TROPOSPHERE AND IONOSPHERE - GPS Satellite Surveying - page 221

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For accurate relative positioning with carrier phase observations, single-frequency
users still depend on the elimination of ionospheric effects through single or double
differencing, as discussed in connection with Equations (5.20) and (5.28). Better
ionospheric corrections will be available to single-frequency users in the near future
from services provided by the IGS or other entities.

6. 6.2 Ionospheric-Free Functions

Since the ionospheric code delay and the phase advance are dependent on frequency,
it is possible to eliminate the ionospheric effects for dual-frequency observation.
Using simplified notation, the pseudoranges of Equation (5.7) for L1 and L2 can
be expressed as

c d T GD + ¯

P 1 = ρ − cd t + t + I 1 ,P + T + δ 1 ,P + ε 1 ,P (6.89) [22

c d

f T GD +

P 2 = ρ −

+ ¯ + α

I 2 ,P +

+ δ 2 ,P +

cd t t T ε 2 ,P (6.90)

Lin
—
- ——
Lon
PgE

The objective is to find functions that do not depend on the ionosphere. Using the
coefficients α f , β f , γ f and δ f defined in (5.13) to (5.16), the ionospheric-free pseu-

dorange function P IF ,

− α f P 2 − α f P 1 = ρ −

1

cdt P IF ≡ β f P 1 − γ f P 2 = 1 cd t + + T + δ P, IF + ε P, IF

(6.91)

[22

se rves this purpose. In Equation (6.91) the ionospheric terms cancel. The symbols
δ P, IF and ε P, IF are functions of δ 2 ,P , ε 1 ,P and ε 2 ,P . The satellite code phase

of fset T GD has also canceled, whereas the other hardware delays and multipath terms
do not cancel (but are not listed explicitly in (6.91)).
The dual-frequency carrier phase equations (5.10) in units of cycles are in simpli-
fie d notation

δ 1 ,P ,

f 1
c ρ +

f 1
c I 1 ,P +

f 1
c T

f 1 d t

ϕ 1 = N 1 − f 1 d t + − + δ 1 ,ϕ + ε 1 ,ϕ (6.92)

f 2
c ρ +

f 2
c I 2 ,P +

f 2
c T

f 2 d t

ϕ 2 = N 2 − f 2 d t + − + δ 2 ,ϕ + ε 2 ,ϕ (6.93)

The ionospheric-free carrier phase function ϕ IF is

f 1
c ρ −

f 1
c T

¯

ϕ IF ≡ β f ϕ 1 − δ f ϕ 2 = f 1 d t + f 1 d t + β f N 1 − δ f N 2 + + δ ϕ, IF + ε ϕ, IF

(6.94)

where δ 2 ,ϕ , ε 1 ,ϕ , and ε 2 ,ϕ . The ionospheric-

free phase function (6.94) does not contain the ionospheric term. Unfortunately, the
integer-nature of the ambiguities has been lost, because the multipliers

δ ϕ, IF and ε ϕ, IF are functions of δ 1 ,ϕ ,

β f and δ f are