Joint Detection and Localization of an Unknown Number of Sources Using the Algebraic Structure of the Noise Subspace

Matthew W. Morency*, Sergiy A. Vorobyov, Geert Leus

*Corresponding author for this work

Research output: Contribution to journalArticleScientificpeer-review

7 Citations (Scopus)
7 Downloads (Pure)


Source localization and spectral estimation are among the most fundamental problems in statistical and array signal processing. Methods that rely on the orthogonality of the signal and noise subspaces, such as Pisarenko's method, MUSIC, and root-MUSIC, are some of the most widely used algorithms to solve these problems. As a common feature, these methods require both a priori knowledge of the number of sources and an estimate of the noise subspace. Both requirements are complicating factors to the practical implementation of the algorithms and, when not satisfied exactly, can potentially lead to severe errors. In this paper, we propose a new localization criterion based on the algebraic structure of the noise subspace that is described for the first time to the best of our knowledge. Using this criterion and the relationship between the source localization problem and the problem of computing the greatest common divisor (GCD), or more practically approximate GCD, for polynomials, we propose two algorithms, which adaptively learn the number of sources and estimate their locations. Simulation results show a significant improvement over root-MUSIC in challenging scenarios such as closely located sources, both in terms of detection of the number of sources and their localization over a broad and practical range of signal-to-noise ratios. Furthermore, no performance sacrifice in simple scenarios is observed.

Original languageEnglish
Article number8387523
Pages (from-to)4685-4700
Number of pages16
JournalIEEE Transactions on Signal Processing
Issue number17
Publication statusPublished - 2018

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.


  • Algebraic geometry
  • approximate greatest common devisor
  • direction-of-arrival estimation
  • noise subspace
  • polynomial ideals
  • source localization
  • spectral estimation


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