DescriptionA novel algorithm for localization of Autonomous Underwater Vehicles (AUVs) operating in under-the-ice environments is proposed along with a mathematical analysis for the same. The objective is to accurately predict the position of a mobile AUV via cooperation with neighboring vehicles by utilizing a Doppler-based approach. Current existing localization techniques require either an anchor or surfacing AUV to acquire a GPS fix or rely on a system of expensive and difficult to deploy hardware. Our Doppler-based approach is based on observed Doppler shifts, which are measured opportunistically from ongoing communications between AUVs. These observed Doppler shifts can be used to project the subsequent positions of the AUV and limit the internal uncertainty associated with traditional localization techniques. An AUV's internal uncertainty is the uncertainty in the position of a mobile vehicle as estimated by itself, e.g., via localization techniques. In addition, this Doppler-based approach has minimal network overhead when compared to traditional localization techniques and does not require synchronization between AUVs. The main focus of this thesis is to quantify (via simulations) the solution behavior as well as its sensitivity to possible sources of errors.