In the field of target localization, improving direction-of-arrival (DOA) estimation methods for weak targets in the context of strong interference remains a significant challenge. This paper presents a robust DOA estimator for localizing weak signals of interest in an environment with strong interfering sources that improve passive sonar DOA estimation. The presented estimator combines a multiple-measurement-vector orthogonal matching pursuit (MOMP) algorithm and a dimension-reduced matrix filter with deep nulling (DR-MFDN). Strong interfering sources are adaptively suppressed by employing the DR-MFDN, and the beam-space passband robustness is improved. In addition, Gaussian pre-whitening is used to prevent noise colorization. Simulations and experimental results demonstrate that the presented estimator outperforms a conventional estimator based on a dimension-reduced matrix filter with nulling (DR-MFN) and the multiple signal classification algorithm in terms of interference suppression and localization accuracy. Moreover, the presented estimator can effectively handle short snapshots, and it exhibits superior resolution by considering the signal sparsity.