AI-Aided ESPRIT for Joint DoA Estimation and Uncertainty Extraction

Abstract: DoA estimation often requires not only accurate recovery of source directions, but also reliable characterization of the uncertainty in these estimates. While classical subspace methods such as ESPRIT provide principled uncertainty analyses, their performance and uncertainty quantification rely on restrictive assumptions. Recent deep learning approaches alleviate these limitations and enable robust. DoA estimation in challenging conditions, but generally provide point estimates and lack principled uncertainty characterization. In this work, we develop an AI-aided framework for joint DoA estimation and uncertainty quantification that combines the robustness of model-based deep learning with the analytical foundations of classical subspace methods. Building on AI surrogate covariance recovery, we extend existing ESPRIT uncertainty analyses to characterize the full covariance structure of the DoA estimation error and integrate this characterization into a subspace-oriented deep learning architecture. We further propose a dedicated learning strategy that jointly promotes accurate DoA recovery and faithful uncertainty estimation. The resulting methodology preserves the interpretable processing pipeline of classical subspace methods while enabling reliable operation in regimes where conventional approaches struggle. Our numerical studies demonstrate that the proposed framework consistently achieves accurate DoA estimation together with reliable uncertainty characterization across diverse challenging scenarios, including coherent sources, limited snapshots, and array calibration errors.