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In this article, we complement recent results on the convergence of the stateestimate obtained by applying the discrete-time Kalman filter on a time-sampledcontinuous-time system. As the temporal discretization is refined, the estimateconverges to the continuous-time estimate given by the Kalman--Bucy filter. Weshall give bounds for the convergence rates for the variance of the discrepancybetween these two estimates. The contribution of this article is to generalizethe convergence results to systems with unbounded observation operators underdifferent sets of assumptions, including systems with diagonaliz-ablegenerators, systems with admissible observation operators, and systems withanalytic semigroups. The proofs are based on applying the discrete-time Kalmanfilter on a dense, numerable subset on the time interval [0,T] and bounding theincrements obtained. These bounds are obtained by studying the regularity ofthe underlying semigroup and the noise-free output.

Convergence of discrete-time Kalman filter estimate to continuous-time estimate for systems with unbounded observation