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Global positioning technologies such as GPS are ubiquitously available for modern smartphones, on-board navigation computers of vehicles, sports appliances, and so on. Positioning enables new networking and application solutions, but suffers from insufficient positioning accuracy. We present a way for improving the accuracy of a global positioning system by adding a local positioning system giving relative positions of a group of mobile entities more accurate than the global system communicated among the mobile entities. The improvement is based on transforming the global coordinate system into the local coordinate system and back by translation and rotation operations. In this paper, we detail the geometric operations and present a novel derivation of how to compute the optimal rotation angle based on covariance measures. Further, we provide estimates for the overall prediction error when using the local positioning system in addition to a global one and a proof of the convergence of the approach. Two major results are the fact that error correlations in the global positioning system increase the prediction error, while error correlations in the local positioning system decrease the overall prediction error. In a case study, we present results from randomized experiments, as well as from GPS and Differential GPS (DGPS) measurements. Both sets of experiments confirm the theoretical findings.