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We derive fast wideband algorithms, based on measurements of the acoustic intensity, for determining the bearings of a target using an acoustic vector sensor (AVS) situated in free space or on a reflecting boundary. We also obtain a lower bound on the mean-square angular error (MSAE) of such estimates. We then develop general closed-form weighted least-squares (WLS) and reweighted least-squares algorithms that compute the three-dimensional (3-D) location of a target whose bearing to a number of dispersed locations has been measured. We devise a scheme for adaptively choosing the weights for the WLS routine when measures of accuracy for the bearing estimates, such as the lower bound on the MSAE, are available. In addition, a measure of the potential estimation accuracy of a distributed system is developed based on a two-stage application of the Cramer-Rao bound. These 3-D results are quite independent of how bearing estimates are obtained. Naturally, the two parts of the paper are tied together by examining how well distributed arrays of AVSs located on the ground, seabed, and in free space can determine the 3-D position of a target The results are relevant to the localization of underwater and airborne sources using freely drifting, moored, or ground sensors. Numerical simulations illustrate the effectiveness of our estimators and the new potential performance measure.