Differential GPS - Understanding GPS: Principles and Applications - page 385

Satellite

d m

d s

d u

φ

φ m

p

Reference
station

User

Figure 8.3 Horizontal tropospheric delay difference.

the triangle lies in a vertical plane.) This yields the following equation for the delay
difference where, for the moment, we hold N s constant:

csc φ

( )

Tropo Tropo

ε − ε ≤ p ⋅

m

⋅ 14588 . + 00029611 . ⋅ N

u m s

d

(8.3)

s

[ ] (

)

( )

2

− 230 . − 230 .

− 030 . 48 ⋅ 000586 . ⋅ N s − 360 + 294 ⋅ φ − φ

m

The second term of the right-hand side of (8.3) was added to fit data at low ele-
vation angles—about 10º or less—and is negligible for higher GPS elevation angles
(i.e., greater than 10º). For higher elevation angles, the difference in tropospheric
delay error is proportional to the separation between the user and reference station.
Suppose, for example, that the elevation angle is 45º and p 100 km. Then, if

we use a midrange value for N s of 360, we find from the model that the deviation of
the tropospheric correction at the user position differs from that at the reference sta-
tion position by an amount

=

csc φ

( )

Tropo Tropo

ε − ε ≤ p ⋅

m

⋅ 14588 . + 00029611 . ⋅ N

u m S

d

s

45
210

csc °

( ) ( )

= 100 k m ⋅ × 14588 . + 00029611 . × 360

4

× km

≈ 002 . m

Thus, the error is on the order of 2 cm. The variation of the deviation as a func-
tion of separation due to elevation angle differences is shown in Figure 8.4. Note
that over the entire 100-km separation, the variation of delay difference due to vari-
ation in the surface refractivity is less than 1.5 mm for this tropospheric model, an
order of magnitude smaller than that due to a variation in elevation angle from 10º
to 90º. Thus, allowing N s to vary in the derivation of (8.3) would have produced a