Positioning Techniques for Fewer than Four GPS Satellites

Global Navigation Satellites Systems (GNSS) such as the Global Positioning Systems (GPS) are well known for their ability to obtain position regardless of where in the world they operate. In order to function properly, GPS generally requires that a minimum of 4 satellite signals be present at any given time, in order to solve for three dimensions, and local receiver time offset. This minimum requirement of 4 satellite signals is particularly difficult to achieve in urban canyons due to the signals being blocked by skyscrapers in these areas. This paper investigates GPS positioning in conditions of fewer than 4 satellites particularly when there are only 2 satellites. The proposed technique uses the difference of the pseudorange between two satellites to yield a hyperboloid of two sheets with the position of the satellites as the foci. This hyperboloid is then intersected with the earth spheroid to produce a curve on which the receiver theoretically lies. The proposed technique is tested with GPS data collected from the Sydney Central Business District (CBD) and also a rooftop mounted GPS antenna.