TROPOSPHERE AND IONOSPHERE - GPS Satellite Surveying - page 222

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not integers. Using (6.94) alone, in either undifferenced or double-differenced form,
only the N 1 and N 2 linear ambiguity combination is estimable. Any hardware delays
in receiver or satellite that are constant in time will also be absorbed by the estimated
ambiguities.

6. 6.3 Ionospheric Functions

Because the ionosphere delays the codes by the same amount as it advances the carrier
phases, the difference of both observations depends on twice the ionosphereic delay
while some other terms cancel. Differencing (6.89) and (6.92), and recalling that
I 1 ,P

=− I 1 , Φ , one obtains for a single frequency

c
f 1

R 1 ,I ≡ P 1 − Φ 1 = 2 I 1 ,P − N 1 + cT GD + δ 1 ,R,I + ε 1 ,R,I (6.95)

[22

where δ 1 , Φ , ε 1 ,P , and ε 1 , Φ . The multipath of the

ps eudorange measurement typically sets the accuracy limit for this function. Since the
am biguity is not known, this function does not give the absolute ionospheric delay.
Th e initial ambiguity and the code phase offsets cancel when differencing over time,

δ 1 ,R,I and ε 1 ,R,I are functions of δ 1 ,P ,

Lin
—
3.5
——
Nor
PgE

2 I 1 ,P (t 2 ) I 1 ,P (t 1 ) =

2 × 40 . 30

f 1

R 1 (t 1 ,t 2 ) = − [TEC (t 2 ) − TEC (t 1 ) ] (6.96)

as long as the general hardware and multipath terms are constant.
Differencing the dual-frequency pseudoranges (6.89) and (6.90) gives

[22

P 2 = 1 − α f I 1 ,P + c 1 − α f T GD + δ P,I +

P I ≡ P 1 − ε P,I (6.97)

where δ 2 ,P , ε 1 ,P , and ε 2 ,P . This function readily

shows the difficulties encountered when measuring the total ionosphere, or the TEC,
with dual-frequency receivers. The system specification for the stability of the satel-
lite offset T GD is

δ P,I and ε P,I are functions of δ 1 ,P ,

3 ns (2-sigma) level. This poses a limitation on determining the
TEC, because 3 ns of differential delay between L2 minus L1 corresponds to 0.9 m
delay or 8.5 TECU and has resulted in efforts to determine these delays more accu-
rately. The separation of the hardware delays and the TEC estimates becomes possible
because the impact of the ionosphere depends on the elevation angle, whereas that of
the satellite hardware delay does not.
The ionospheric function for the carrier phases follows readily from (6.92) and
(6.93),

±

c 1

− α f I 1 ,P + δ ϕ,I +

f 1
f 2

f 1
f 2

f 1

ϕ I ≡ ϕ 1 − ϕ 2 = N 1 − N 2 − ε ϕ,I (6.98)

where δ ϕ,I is a function of the carrier phase hardware delays and multipath.

The hardware delays are not listed explicitly. The ionospheric function (6.98) re-
flects the time variation of the TEC. This variation can be measured accu-