ℋ∞ estimation problems in discrete-time via J-spectral factorization

In this paper, the ℋ_∞ estimation problem for discrete-time linear time-invariant systems is considered. We propose a new technique based on J-spectral factorization. It allows one to treat filtering, prediction and smoothing problems in a unifying framework and does not require the assumption of system stability. The main advantage of the proposed technique is that, for smoothing and prediction problems, the state-space dimension, and hence the complexity of the method, is the same as for the filtering problem