The present invention combines the relative insensitivity of the phase angle differences of a radio signal to the signal distortions inherent in an urban environment with digital signal processing techniques to produce an accurate and economical way to locate a mobile transmitter station such as a mobile telephone in a cellular telephone network. Phase angle measurements indicative of the angle of direction of a mobile transmitter station from each of a plurality of land stations are obtained by translated Hilbert transformation and are processed to produce a probability density function. The probability density functions are combined after a CHI-squared analysis to produce an area of uncertainty representing the position of the mobile transmitter station. The radio frequency signals emitted from the mobile transmitter station need have no special characteristic for the localization process. Thus, the present invention may easily work as an adjunct to an unrelated communications system such as a cellular telephone system.