The objective of this thesis is the algorithmic enhancement and initial evaluation of an underwater acoustic positioning system which is designed to determine the position and orientation of a mobile nuclear reactor vessel inspection robot. Although a great deal of research has been done in the area of underwater acoustic positioning, this work differs from previous work in three significant ways. First, most applied acoustic positioning systems have been designed for the offshore oil drilling industry, and thus their requirements and restrictions are dictated by an oceanic environment. Second, most previous work has focused only upon acquiring the position of a point from the acoustic system. The inspection robot operation requires accurate positioning and orientation. Finally, the accuracy of acoustic positioning systems is generally dependent upon an evaluation of the speed of sound. However, this parameter is highly dependent upon water temperature. As will be discussed, the reactor vessel water temperature may not be uniform or constant, which makes the design of a precise positioning system difficult. Original methods to overcome this obstacle are discussed and evaluated. Also examined are configurations and constraints of the acoustic transceivers, the numerical solution procedures utilized, and the resulting errors associated with the developed methods. / Master of Science