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Modern Geomatics Technologies and Applications

the ideal case: The satellite 1 sends a signal at time 1 and it is received at at time 2 . The receiver , using its clock which
measures 1 and the message sent by 1 at time 2 , obtains the time ∆ 1 = 1 − 2 , which corresponds to the distance 1 :

= ‖ ‖ ∶ ∆ = ‖ ‖ (1)

Figure 1. Earth orbiting of four famous GNSS systems [5].

The point is thus located on the sphere ∑ of radius 1 centered on 1 . Likewise, the satellite 2 sends a signal, and
1
by measuring the time interval∆ 2 , this tells us that lies on the sphere ∑ of radius 2 centered on 2 . The point is thus on
2
the intersection of the spheres ∑ and∑ , which is a circle. With the satellite 3 , we obtain a third sphere ∑ , whose intersection
1 2 3
with ∑ ∩ ∑ gives just two points. One of these two points is therefore true location . In this ideal case, three satellites
1 2
therefore suffice to locate . However, to achieve this, the clock at would have to have the same quality as those carried
aboard the satellites, and this would be impossible because such clocks are cumbersome and very expensive. A fourth satellite
is thus needed to make up for the inaccuracy of this clock. Figure 2 shows the basic principle of GNSS positioning. With known
position of four satellites and signal travel distance , the user position can be computed.

Figure 2. The basic principle of GNSS positioning [4, 6]
A GNSS signal is transmitted from a satellite in order to measure the distance between the satellite and a receiver. Each
GNSS has its signal transmitted on specific radio frequencies. The GNSS satellites continuously transmit signals at two or more
frequencies in the L band [7]. These signals contain ranging codes and navigation data to allow users to compute both the travel

2