From Partial Calibration to Full Potential: A Two-Stage Sparse DOA Estimation for Incoherently-Distributed Sources with Partly-Calibrated Arrays

Direction-of-arrival (DOA) estimation for incoherently distributed (ID) sources is crucial for Industrial Internet of Things (IIoT) applications operating in complex multipath environments, yet it remains challenging due to the combined effects of angular spread and gain-phase uncertainties in cost-sensitive antenna arrays. This paper presents a two-stage sparse DOA estimation framework, transitioning from partial calibration to full potential, under the generalized array manifold (GAM) framework. In the first stage, coarse DOA estimates are obtained by exploiting the output from a subset of partly-calibrated arrays (PCAs). In the second stage, these estimates are utilized to determine and compensate for gain-phase uncertainties across all array elements. Then a sparse total least-squares optimization problem is formulated and solved via alternating descent to refine the DOA estimates. Simulation results demonstrate that the proposed method achieves superior estimation accuracy compared to existing approaches, while maintaining robustness against both noise and angular spread effects in practical industrial environments.