Articles | Volume 9
Adv. Radio Sci., 9, 203–208, 2011
https://doi.org/10.5194/ars-9-203-2011
Adv. Radio Sci., 9, 203–208, 2011
https://doi.org/10.5194/ars-9-203-2011

  01 Aug 2011

01 Aug 2011

Iterative least squares method for global positioning system

Y. He1 and A. Bilgic2 Y. He and A. Bilgic
  • 1Institute for Integrated Systems, Ruhr University Bochum, 44780 Bochum, Germany
  • 2KROHNE Messtechnik GmbH, Ludwig-Krohne-Str. 5, 47058 Duisburg, Germany

Abstract. The efficient implementation of positioning algorithms is investigated for Global Positioning System (GPS). In order to do the positioning, the pseudoranges between the receiver and the satellites are required. The most commonly used algorithm for position computation from pseudoranges is non-linear Least Squares (LS) method. Linearization is done to convert the non-linear system of equations into an iterative procedure, which requires the solution of a linear system of equations in each iteration, i.e. linear LS method is applied iteratively. CORDIC-based approximate rotations are used while computing the QR decomposition for solving the LS problem in each iteration. By choosing accuracy of the approximation, e.g. with a chosen number of optimal CORDIC angles per rotation, the LS computation can be simplified. The accuracy of the positioning results is compared for various numbers of required iterations and various approximation accuracies using real GPS data. The results show that very coarse approximations are sufficient for reasonable positioning accuracy. Therefore, the presented method reduces the computational complexity significantly and is highly suited for hardware implementation.