Study of the algorithm for GPS positioning and velocity measurement

The mathematical models of positioning and velocity measurement for the global positioning system (GPS) were given. The iterative algorithm under normal condition was discussed based on Gauss-Newton method. The solution under the condition, that there are only three visible satellites or geometric precision factor is too large, was given, and the complete iterative algorithm was obtained, in which the positioning solution is obtained iteratively, and the satellite signal propagation time is renewed in iterative process, then the velocity is obtained from the satellite signal propagation time and normal matrix is gained in last iteration.