Performance of Stand-Alone GPS - Understanding GPS: Principles and Applications - page 314

ionospheric delay can be approximated by half a cosine function of the local time
during daytime and by a constant level during nighttime [15]. The original
Klobuchar model was adapted by the GPS CS and the correction algorithm is
provided in [4, 16].
Almost three times as much delay is incurred when viewing satellites at low ele-
vation than at the zenith. For a signal arriving at vertical incidence, the delay ranges
from about 10 ns (3m) at night to as much as 50 ns (15m) during the day. At low sat-
ellite viewing angles (0º through 10º), the delay can range from 30 ns (9m) at night
up to 150 ns (45m) during the day [15]. A typical 1-sigma value for residual iono-
spheric delays, averaged over the globe and over elevation angles, is 7m [17].

7.2.4.2 Tropospheric Delay
The troposphere is the lower part of the atmosphere that is nondispersive for fre-
quencies up to 15 GHz [13]. Within this medium, the phase and group velocities
associated with the GPS carrier and signal information (PRN code and navigation
data) on both L1 and L2 are equally delayed with respect to free-space propagation.
This delay is a function of the tropospheric refractive index, which is dependent on
the local temperature, pressure, and relative humidity. Left uncompensated, the
range equivalent of this delay can vary from about 2.4m for a satellite at the zenith
and the user at sea level to about 25m for a satellite at an elevation angle of approxi-
mately 5º [13].
From (7.16), we see that the path length difference attributed to the tropo-
spheric delay is

User
SV

( )

∫

∆ S = n s − 1

tropo

where the integration is along the signal path. The path length difference can also be
expressed in terms of refractivity,

User
SV

− 6

∫

∆ S = 10 Nds (7.24)

tropo

where the refractivity, N , is defined by

( )

6

Nn ≡ 10 − 1

The refractivity is often modeled as including both a dry (hydrostatic) and wet
(nonhydrostatic) component [18]. The dry component, which arises from the dry
air, gives rise to about 90% of the tropospheric delay and can be predicted very
accurately. The wet component, which arises from the water vapor, is more difficult
to predict due to uncertainties in the atmospheric distribution. Both components
extend to different heights in the troposphere; the dry layer extends to a height of
about 40 km, while the wet component extends to a height of about 10 km.
We define N d ,0 and N w ,0 as the dry and wet component refractivities, respectively,
at standard sea level. To express both N d ,0 and N w ,0 in pressure and temperature, the
formulas of [19] can be used: