Probable regions for emitter localization

A probable region (PR) for the location of an emitter is useful for quantifying the reliability of a location estimate and for defining a search region. Previous investigations have yielded equations that define PRs having the form of error or uncertainty ellipses (or ellipsoids) given the assumption of Gaussian probability density functions (pdfs). The new derivation proposed in this paper differs in the use of polar or spherical coordinates instead of Cartesian coordinates. In addition to being simpler in some respects, it has the further advantage of being extensible to other PRs that contain arbitrary regions-of-interest. Numerical examples give results that are in close agreement with the theoretical values.