Performance of Stand-Alone GPS - Understanding GPS: Principles and Applications - page 313

Satellite

IPP

Ionosphere

φ

h I

U

Earth

R e

Ψ pp

U-User position
IPP - Ionospheric pierce point
- Radius of the Earth R

e

Figure 7.4 Ionospheric modeling geometry.

ρ −

−

γρ
γ

ρ =

L 2 L 1

(7.22)

ionospheric − free

1

( f L 1 / f L 2 ) 2 . Although ionospheric delay errors are removed, this approach
has the drawback that measurement errors are significantly magnified through the
combination. A preferred approach is to use the L1 and L2 pseudorange measure-
ments to estimate the ionospheric error on L1 using the following expression:

where γ =

2

f

( )

∆ S =

L 2

ρρ (7.23)

iono corr , L 1 L 2

2 2

f − f

L 1

L 2 L 1

The path length difference on L2 can be estimated by multiplying ∆ S iono corr L by

,

1

( )

2

( )

2

f 12 = 77 60

These estimated corrections may be smoothed over time, since ionospheric delay
errors typically do not change very rapidly and are subtracted from pseudorange
measurements made by each frequency.
In case of a single-frequency receiver, it is obvious that (7.23) cannot be used.
Consequently, models of the ionosphere are employed to correct for the ionospheric
delay. One important example is the Klobuchar model, which removes (on average)
about 50% of the ionospheric delay at midlatitudes through a set of coeffi-
cients included in the GPS navigation message. This model assumes that the vertical