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

Toni Karvonen, Silvere Bonnabel, Simo Särkkä, Eric Moulines

Research output: Chapter in Book/Report/Conference proceedingConference contributionScientificpeer-review

5 Citations (Scopus)
253 Downloads (Pure)


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.
Original languageEnglish
Title of host publicationProceedings of 57th IEEE Conference on Decision and Control, CDC 2018
Number of pages6
ISBN (Electronic)9781538613955
Publication statusPublished - 18 Jan 2019
MoE publication typeA4 Conference publication
EventIEEE Conference on Decision and Control - Miami, United States
Duration: 17 Dec 201819 Dec 2018
Conference number: 57

Publication series

NameProceedings of the IEEE Conference on Decision & Control
ISSN (Print)0743-1546


ConferenceIEEE Conference on Decision and Control
Abbreviated titleCDC
Country/TerritoryUnited States


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


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