TY - JOUR
T1 - Convergence of discrete-time Kalman filter estimate to continuous-time estimate for systems with unbounded observation
AU - Aalto, Atte
N1 - Publisher Copyright:
© 2018, Springer-Verlag London Ltd., part of Springer Nature.
PY - 2018/9/1
Y1 - 2018/9/1
N2 - 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 refined, the estimate converges to the continuous-time estimate given by the Kalman–Bucy filter. 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 different 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 filter 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.
AB - 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 refined, the estimate converges to the continuous-time estimate given by the Kalman–Bucy filter. 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 different 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 filter 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.
KW - Boundary control systems
KW - Infinite-dimensional systems
KW - Kalman filter
KW - Sampled data
KW - Temporal discretization
UR - http://www.scopus.com/inward/record.url?scp=85048870309&partnerID=8YFLogxK
U2 - 10.1007/s00498-018-0214-4
DO - 10.1007/s00498-018-0214-4
M3 - Article
AN - SCOPUS:85048870309
SN - 0932-4194
VL - 30
JO - Mathematics of Control, Signals, and Systems
JF - Mathematics of Control, Signals, and Systems
IS - 3
M1 - 9
ER -