Constrained Least Squares for Extended Complex Factor Analysis

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

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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.

Original languageEnglish
Title of host publication2018 IEEE 10th Sensor Array and Multichannel Signal Processing Workshop (SAM)
Number of pages5
ISBN (Electronic)978-1-5386-4752-3
ISBN (Print)978-1-5386-4753-0
Publication statusPublished - 2018
Event10th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2018 - Sheffield, United Kingdom
Duration: 8 Jul 201811 Jul 2018
Conference number: 10


Conference10th IEEE Sensor Array and Multichannel Signal Processing Workshop, SAM 2018
Country/TerritoryUnited Kingdom

Bibliographical note

Green Open Access added to TU Delft Institutional Repository ‘You share, we take care!’ – Taverne project

Otherwise as indicated in the copyright section: the publisher is the copyright holder of this work and the author uses the Dutch legislation to make this work public.


  • Factor Analysis
  • Non-Linear Optimization
  • Covariance Matching

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