The nodes in a sensor network are often deployed in random locations. However, most applications require that the location and/or orientation of the nodes be known, so post-deployment algorithms for self-localization of the sensor nodes are important. We consider using a mobile access point (AP) for sensor node localization in a randomly deployed sensor network. We focus on the particular case in which the sensors measure the acoustic Doppler shift in a tone that is emitted from the mobile AP. In addition to the acoustic emission, the mobile AP broadcasts a radio signal that contains AP position, velocity, timing, and parameters of the acoustic signal. We demonstrate that atmospheric turbulence has a significant impact on the accuracy of sensor localization, degrading performance by as much as two orders of magnitude relative to an ideal, planewave propagation model. We present Cramer-Rao bounds (CRBs) for sensor localization accuracy and compare the performance of algorithms to the CRBs under "cloudy" and "sunny" weather conditions.