Subspace-based system identification is typically based on an estimate of the extended observability matrix. It is thus of great interest to investigate, and also optimize, the estimate of the observability matrix. Of special interest in this paper is the fact that the influence of certain weighting matrices is an unresolved issue in the literature on subspace identification. Here, an asymptotic analysis of the estimated observability matrix is presented. The main result of the analysis is that novel weighting matrices and pre-filters of instrumental variables are derived.