Theoretical analysis of beamforming steering vector formulations for acoustic source localization

In three-dimensional acoustic source localization, setting the steering vector is an important choice. Four formulations are frequently used. noiseless case, two of them yield a correct estimation position, others yielding amplitude source, assuming its position known. Here, noisy measurements considered, and compared in terms bias variance estimated amplitude, allowing more informative assessment their performances. An approximated value biased given. Maximum likelihood parameters derived, showing that it involves combination formulations, for estimation, followed by estimation. This analysis does not rely on specific form Green function, remains relevant general propagation media.