Simultaneous signal subspace rank and model selection with an application to single-snapshot source localization

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Abstract

This paper proposes a novel method for model selection in linear regression by utilizing the solution path of `1 regularized least-squares (LS) approach (i.e., Lasso). This method applies the complex-valued least angle regression and shrinkage (c-LARS) algorithm coupled with a generalized information criterion (GIC) and referred to as the c-LARS-GIC method. c-LARS-GIC is a two-stage procedure, where firstly precise values of the regularization parameter, called knots, at which a new predictor variable enters (or leaves) the active set are computed in the Lasso solution path. Active sets provide a nested sequence of regression models and GIC then selects the best model. The sparsity order of the chosen model serves as an estimate of the model order and the LS fit based only on the active set of the model provides an estimate of the regression parameter vector. We then consider a source localization problem, where the aim is to detect the number of impinging source waveforms at a sensor array as well to estimate their direction-of-arrivals (DoAs) using only a single-snapshot measurement. We illustrate via simulations that, after formulating the problem as a grid-based sparse signal reconstruction problem, the proposed c-LARS-GIC method detects the number of sources with high probability while at the same time it provides accurate estimates of source locations.

Details

Original languageEnglish
Title of host publication2018 26th European Signal Processing Conference, EUSIPCO 2018
Publication statusPublished - 29 Nov 2018
MoE publication typeA4 Article in a conference publication
EventEuropean Signal Processing Conference - Rome, Italy
Duration: 3 Sep 20187 Sep 2018
Conference number: 26

Publication series

NameEuropean Signal Processing Conference
ISSN (Print)2219-5491
ISSN (Electronic)2076-1465

Conference

ConferenceEuropean Signal Processing Conference
Abbreviated titleEUSIPCO
CountryItaly
CityRome
Period03/09/201807/09/2018

    Research areas

  • direction-of-arrival estimation, least squares approximations, parameter estimation, probability, regression analysis, signal reconstruction, signal sources, vectors

ID: 31344061