Prediction, filtering, smoothing and deconvolution in a discrete H infinity setting: A game theory approach

Abstract

The problems of prediction, ® ltering, smoothing and deconvolution are formulated and solved for a discrete time linear system in an H ¥ setting over a ® nite interval. The measurement noise and process noise have bounded energies. The case with known initial conditions is considered. The approach uses a basic quadratic game theory in a discrete time-domain H ¥ setting.

A game theory approach to H/sub /spl infin// deconvolution filter design

“…Its applications can be found in [1], [2], [8]-[11] which use H2 or H", criterion. Hoc> deconvolution filters have been pro posed by using polynomial approach, transfer function approach, variations argument approach and bounded real lemma approach for the time invariant linear system [I ], [5]- [7]. Compared with the H2 filters (Kalman filters), since the H «> filters can be less sensitive to parametric variations and do not require a priori knowledge of noise statistics but only the bounded energy of noise, they are more suited for practical applications [1), [2].…”