Determining a Position on a Plane Using Satellite Signals (Especially for GATE-Geospatial 2022)

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Imagine that you are wandering across a vast plateau and would like to know where you are. Two satellites are orbiting far above you transmitting their own on-board clock times and positions.

Global Positioning Systems: Mapping Changing World
  • By using the signal transit time to both satellites you can draw two circles with the radii S1 and S2 around the satellites. Each radius corresponds to the distance calculated to the satellite.
  • All possible distances to the satellite are located on the circumference of the circle. If the position above the satellites is excluded, the location of the receiver is at the exact point where the two circles intersect beneath the satellites.

Two Satellites

  • Two satellites are enough to determine a position on the X/Y plane.
Determining Position on a Plane

Three Satellites

  • A position must be determined in three-dimensional space, rather than on a plane. As the difference between a plane and three-dimensional space consists of an extra dimension (height Z) , an additional third satellite must be available to determine the true position.
  • If the distance to the three satellites is known, all possible positions are located on the surface of three spheres whose radii correspond to the distance calculated. The position sought is at the point where all three surfaces of the spheres intersect.
Global Positioning System as Time Reference in Astrophysics

Sometimes a third measurement leads to two points, however only one of them is realistically possible.

Positions to Two Points

All statements made so far will only be valid, if the terrestrial clock and the atomic clocks on board the satellites are synchronized, i.e.. signal transit time can be correctly determined.

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