Fundamentals of Satellite Navigation - Understanding GPS: Principles and Applications - page 53

receiver at t 2 . The propagation time is represented by t . Within the receiver, an

identical coded ranging signal is generated at t , with respect to the receiver clock.
This replica code is shifted in time until it achieves correlation with the received
satellite-generated ranging code. If the satellite clock and the receiver clock were
perfectly synchronized, the correlation process would yield the true propagation
time. By multiplying this propagation time,

∆

t , by the speed of light, the true (i.e.,
geometric) satellite-to-user distance can be computed. We would then have the ideal
case described in Section 2.1.2.1. However, the satellite and receiver clocks are gen-
erally not synchronized.
The receiver clock will generally have a bias error from system time. Further, sat-
ellite frequency generation and timing is based on a highly accurate free running
cesium or rubidium atomic clock, which is typically offset from system time. Thus,
the range determined by the correlation process is denoted as the pseudorange .The
measurement is called pseudorange because it is the range determined by multiply-
ing the signal propagation velocity, c , by the time difference between two
nonsynchronized clocks (the satellite clock and the receiver clock). The measurement
contains (1) the geometric satellite-to-user range, (2) an offset attributed to the differ-
ence between system time and the user clock, and (3) an offset between system time
and the satellite clock. The timing relationships are shown in Figure 2.17, where:

∆

T s = System time at which the signal left the satellite

T u = System time at which the signal reached the user receiver

Offset of the satellite clock from system time [advance is positive;
retardation (delay) is negative]
t u =

t =

Offset of the receiver clock from system time

T s + t = Satellite clock reading at the time that the signal left the satellite

T u + t u = User receiver clock reading at the time the signal reached the user

receiver
c = speed of light

(Geometic range time equivalent)

∆ t

t u

δ t

time

T uu +

T u

Tt

S + δ

T S

(Pseudorange time equivalent)

Figure 2.17 Range measurement timing relationships.