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In this paper, we study the approximate maximum likelihood (AML) algorithm that estimates the direction of arrivals (DOA) of multiple acoustic sources. The AML algorithm yields the DOAs of multiple sources by enabling an alternating projection procedure based on sequentially iterative search over the single-source parameter space. Through our evaluations on blind beamforming, we have been able to not only use a sensor array with the 2-D AML algorithm that estimates the azimuth angles for multiple sources in the far field of the array but also employ the 3-D AML algorithm that estimates the azimuth and elevation angles. To present a few justifying examples, we consider two acoustic sources and present Cramér-Rao bound (CRB) on the DOA estimation given by a 3-D array. Also, we adopt the concept of isotropic array that yields constant CRB on azimuth angles over the whole azimuth range and constant CRB on elevation angles over the whole elevation range. We have also shown by simulations and experimentally collected data that the 3-D AML algorithm exhibits superior source separation capability over its 2-D counterpart for multiple sources located at different azimuth and elevation angles.