In this paper we consider the problem of finding a filter that minimizes the worst case magnitude (l(infinity)) of the estimation error in the case of linear time-invariant systems subjected to unknown but magnitude-bounded (l(infinity)) inputs. These inputs consist of process and observation noise, as well as initial conditions; also, the optimization problem is considered over an infinite time horizon. Taking a model matching approach, suboptimal solutions are presented that stem from the resulting l(infinity)-induced norm-minimization problem.