Differential GPS - Understanding GPS: Principles and Applications - page 440

( , )

τλ φ
22 1 ( , )

τλ φ
12 2

φ 2

τλ φ
pp

( , )

pp pp

( , ) ( , ) τλφ

41 1

τλ φ
31 2

φ 1

Longitude, λ

λ 1 λ 2

Figure 8.32 Finding the relative IPP position.

R
Rh

π

ψ =−− E sin

− 1 E

⋅ cos E

pp

2 +

E

where R E is the radius of the Earth, h is the altitude of the IPP, and E is the elevation
angle of the satellite from the user position. The user then calculates the latitude,

pp ,

and longitude,

pp , of the IPP, as follows:

(

)

φ = sin

− 1

sin φ ⋅ cos ψ + cos φ ⋅ sin ψ ⋅ cos A

pp u pp u pp

sin ψ ⋅ sin A

pp

− 1

λ =+− λ π si n

pp u

cos φ

pp

π

if φ >° 70 , and tan ψ cos A > tan − φ

u pp u

2

π

or if φ <− 70 ° , a nd tan ψ cos A < tan − φ

u pp u

2

sin ψ ⋅ sin A

pp

− 1

λ =+ λ sin , otherwise

pp u

cos φ

pp

where the angles φ u are the azimuth and elevation angles, respectively, of the

satellite from the user's position. Then the receiver determines the most suitable set
of predefined grid points in the proximity of the IPP for each visible satellite. If no
suitable set is available, then an ionospheric correction is unavailable for that partic-

λ u and