Title :
A unified approach to linear estimation for discrete-time systems. II. H∞ estimation
Author :
Zhang, Huanshui ; Xie, Lihua ; Soh, Yeng Chai
Author_Institution :
Sch. of Electr. & Electron. Eng., Nanyang Technol. Univ., Singapore, Singapore
Abstract :
This paper focuses on developing a unified state-space approach to the H∞ filtering, multistep prediction and fixed-lag smoothing. It is shown that the H∞ estimation is in fact an H2 estimation for an associated system with current and delayed measurements in Krein space. A necessary and sufficient condition for the existence of an H∞ estimator is therefore derived using an innovation analysis method together with projection in Krein space. More importantly, the approach leads to a solution for the long standing H∞ fixed-lag smoothing problem. Our approach does not require augmenting the state of the system and is similar to the forward and backward procedure in the H2 fixed-lag smoothing. The H∞ steady state estimation is also solved in terms of a Riccati equation of the same dimension as the system state
Keywords :
H∞ optimisation; Riccati equations; discrete time systems; filtering theory; identification; linear systems; prediction theory; state-space methods; H∞ estimation; H∞ filtering; Krein space; Riccati equation; delayed measurements; discrete-time systems; innovation analysis method; linear discrete systems; linear estimation; multistep prediction; necessary and sufficient condition; state estimation; unified state-space approach; Current measurement; Delay estimation; Extraterrestrial measurements; Filtering; Riccati equations; Smoothing methods; State estimation; Steady-state; Sufficient conditions; Technological innovation;
Conference_Titel :
Decision and Control, 2001. Proceedings of the 40th IEEE Conference on
Conference_Location :
Orlando, FL
Print_ISBN :
0-7803-7061-9
DOI :
10.1109/.2001.980720