An acoustic source can be localized by exploiting the fact that, if the range is not too great, the wavefront of the incoming acoustic energy can be assumed to be circular. This is sometimes called ‘‘Wavefront Curvature Ranging.’’ Here, the estimation of range reduces to the estimation of the radius of a circle. In fact, if sufficient horizontal and vertical aperture is available, range, bearing and elevation can be estimated, given a minimum of four receivers. The technique is based on the measurement of the relative phases between pairs of receivers. In this paper, two methods of improving the performance of such localizers are investigated. In the case where the receivers are mounted on a moving platform, it is shown that exploitation of this motion can improve performance by utilizing information that is usually ignored in phase measurements. Also, since the motion introduces a time dependence in the true values of the time delays, a limit on the accuracy of their measurement is incurred. A recursive estimation process is proposed as a remedy for this problem. These techniques will be demonstrated by using simulated data.