posted on 2025-05-10, 23:43authored byEduardo Rohr, Damián Marelli, Minyue FuMinyue Fu
In this paper we study statistical properties of the error covariance matrix of a Kalman filter, when it is subject to random measurement losses. We introduce a sequence of tighter upper bounds for the asymptotic expected error covariance (EEC). This sequence starts with a given upper bound in the literature and converges to the actual asymptotic EEC. Although we have not yet shown the monotonic convergence of this whole sequence, monotonic convergent subsequences are identified. The feature of these subsequences is that a tighter upper bound is guaranteed if more computation is allowed. An iterative algorithm is provided for computing each of these upper bounds. A byproduct of this paper is a more compact proof for a known necessary condition on the measurement arrival probability for the asymptotic EEC to be finite. A similar analysis leads to a necessary condition on the measurement arrival probability for the error covariance to have a finite asymptotic variance.
History
Source title
Proceedings of the 49th IEEE Conference on Decision and Control
Name of conference
49th IEEE Conference on Decision and Control (CDC 2010)
Location
Atlanta, GA
Start date
2010-12-15
End date
2010-12-17
Pagination
5881-5886
Publisher
Institute of Electrical and Electronics Engineers (IEEE)
Place published
Piscataway, NJ
Language
en, English
College/Research Centre
Faculty of Engineering and Built Environment
School
School of Electrical Engineering and Computer Science