Joint Detection and Localization of an Unknown Number of Sources Using Algebraic Structure of the Noise Subspace
Type
PreprintKAUST Grant Number
OSR-2015-Sensors-2700Date
2018-05-22Permanent link to this record
http://hdl.handle.net/10754/632000
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Show full item recordAbstract
Source localization and spectral estimation are among the most fundamental problems in statistical and array signal processing. Methods which 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 apriori 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 SNRs. Further, no performance sacrifice in simple scenarios is observed.Sponsors
This work was supported in parts by the KAUST-MIT-TUD consortium grant OSR-2015-Sensors-2700 and Academy of Finland reserach grant No. 299243. Matthew W. Morency is supported in part by the Natural Sciences and Engineering Research Council of Canada PGS-D award.Publisher
arXivarXiv
1805.08421Additional Links
http://arxiv.org/abs/1805.08421v1http://arxiv.org/pdf/1805.08421v1