Ionospheric Effects on Microwave Signals - Atmospheric Effects in Space Geodesy - page 55

add it to the theoretical delay and thus “correct” or “calibrate” the group delay at
X-band. This approach should not be applied as the observable would be corrected
using the measurement itself. For geodetic analysis the ionosphere-free linear com-
bination should be used, although the ionospheric correction Eq. 82 is usually stored
in databases together with all the other information.

Ambiguity Resolution and Ionosphere Delays

Due to the finite number and spacing of the video channels, the delay resolution
function is repeating after a certain time lag, which introduces an ambiguity term
in the obtained delays. Thereby the ambiguity spacing is equal to the inverse of
the greatest common measure of the frequency spacing of the video channels. For
most geodetic experiments this spacing is between 50 and 200ns depending on the
selection of the video channels in each band. Although the ambiguity correction is
an integer multiple of the basic spacing, it is degraded to a real number when the
ionosphere linear combination (Eq. 81 ) is applied. Moreover, as ambiguity shifts can
happen independently in either of the bands, the ionosphere free combination can-
not be applied for geodetic estimation purposes until all ambiguity terms have been
fixed. This is usually done in an iterative procedure, where the initial ionosphere
free linear combination is used in a basic geodetic adjustment for which only clock
and troposphere are parameterized. Based on the residuals of this estimation, ambi-
guity shifts are detected and a new ionosphere free linear combination is formed.
Depending on the data quality and the geometry of the VLBI session more than two
iterations are necessary to fix all ambiguities. Thereby, delays can be shifted to an
arbitrary ambiguity reference, since this constant term will later be absorbed in the
station clock offset. Nevertheless, closure conditions need to be taken into account
during the ambiguity fixing process, in order not to introduce artificial clock breaks.

Instrumental Biases

In fact, real observations do not exactly correspond to Eq. 80 , but rather contain an
extra delay term caused by instrumental imperfectness. As mentioned by Ray and
Corey ( 1991 ) an additional delay is caused by instrumental delays in the different
bands, which change the delay observable to

f gx + τ inst , x ,

τ gx = τ if +

f gs + τ inst , s ,

τ gs = τ if + (83)

f px + τ inst , x ,

τ px = τ if −

f ps + τ inst , s .

τ ps = τ if −