Differential GPS - Understanding GPS: Principles and Applications - page 384

where ε S is the error in the satellite's estimated position.

Equation (8.1) implies that the error increases directly with the separation
between the reference station measuring the error and the user receiver employing
the correction. Suppose, for example, that the error in the satellite's estimated posi-
tion is 5m and suppose the user is 100 km from the reference station. Then the error
in the correction due to that separation is less than

5
210

m

×

100 km = 2 5 . cm

4

× km

for elevation angles 5º.

Broadcast ephemeris errors change very slowly over time, with typical growth
rates of the three-dimensional ephemeris error of 2-6 cm/min [1]. Error growth has
been observed to be approximately linearly proportional to elapsed time for inter-
vals up to 30 minutes [1].

>

8.2.3 Tropospheric Errors
As discussed in Section 7.2.4.2, the speed of electromagnetic radiation varies,
depending on temperature, pressure, and relative humidity, as it passes through the
troposphere. Considerations of the physics behind tropospheric delays are provided
in Section 7. 2.4.2. In this section, we obtain an estimate of the kind of delay differ-
ence we can expect from the signal traveling through the troposphere and choose a
model described in [3], which expresses the tropospheric delay of a signal from a
GPS satellite to a user at the Earth's surface, as follows:

( )

Tropo

ε = csc φ ⋅ 14588 . + 00029611 . ⋅ N

u s

(8.2)

[ ]

( )

2

− 03048 . ⋅ 000586 . ⋅ N − 360 + 294 ⋅ φ

− 230 .

s

where:

ε Tropo = tropospheric delay experienced by the user in meters,

φ = elevation angle from the user to the satellite in degrees

N s =

surface refractivity

If we denote the elevation angle of the satellite from the reference station by φ m ,

then from Figure 8.3 we can determine the difference csc φ m in terms of the

horizontal distance p between the user and reference station and the height d s of the
satellite, as follows:

φ − csc

d
d

d
d

dd
d

− cos φ

csc φ − csc φ =

u

−

m

=

u m

≤⋅ p

m

m

d

s s s s

where d m is the distance from the monitoring station to the satellite and d u is the dis-
tance from the user receiver to the satellite. (The inequality sign may be dropped if