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 subproblem. 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.

中文翻译：

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GPS定位问题：一种新模型及其全局优化

我们针对GPS定位问题建立了新的分数平方最小二乘（FSLS）优化模型。它提供了比经典平方最小二乘模型更准确的解决方案。我们将（FSLS）重新表述为单变量优化，其中功能评估对应于广义信任区域子问题。我们采用分支定界算法进行全局求解（FSLS）并建立收敛。它进一步激发了更快的迭代启发式算法。数值例子说明了新模型（FSLS）的准确性和两种算法的效率。