Simultaneous Signal Subspace Rank and Model Selection with an Application to Single-snapshot Source Localization

TL;DR

This paper introduces c-LARS-GIC, a new method combining Lasso solution paths and information criteria for model selection, effectively estimating the number and parameters of sources in single-snapshot localization tasks.

Contribution

The paper presents a novel two-stage approach that integrates complex-valued LARS and GIC for accurate model order detection and source localization from single measurements.

Findings

High probability detection of source number

Accurate estimation of source locations

Effective single-snapshot source localization

Abstract

This paper proposes a novel method for model selection in linear regression by utilizing the solution path of $\ell_1$ 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 (DoA-s) 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.