Performance of Stand-Alone GPS - Understanding GPS: Principles and Applications - page 307

where:

F = − 4.442807633 × 10 −10 s/m 1/2

e = satellite orbital eccentricity

a semimajor axis of the satellite orbit

E k =

=

eccentric anomaly of the satellite orbit

Reference [9] states that this relativistic effect can reach a maximum of 70 ns
(21m in range). Correcting the satellite clock for this relativistic effect will result in a
more accurate estimation of the time of transmission by the user.
Due to rotation of the Earth during the time of signal transmission, a relativistic
error is introduced, known as the Sagnac effect , when computations for the satellite
positions are made in an ECEF coordinate system (see Section 2.2.2). During the
propagation time of the SV signal transmission, a clock on the surface of the Earth
will experience a finite rotation with respect to an ECI coordinate system (see Sec-
tion 2.2.1). Figure 7.3 illustrates this phenomenon. Clearly, if the user experiences a
net rotation away from the SV, the propagation time will increase, and vice versa. If
left uncorrected, the Sagnac effect can lead to position errors on the order of 30m
[12]. Corrections for the Sagnac effect are often referred to as Earth rotation
corrections .

Satellite at time
of transmission

+ ∆ρ ρ

ρ

Receiver at time
of reception

Receiver at time
of transmission

R E

Earth's rotation

Figure 7.3 The Sagnac effect.