. s. 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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