This thesis develops and demonstrates an approach for estimating the three-dimensional (3D) location of a vocalizing underwater marine mammal using acoustic arrival time measurements at three spatially separated receivers while providing rigorous location uncertainties. To properly account for uncertainty in the measurements of receiver parameters (e.g., 3D receiver locations and synchronization times) and environmental parameters (water depth and sound speed correction), these quantities are treated as unknowns constrained with prior estimates and prior uncertainties. While previous localization algorithms have solved for an unknown scaling factor on the prior uncertainties as part of the inversion, in this work unknown scaling factors on both the prior and arrival time uncertainties are estimated. Maximum a posteriori estimates for sound source locations and times, receiver parameters, and environmental parameters are calculated simultaneously. Posterior uncertainties for all unknowns are calculated and incorporate both arrival time and prior uncertainties. Simulation results demonstrated that, for the case considered here, linearization errors are generally small and that the lack of an accurate sound speed profile does not necessarily cause large uncertainties or biases in the estimated positions. The primary motivation for this work was to develop an algorithm for locating underwater Pacific walruses in the coastal waters around Alaska. In 2009, an array of approximately 40 underwater acoustic receivers was deployed in the northeastern Chukchi Sea (northwest of Alaska) from August to October to record the vocalizations of marine mammals including Pacific walruses and bowhead whales. Three of these receivers were placed in a triangular arrangement approximately 400 m apart near the Hanna Shoal (northwest of Wainwright, Alaska). A sequence of walrus knock vocalizations from this data set was processed using the localization algorithm developed in this thesis, yielding a track whose estimated swim speed is consistent with current knowledge of normal walrus swim speed. An examination of absolute and relative walrus location uncertainties demonstrated the usefulness of considering relative uncertainties for applications where the precise location of the mammal is not important (e.g., estimating swim speed). / Graduate