In this article, we present a novel approach to solving the localization problem in cellular networks. The goal is to estimate a mobile user’s position, based on measurements of the signal strengths received from network base stations. Our solution works by building Gaussian process models for the distribution of signal strengths, as obtained in a series of calibration measurements. In the localization stage, the user’s position can be estimated by maximizing the likelihood of received signal strengths with respect to the position. We investigate the accuracy of the proposed approach on data obtained within a large indoor cellular network.