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 proceeding › Conference contribution › Scientific › peer-review
Researchers
Research units
- Ecole Polytechnique
- Mines ParisTech
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.
Details
| Original language | English |
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| Title of host publication | Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018 |
| Publication status | Published - 18 Jan 2019 |
| MoE publication type | A4 Article in a 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 | United States |
| City | Miami |
| Period | 17/12/2018 → 19/12/2018 |
- differential equations, mathematical model, covariance matrices, Kalman filters, Riccati equations, upper bound, numerical models, CONVERGENCE, STOCHASTIC STABILITY, EQUATION
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