arXiv:2610.38123v2 Announce Type: replace Abstract: Covariance learning (CL) estimates source powers and sensor-noise variance by minimizing the Type-II (marginal) negative log-likelihood of the array measurements. We develop both grid-based and gridless CL direction-of-arrival (DOA) estimators applicable to arbitrary sparse linear array (SLA) geometries. The grid-based DOA estimator minimizes the Type-II objective on an angular grid via successive convex approximation (SCA) and estimates the noise variance by a scalar bisection search. The gridless DOA estimator then refines each grid-based DOA over the continuum using a Newton method. Simulations on a six-sensor nested array, including an underdetermined case with nine sources, show that the proposed DOA estimators outperform state-of-the-art methods, despite jointly estimating the sensor noise variance.