Browsing by Author "Bonnabel, Silvere"

Now showing 1 - 2 of 2

Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics
(2019-01-18) Karvonen, Toni; Bonnabel, Silvere; Särkkä, Simo; Moulines, Eric
A4 Artikkeli konferenssijulkaisussa
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.
On Stability of a Class of Filters for Nonlinear Stochastic Systems
(2020) Karvonen, Toni; Bonnabel, Silvere; Moulines, Eric; Särkkä, Simo
A1 Alkuperäisartikkeli tieteellisessä aikakauslehdessä
This article develops a comprehensive framework for stability analysis of a broad class of commonly used continuous- and discrete-time filters for stochastic dynamic systems with nonlinear state dynamics and linear measurements under certain strong assumptions. The class of filters encompasses the extended and unscented Kalman filters and most other Gaussian assumed density filters and their numerical integration approximations. The stability results are in the form of time-uniform mean square bounds and exponential concentration inequalities for the filtering error. In contrast to existing results, it is not always necessary for the model to be exponentially stable or fully observed. We review three classes of models that can be rigorously shown to satisfy the stringent assumptions of the stability theorems. Numerical experiments using synthetic data validate the derived error bounds.