Global Positioning System: The Mathematics of GPS Receivers

We will see that receivers use very simple mathematics, but that they use it in highly ingenious ways. Being able to locate our position on the surface of the earth has always been important for commercial, scientific, and military reasons. The development of navigational methods has provided many mathematical challenges, which have been met and overcome by some of the best mathematicians of all time. Navigation by means of celestial observation, spherical trigonometry, and hand computation had almost reached its present form by the time of Captain James Cook's 1779 voyage to the Hawaiian Islands. For the next 150 years these methods were used to determine our location on land or sea. In the 1940s electronic navigation began with the use of fixed, land-based, radio transmitters. The present-day LOng RAnge Navigation (LORAN-C) system uses sequenced chains of such transmitters. The use of satellites in navigation became common in the 1970s, with the introduction of the Navy Navigation Satellite System (NAVSAT or TRANSIT). This system uses the Doppler shift in radio frequencies to determine lines of position and locations.