Invariance of subspace based estimators

Subspace-based estimates, i.e., estimates obtained by exploiting the orthogonality between a sample subspace and a parameter-dependent subspace, have proved useful in many applications, including array processing and system identification. The purpose of this paper is to complement the already available theoretical results generally obtained in specific contexts. We discuss the generalization of the optimal weighted subspace fitting approach introduced by Viberg in the DOA estimation context; we exhibit some invariance properties of optimally weighted estimate, and we show the equivalence between subspace fitting and subspace matching.