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

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openAccess

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A4 Artikkeli konferenssijulkaisussa

Date

2019-01-18

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Language

en

Pages

6
7176-7181

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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.

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Keywords

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

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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