TY - CHAP
T1 - On the Effects of the Initial Condition in State Estimation for Discrete-Time Linear Systems
AU - Sowers, Richard B.
AU - Makowski, Armand M.
N1 - Copyright:
Copyright 2018 Elsevier B.V., All rights reserved.
PY - 1993/1/1
Y1 - 1993/1/1
N2 - We consider the one-step prediction problem for discrete-time linear systems in correlated Gaussian white plant and observation noises, and non-Gaussian initial conditions. Explicit representations are obtained for the MMSE and LLSE (or Kaiman) estimates of the state given past observations, as well as for the expected square of their difference. These formulae are obtained with the help of the Girsanov transformation for Gaussian white noise sequences, and explicitly display the effects of the distribution of the initial condition. With the help of these formulae, we investigate the large-time asymptotics of Et, the expected squared difference between the MMSE and LLSE estimates at time t. We characterize the limit of the error sequence {Et, t = 1,2,…} and obtain some related rates of convergence. A complete large-time analysis is provided for the scalar case.
AB - We consider the one-step prediction problem for discrete-time linear systems in correlated Gaussian white plant and observation noises, and non-Gaussian initial conditions. Explicit representations are obtained for the MMSE and LLSE (or Kaiman) estimates of the state given past observations, as well as for the expected square of their difference. These formulae are obtained with the help of the Girsanov transformation for Gaussian white noise sequences, and explicitly display the effects of the distribution of the initial condition. With the help of these formulae, we investigate the large-time asymptotics of Et, the expected squared difference between the MMSE and LLSE estimates at time t. We characterize the limit of the error sequence {Et, t = 1,2,…} and obtain some related rates of convergence. A complete large-time analysis is provided for the scalar case.
UR - https://www.scopus.com/pages/publications/85023382783
UR - https://www.scopus.com/pages/publications/85023382783#tab=citedBy
U2 - 10.1016/B978-0-12-012756-6.50014-1
DO - 10.1016/B978-0-12-012756-6.50014-1
M3 - Chapter
AN - SCOPUS:85023382783
T3 - Control and Dynamic Systems
SP - 325
EP - 393
BT - Control and Dynamic Systems
ER -