Positioning systems measure the location of one or more objects. As well, most imaging systems inherently perform a positioning function. Positioning systems can be applied in various forms of transport such as general and space aviation or automobiles, but also in geodetic surveying. The aim of this monograph is to establish a general method for the mathematical analysis of positioning systems and to demonstrate the utility of this characterization. The basic approach uses information theory, differential geometry, rate distortion theory and chaos, as well as integrating the more conventional methods of analysis based on estimation and detection theory. This approach allows the derivation of performance limits,estimates of optimal configuration, reasoning about classes of systems, direct comparison between positioning and communication systems, and estimates of the source information rate of moving objects. The book should be of interest to any researcher seeking to gain a better understanding of a positioning or imaging system.