This is a preprint of an article published in Mathematics of Control, Signals, and Systems.
All documents in ORBilu are protected by a user license.
Abstract :
[en] In this article, we complement recent results on the convergence of the state estimate obtained by applying the discrete-time Kalman filter on a time-sampled continuous-time system. As the temporal discretization is re fined, the estimate converges to the continuous-time estimate given by the Kalman-Bucy fi lter. We shall give bounds for the convergence rates for the variance of the discrepancy between these two estimates. The contribution of this article is to generalize the convergence results to systems with unbounded observation operators under di fferent sets of assumptions, including systems with diagonalizable generators, systems with admissible observation operators, and systems with analytic semigroups. The proofs are based on applying the discrete-time Kalman fi lter on a dense, numerable subset on the time interval [0,T] and bounding the increments obtained. These bounds are obtained by studying the regularity of the underlying semigroup and the noise-free output.
Scopus citations®
without self-citations
1