Performance of Stand-Alone GPS - Understanding GPS: Principles and Applications - page 306

True orbit

SV

dr

Broadcast orbit

ρ

a

User

Figure 7.2 Ephemeris error. ( After: [9].)

7.2.3 Relativistic Effects
Both Einstein's general and special theories of relativity are factors in the
pseudorange and carrier-phase measurement process [10, 11]. The need for special
relativity (SR) relativistic corrections arises any time the signal source (in this case,
GPS satellites) or the signal receiver (GPS receiver) is moving with respect to the cho-
sen isotropic light speed frame, which in the GPS system is the ECI frame. The need
for general relativity (GR) relativistic corrections arises any time the signal source
and signal receiver are located at different gravitational potentials.
The satellite clock is affected by both SR and GR. In order to compensate for
both of these effects, the satellite clock frequency is adjusted to 10.22999999543
MHz prior to launch [4]. The frequency observed by the user at sea level will be
10.23 MHz; hence, the user does not have to correct for this effect.
The user does have to make a correction for another relativistic periodic effect
that arises because of the slight eccentricity of the satellite orbit. Exactly half of the
periodic effect is caused by the periodic change in the speed of the satellite relative to
the ECI frame and half is caused by the satellite's periodic change in its gravitational
potential.
When the satellite is at perigee, the satellite velocity is higher and the gravita-
tional potential is lower—both cause the satellite clock to run more slowly. When
the satellite is at apogee, the satellite velocity is lower and the gravitational potential
is higher—both cause the satellite clock to run faster [10, 11]. This effect can be
compensated for by [4]:

∆ t = eaE sin (7.4)

r k