This paper discusses the Maximum Likelihood (ML) algorithm for the self-localization of passive (angular) or active (angle and range) sensors using targets of opportunity. The approach, which is considered in two dimensions, is appropriate when traditional alternatives, such as the use of known-location targets or satellite navigation systems, are unavailable. It is not assumed that the sensors can “see” each other, though they are assumed to take measurements with respect to a common (biased) axis. Unlike previous ML algorithms, we take into account the circular nature of the angular measurements, allowing for more accurate estimates to be obtained. A simple least-squares method is additionally provided for initialization. Simulations demonstrate that the accuracy of the ML estimator approaches the Cramer´-Rao Lower Bound (CRLB), something that similar algorithms have been unable to achieve