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

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

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**Simultaneous signal subspace rank and model selection with an application to single-snapshot source localization.** / Tabassum, Muhammad Naveed; Ollila, Esa.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Scientific › peer-review

### Harvard

*2018 26th European Signal Processing Conference, EUSIPCO 2018.*vol. 2018-September, 8553171, European Signal Processing Conference, IEEE, pp. 1592-1596, European Signal Processing Conference, Rome, Italy, 03/09/2018. https://doi.org/10.23919/EUSIPCO.2018.8553171

### APA

*2018 26th European Signal Processing Conference, EUSIPCO 2018*(Vol. 2018-September, pp. 1592-1596). [8553171] (European Signal Processing Conference). IEEE. https://doi.org/10.23919/EUSIPCO.2018.8553171

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TY - GEN

T1 - Simultaneous signal subspace rank and model selection with an application to single-snapshot source localization

AU - Tabassum, Muhammad Naveed

AU - Ollila, Esa

PY - 2018/11/29

Y1 - 2018/11/29

N2 - 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.

AB - 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.

KW - direction-of-arrival estimation

KW - least squares approximations

KW - parameter estimation

KW - probability

KW - regression analysis

KW - signal reconstruction

KW - signal sources

KW - vectors

UR - http://www.scopus.com/inward/record.url?scp=85059815410&partnerID=8YFLogxK

U2 - 10.23919/EUSIPCO.2018.8553171

DO - 10.23919/EUSIPCO.2018.8553171

M3 - Conference contribution

AN - SCOPUS:85059815410

SN - 978-1-5386-3736-4

VL - 2018-September

T3 - European Signal Processing Conference

SP - 1592

EP - 1596

BT - 2018 26th European Signal Processing Conference, EUSIPCO 2018

PB - IEEE

ER -

ID: 31344061