Asymptotic properties of subspace estimators

Since the proposal of subspace methods in the 1980s and early 1990s substantial efforts have been made in the analysis of the statistical properties of the algorithms. This paper surveys the literature on the asymptotic properties of particular subspace methods used for linear, dynamic, time invariant, discrete time systems. The goals of this paper are threefold: First this survey tries to present the most relevant results on the asymptotic properties of estimators obtained using subspace methods. Secondly the main methods and tools that have been used in the derivation of these results are presented to make the literature more accessible. Thirdly main unsolved questions and rewarding research topics are identified some of which can be attacked using the toolbox discussed in the paper.