Differential GPS - Understanding GPS: Principles and Applications - page 388

14

12

N = 400
N = 350
N = 300

s
s
s

10°

10

8

6

4

N = 400
N = 350
N = 300

s
s
s

45°

2

0

0 2 4 6 8 10 12

Vertical separation (km)

Figure 8.6 Variation in the vertical delay difference with refractivity and elevation angle.

term accounts for the additional path length in the ionosphere when
the direction of the satellite is off the vertical. The ionospheric pierce point is that
point on the displacement vector from the user position to the satellite position mid-
way through the ionosphere, typically taken to be 300 km to 400 km in altitude [5]
(see Figure 8.7).
The difference in delay due to the difference in elevation angles for a horizontal
separation of user and reference station is

The sin φ′

1 403 . 1 403 .

ε

Iono

− ε

Iono

=

′ ⋅

⋅ TEC − ⋅ ⋅ TEC

u m

2 2

sin φ f sin φ ′ f

m

1 1 40 3 .

= − ⋅ ⋅ TEC (8.4)

2

sin φ ′ sin φ ′ f

m

p
d

p
d

40 3 .

⋅ − ′ cos φ ⋅ ⋅ TEC

m

2

f

mm

where:

p distance between the user and the reference station

φ m =

=

elevation angle of the satellite from the reference station

φ m = elevation angle at the reference station's ionospheric pierce point

The TEC usually lies in the range 10 16 to 10 18 electrons/m 2 , with 50 × 10 16 elec-
trons/m 2 typical in the temperate zones, so that the difference in delays experienced
by the reference station and the user 100 km away due to the difference in elevation
angle is typically