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Cell identity (cell ID) is the backbone positioning method of most cellular-communication systems. The reasons for this include availability wherever there is cellular coverage and an instantaneous response. Due to these advantages, technology that enhances the accuracy of the method has received considerable interest. This paper presents a new adaptive enhanced cell-ID (AECID) localization method. The method first clusters high-precision position measurements, e.g., assisted-GPS measurements. The high-precision position measurements of each cluster are tagged with the same set of detectable neighbor cells, auxiliary connection information (e.g., the radio-access bearer), as well as quantized auxiliary measurements [e.g., roundtrip time]. The algorithm proceeds by computation and tagging of a polygon of minimal area that contains a prespecified fraction of the high-precision position measurements of each tagged cluster. A novel algorithm for calculation of a polygon is proposed for this purpose. Whenever AECID positioning is requested, the method first looks up the detected neighbor cells and the auxiliary connection information and performs required auxiliary measurements. The polygon corresponding to the so-obtained tag is then retrieved and sent in response to the positioning request. The automatic self-learning algorithm provides location results in terms of minimal areas with a guaranteed confidence, adapted against live measurements. The AECID method can, therefore, also be viewed as a robust fingerprinting algorithm. The application to fingerprinting is illustrated by an example where quantized path-loss measurements from six base stations are combined.