@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 = "IEEE", pages = "7176--7181", booktitle = "Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018", }