GPS localization problem: a new model and its global optimization

摘要

We establish a new fractional squared least squares (FSLS) optimization model for the GPS localization problem. It provides more accurate solutions than the classical squared least squares model. We reformulate (FSLS) as a univariate optimization, where the functional evaluation corresponds to the generalized trust region sub-problem. We employ the branch and bound algorithm to globally solve (FSLS) and establish the convergence. It further motivates a much faster iterative heuristic algorithm. Numerical examples are presented to show the accuracy of the new model (FSLS) and the efficiency of the two algorithms.