Iterative least squares method for global positioning system

[摘要] The efficient implementation of positioning algorithms is investigated forGlobal Positioning System (GPS). In order to do the positioning, thepseudoranges between the receiver and the satellites are required. The mostcommonly used algorithm for position computation from pseudoranges isnon-linear Least Squares (LS) method. Linearization is done to convert thenon-linear system of equations into an iterative procedure, which requiresthe solution of a linear system of equations in each iteration, i.e. linearLS method is applied iteratively. CORDIC-based approximate rotations are usedwhile computing the QR decomposition for solving the LS problem in eachiteration. By choosing accuracy of the approximation, e.g. with a chosennumber of optimal CORDIC angles per rotation, the LS computation can besimplified. The accuracy of the positioning results is compared for variousnumbers of required iterations and various approximation accuracies usingreal GPS data. The results show that very coarse approximations aresufficient for reasonable positioning accuracy. Therefore, the presentedmethod reduces the computational complexity significantly and is highlysuited for hardware implementation.

[学科分类] 电子、光学、磁材料