The third segment referred as the control segment consists of six ground stations located
around the world to ensure and monitor the good functioning of the GPS satellites see
Figure 2.3. The master ground station located at Schriever Air Force Base in Colorado
Springs runs the system as well as transmits corrections back to the satellites themselves.
The corrections include the satellite’s ephemeris constant and clock offsets.
The idea behind the GPS, as mentioned above, is based on time of arrival TOA, the time
interval for the signal to travel from the satellite to the receiver, which then it is converted
to a range since the signal travels at the speed of light. In other words the GPS uses
satellites in space as reference points. This allow the measuring of the distance between
the satellites, which know exactly their positions, and the receiver, which can compute its
position, by using the time required for the pseudo-random “noise” bit sequence (PRN
code) code to travel from the satellite to the user through an L-band carrier. This time is
then transformed to a distance.
The computation of the receiver’s position relies on the usage of at least four different
pseudorange measurement equations to solve for four unknowns. The pseudorange
measurement equation is based on the distance between the satellites and the receiver.
The visualization of this concept can be described in the following: with one satellite’s
distance we can define that the possible receiver’s locations lie on the surface of a sphere
and that the sphere has the satellite as its center, the second satellite allows the position of
the receiver to narrow down to a circle, which is the product of the intersection of the two
spheres, then a third distance gives a two-point receiver’s position, finally the forth
sphere leads to a unique point receiver’s position as a product of four spheres
intersections centered each on one satellite.