Closed-form and iterative solutions of the problem of the global positioning system

The four user unknowns (three coordinates and the user clock bias) of the global positioning system 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 initialization of commercial global positioning system firmware, typically based on linearized models. The procedures are validated by analyzing numerical results on real global positioning system measurements. Good performance and rate of convergence with respect to other methodologies found in literature testify the cost-effectiveness of our approach.