Positioning systems measure the location of one or moreobjects. As well, most imaging systems inherently perform apositioning function. Positioning systems can be appliedin various forms of transport such as general and spaceaviation or automobiles, but also in geodetic surveying.The aim of this monograph is to establish a general methodfor the mathematical analysis of positioning systems and todemonstrate the utility of this characterization. The basicapproach uses information theory, differential geometry,rate distortion theory and chaos, as well as integrating themore conventional methods of analysis based on estimationand detection theory. This approach allows the derivationof performance limits,estimates of optimal configuration,reasoning about classes of systems, direct comparisonbetween positioning and communication systems, and estimatesof the source information rate of moving objects. The bookshould be of interest to any researcher seeking to gain abetter understanding of a positioning or imaging system.