China now has five navigation-and-positioning satellites, the launch of the fifth Beidou satellite took place in April. The system provides regional coverage of China and surrounds. It is named Beidou after the group of seven stars (Septentrio is Latin for ‘north’) of the constellation Ursa Major, known in many cultures under different designations, in the UK ‘The Plough’, ‘Big Dipper’ in the US and ‘Big Mother Bear’ in Russia. Others see the constellation as resembling a wagon. The first Beidou satellite (1A) was launched on 30th October 2000 followed by 1B on 20th December 2000. Since 2001 China’s army and others have thus had access to a domestic satellite positioning system.
Estimate and Dual
Positioning by two satellites? Has satellite positioning with the turn of the millennium become no longer a trilateration problem for which at least three satellites are needed? From the known position of three satellites and the measured distances between them and the receiver the three coordinates of the receiver can be calculated. A fourth satellite is definitely necessary to eliminate the time bias. These are the basic principles of satellite positioning that every high-school pupil should know, and that is how GPS works. So by what magic does China make do with just two satellites? It’s not magic. Beidou derives an approximation of one of the three coordinates from a digital elevation model (DEM) and eliminates time bias by dual-way transmission. Today DEMs can be accurately generated from a multitude of techniques, including InSAR, Lidar and digital photogrammetry, and are abundantly available. Time bias can be eliminated if the signal is shuttled back and forth from satellite to receiver and receiver to satellite. The satellite clock measures travel time, eliminating, most advantageously, the need for extremely accurate atomic clocks.
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