The Mathematics of GPS

Observations from the Global Positioning System are quite different in nature from traditional surveying observations. Estimation of double differenced observations between two GPS satellites and two dedicated receivers leads to a least-squares problem. Some of the unknowns of this problem are integers and some are reals. Up till today not all aspects of this problem are known. Today most GPS applications are of real-time nature. This involves estimation over time and is done by means of linear filters. We are investigating numerical and speed aspects as well as the stability of these filters. (Kai Borre and Gilbert Strang, M.I.T.)