Constrained Least Squares for Extended Complex Factor Analysis

TL;DR

This paper introduces a computationally efficient method for solving the non-linear least squares problem in factor analysis with unknown colored noise, improving subspace estimation accuracy.

Contribution

It derives a closed-form diagonalization approach for matrices in the Gauss-Newton algorithm, enabling faster updates of unknown parameters in factor analysis.

Findings

The proposed method reduces computational complexity.

Numerical simulations demonstrate improved convergence.

Efficient parameter updates without matrix construction.

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.