Globally solving the fractional squared least squares model for GPS localization

The article addresses the global positioning system (GPS) localization problem, which involves estimating a user’s position and clock error from a set of pseudoranges to satellites. Traditional methods, such as the least squares (LS) model, face challenges due to their nonsmooth and nonconvex nature. The squared least squares (SLS) formulation, although belonging to hidden convex optimization, often lacks accuracy. The fractional squared least squares (FSLS) formulation, proposed by Wang et al., offers a high-accuracy solution but can be further optimized. The authors introduce a new underestimation approach that utilizes function values at both endpoints to develop a tighter bound, significantly improving the efficiency of the branch and bound algorithm. Numerical results demonstrate the superior performance of this approach in terms of lower bound quality and computational efficiency. The article concludes by highlighting future work to enhance the algorithm with more adaptive partitioning strategies.