Constrained Least Squares for Extended Complex Factor Analysis
A.M. Mouri Sardarabadi (Rijksuniversiteit Groningen)
AJ van der Veen (TU Delft - Signal Processing Systems)
L.V.E. Koopmans (Rijksuniversiteit Groningen)
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Abstract
For subspace estimation with an unknown colored noise, Factor Analysis (FA) and its extensions, denoted as Extended FA (EFA), are good candidates for replacing the popular eigenvalue decomposition (EVD). Finding the unknowns in (E)FA can be done by solving a non-linear least square problem. For this type of optimization problems, the Gauss-Newton (GN) algorithm is a powerful and simple method. The most expensive part of the GN algorithm is finding the direction of descent by solving a system of equations at each iteration. In this paper we show that for (E)FA, the matrices involved in solving these systems of equations can be diagonalized in a closed form fashion and the solution can be found in a computationally efficient way. We show how the unknown parameters can be updated without actually constructing these matrices. The convergence performance of the algorithm is studied via numerical simulations.