Constrained Least Squares for Extended Complex Factor Analysis

Ahmad Mouri Sardarabadi; Alle-Jan van der Veen; L. V. E. Koopmans

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arXiv · 1804.00430

Constrained Least Squares for Extended Complex Factor Analysis

Ahmad Mouri Sardarabadi·Alle-Jan van der Veen·L. V. E. Koopmans

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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.

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Ahmad Mouri Sardarabadi, Alle-Jan van der Veen, L. V. E. Koopmans. 2018-04-02. Constrained Least Squares for Extended Complex Factor Analysis. https://arxiv.org/abs/1804.00430

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