Differential GPS - Understanding GPS: Principles and Applications - page 441

ular satellite. If four suitable surrounding grid points are found, the receiver deter-
mines the IPP position relative to those four points, using Figure 8.18, from the
following equations:

λ λ
λλ

−
−

φφ
φφ

−
−

pp 1 pp 1

x = y = for IPPs between 85°N and 85°S

pp pp

2 1 2 1

φ −°

°

85

pp

y =

pp

10

for IPPs above 85°N and below 85°S

λ −

°

λ

( )

pp 1

x = ⋅ 12 − y + y

pp pp pp

90

The interpolation is weighted, with greater weights given to the nearer grid points.
The weights are given by

Wxy =⋅

1 pp pp

( )

Wx =− 1 ⋅ y

2 pp pp

(

) ( )

Wx =− 1 ⋅ 1 − y

3 pp pp

( )

Wx =⋅ 1 − y

4 pp pp

Finally, the vertical delay,

pp , at the IPP is determined by

4

( )

= ∑ 1

τλφ , = W ⋅ τ (8.49)

pp pp pp i i

i

where the are the vertical delays at the four grid points provided in the ionospheric
delay corrections message (message type 26).
If only three of the four suitable surrounding grid points are available, the calcu-
lation of the weights is modified slightly, as follows:

Wy
Wx

=
=−

1 pp

1 − y

2 pp pp

Wx =

3 pp

The same delay formula (8.49) is used, except that the sum is over three
weightings. The remaining ionospheric delay calculation accounts for a difference
in delay from the vertical and is a function of the elevation angle to the satellite. To
obtain the ionospheric correction, which is added to the pseudorange measurement,
the vertical delay τλ φ

pp

( , ) is multiplied by the obliquity factor, F , where

pp pp

1
2

−

2

RE
Rh

cos

F =− 1

E

+

E