The thesis describes the development and testing of a robust quality control system for GPS navigation and kinematic positioning. The system is built upon the successful combination of well-known classical statistics with modern robust statistics. Good performance in failure detection and identification, minimum implementation effort as well as automation are the main criteria employed in the development of the system. Theoretical and numerical aspects behind the system are presented along with the introduction of important concepts and the derivation of useful equations. The system was tested by applying it to integrity monitoring in GPS navigation and cycle slip detection and identification in GPS kinematic positioning and results show that significant improvements have been achieve as compared to the conventional approach.