Differential GPS - Understanding GPS: Principles and Applications - page 387

Satellite

User

φ

h

Reference
station

Figure 8.5 Vertical tropospheric delay difference.

and the difference in delays is

Tropo Tropo

ε − ε = 36 . mmm − 16 = 2

h m

360 and that the elevation angle is 45º, the delay at a height
of 1 km is only 45% of the 3.6-m delay, calculated from (8.2) at the reference sta-
tion, or 1.6m. The difference is 2m.
The variation in the difference in tropospheric delays between a signal reaching
the ground having a refractivity of N s and the signal at an altitude h above the
ground is shown in Figure 8.6 for two different elevation angles of the satellite.
Although vertical tropospheric delays do not change very rapidly with time for
a stationary receiver, slant tropospheric delays can change due to the rate of change
of elevation angle. For stationary users, the elevation angle to a GPS satellite can
vary at a rate up to 0.5º/min due just to the motion of the satellite. For a satellite at
5º, this can lead to tropospheric delay changing at a rate of up to 2 m/min. For satel-
lites above 10º, the maximum rate of change is around 0.64 m/min. A receiver on a
moving platform that is rapidly changing altitude can experience an even higher
rate of change in tropospheric error due to the altitude dependence discussed earlier.

That is, assuming N s =

8.2.4 Ionospheric Errors
As given in Section 7.2.4.1, we have the following relationship between the delay,
ε

Iono

, expressed in units of length, due to the ionosphere, the frequency, f , of the sig-
nal, the elevation angle,

, at the ionospheric pierce point, and the total electron
content, TEC , along the path of the signal:

φ′

1 . 3

Iono

ε =

′ ⋅

⋅ TEC

sin φ f

2