This article is concerned with the convergence of the state estimate obtained
from the discrete time Kalman filter to the continuous time estimate as the
temporal discretization is refined. We derive convergence rate estimates for
different systems, first finite dimensional and then infinite dimensional with
bounded or unbounded observation operators. Finally, we derive the convergence
rate in the case where the system dynamics is governed by an analytic
semigroup. The proofs are based on applying the discrete time Kalman filter on
a dense numerable subset of a certain time interval [0,T].Comment: Author's version of the manuscript accepted for publication in
International Journal of Contro
