Bernese GPS Software Version 5.0 - Bernese GNSS Software

12. Ionosphere Modeling and Estimation
12.2.2 Characterizing the Ionosphere
The state of the ionosphere may be described by the electron density ne in units of electrons
per cubic meter. The impact of the state of the ionosphere on the propagation of radio waves
is characterized by the Total Electron Content E:
E =
S
R
ne(s)ds. (12.1)
The integral gives the total number of free electrons included in a rotation cylinder with a
cross-section area of one square meter, aligned along the signal path s between receiver R
and satellite S. In geodetic applications, the TEC E is measured in so-called TEC Units
(TECU), where one TECU corresponds to 10 16 electrons per square meter (10 16 /m 2 ). For
comparisons, the vertical TEC Ev is formed as
Ev = E cos z ′ , (12.2)
where z ′ is the zenith distance of the signal path with respect to the vertical in a mean
altitude of the ionospheric shell.
The ionosphere is a dispersive medium in the radio-band – as opposed to the troposphere
(see Chapter 11). This implies that ionospheric refraction depends on the frequency of the
signal observed. Neglecting higher-order terms, we may write the ionospheric refraction
coefficient for carrier phase measurements as
nI = 1 − ane
, (12.3)
f2 where a is a constant, ne is the electron content along the signal propagation path, and f
is the carrier frequency. The integration of Eqn. (12.3) along the entire propagation path s,
taking into account Eqn. (12.1), yields the total effect of ionospheric refraction on phase
measurements
∆̺I =
where E is the slant TEC.
(nI − 1)ds = −
s
aE
f2 with a = 4.03 · 10 17 m s −2 TECU −1 , (12.4)
Formulae (12.3) and (12.4) indicate that the refractivity nI −1, and thus the refraction effect,
is proportional to the inverse of the frequency squared. Consequently, if two frequencies are
available, the ionospheric delay may be eliminated by forming the so-called ionosphere-free
(L3) linear combination according to Eqns. (2.41) and (2.42).
In the observation equation (Eqn. (2.34)), we defined a term I i k
the ionospheric delay on L1:
I i k
= aE
f 2 1
Hence, the ionospheric delay may be written as
that is synonymous with
with f1 = 1.57542 · 10 9 s −1 . (12.5)
∆̺I = ∓ f2 1
f2 Ii k , (12.6)
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