Closed-form and iterative solutions to the GPS positioning problem

The well-known nonlinear single-point global positioning system (GPS) based on positioning determination problem is approached in this paper via a closed-form algebraic solution and an iterative computational algorithm, working in the code (or range) domain. The four user unknowns (three coordinates and the user clock bias) of the GPS single-point code-range static positioning problem are evaluated by means of pseudorange measurements and a minimal number of satellites. The presented methodologies, not needing model linearization and computation of trial (initial) values of the unknowns, provide fast and reliable initialisation of commerciai GPS firmware, typically based on linearized models. The procedures are validated by analysing numerical results on real GPS measurements. Good performance and rate of convergence with respect to other methodologies found in literature testify the cost effectiveness of our approach.