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Spherical microphone array eigenbeam (EB)-ESPRIT gives an elegant closed-form solution for 3D broadband source localization based on the spherical harmonics (eigenbeam) framework. However, in practical implementations, there are still several issues not being rigorously studied, e.g. how to avoid the ill-conditioning of an EB-ESPRIT matrix, solve the ambiguity problem, handle a large number of sources, and localize coherent broadband sources, etc. In this work, we propose to use the condition number of the EB-ESPRIT matrix as a robustness measure, and to use Wigner-D weighting to avoid the ill-conditioning issue and improve the robustness. In addition, power spectrum testing, frequency smoothing, and manifold vector extension techniques are employed to address the ambiguity, coherent source localization, and large source number problems, respectively. Experimental results based on measurements taken with a real spherical microphone array in a room environment show the effectiveness of the proposed methods.