This paper studies a two stage approach to state space identification with certain optimality properties. The first stage is essentially a linear correlation stage via orthonormal filtering to reduce the problem to a setup with small equivalent noise. The second stage is an optimal Hankel norm model reduction step. This two stage algorithm is shown to be consistent for a large class of stable, possibly infinite dimensional, linear time-invariant systems under a very mild condition on the additive noise. The consistency analysis is based on a non-probabilistic framework for noise which allows the inclusion of large classes of non-ergodic and non-stationary noise, possibly having deterministic components, with maximum transparency. Furthermore, l(1) and H-infinity convergence results are derived for a popular class of orthonormal basis expansions based on shift operators. These bases include, e.g. Laguerre bases.