In this paper we consider the problem of finding a filter that minimizes the worst-case magnitude (l(x)) of the estimation error in the case of linear periodically time-varying systems subjected to unknown but magnitude-bounded (l(x)) inputs, These inputs consist of process and observation noise, and the optimization problem is considered ol er an infinite-time horizon, Lifting techniques are utilized to transform the problem to a time invariant l(1)-model matching problem subject to additional constraints, Taking advantage of the particular structure of the estimation problem, it is shown how standard methods of l(1) optimization, in particular the delay augmentation technique, can be suitably modified to solve this nonstandard problem.