Exploiting the Data-Driven Regularizer in Group Delay-Based Sparse Recovery Algorithms for Robust 2D-DoA Estimation

The choice of the regularization parameter ($\eta$) plays a vital role in sparse recovery (SR) algorithms for robust direction-of-arrival (DoA) estimation. Contrary to widely spaced sources, the ($\eta$) is generally determined empirically for contiguous sources. Therefore, the first contribution of this work presents the possibility of using data-driven approaches, such as Gaussian process regression (GPR), to select $\eta$ for DoA estimation of contiguous sources. Second, with the $\eta$ chosen via GPR, we propose a 2D-DoA estimation as an extension to 1-D optimum MUSIC group delay-$\ell _{1}$-singular value decomposition (SVD) (optMGD-$\ell _{1}$-SVD) capable of localizing contiguous sources with few sensors and snapshots. Herein, azimuth and elevation are estimated independently on subarrays of an L-shape array with a pairing technique utilizing cross-correlation matrix to avoid the pairing mismatch. This integrated proposed approach is referred to as GoptMGD-$\ell _{1}$-SVD in this work. The proposed method is evaluated in terms of average-root-mean-square-error and resolution probability, where the proposed method is found to achieve better performance at lower signal-to-noise ratio ($< -10$ dB) for contiguous sources.