TY - GEN
T1 - Bounds on the Covariance Matrix of a Class of Kalman-Bucy Filters for Systems with Non-Linear Dynamics
AU - Karvonen, Toni
AU - Bonnabel, Silvere
AU - Särkkä, Simo
AU - Moulines, Eric
PY - 2019/1/18
Y1 - 2019/1/18
N2 - 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.
AB - 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.
KW - Differential equations
KW - Mathematical model
KW - Covariance matrices
KW - Kalman filters
KW - Riccati equations
KW - Upper bound
KW - Numerical models
KW - Convergence
KW - Stochastic stability
KW - Equation
UR - http://www.scopus.com/inward/record.url?scp=85062175916&partnerID=8YFLogxK
U2 - 10.1109/CDC.2018.8619726
DO - 10.1109/CDC.2018.8619726
M3 - Conference contribution
VL - 2018-December
T3 - Proceedings of the IEEE Conference on Decision & Control
SP - 7176
EP - 7181
BT - Proceedings of 57th IEEE Conference on Decision and Control, CDC 2018
PB - IEEE
ER -