Constrained Least Squares for Extended Complex Factor Analysis
Abstract
For subspace estimation with an unknown colored noise, Factor Analysis (FA) is a good candidate for replacing the popular eigenvalue decomposition (EVD). Finding the unknowns in factor analysis 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 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.
Cite
@article{arxiv.1804.00430,
title = {Constrained Least Squares for Extended Complex Factor Analysis},
author = {Ahmad Mouri Sardarabadi and Alle-Jan van der Veen and L. V. E. Koopmans},
journal= {arXiv preprint arXiv:1804.00430},
year = {2018}
}