Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics
Loading...
Access rights
openAccess
URL
Journal Title
Journal ISSN
Volume Title
A4 Artikkeli konferenssijulkaisussa
This publication is imported from Aalto University research portal.
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
View publication in the Research portal (opens in new window)
View/Open full text file from the Research portal (opens in new window)
Other link related to publication (opens in new window)
Date
2019-01-18
Major/Subject
Mcode
Degree programme
Language
en
Pages
6
7176-7181
7176-7181
Series
Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018, Proceedings of the IEEE Conference on Decision & Control
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.Description
Keywords
Differential equations, Mathematical model, Covariance matrices, Kalman filters, Riccati equations, Upper bound, Numerical models, Convergence, Stochastic stability, Equation
Other note
Citation
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