Closed-form and Iterative Solutions to the Global Positioning System 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 initialization of commercial GPS firmware, typically based on linearized models. The procedures are validated by analysing numerical results or real GPS measurements.