Ground GNSS Ionosphere Sounding - GNSS Remote Sensing: Theory, Methods and Applications - page 83

Fig. 4.9 Flowchart of 3-D
GNSS ionospheric
tomography

Reconstruction solution

No
(iteration)

Yes

y − A . x k +1 < e

x 0

x k

x k +1

λ

a ij

⎛ y i ⎞

k

⎜
⎝

⎟
⎠

k

〈 a

i x

. 〉

The electron density matrix x is therefore corrected iteratively by the ratio of the
measured STEC and the simulated STEC with a relaxation parameter of k until
the residual does not change (see Fig. 4.9 ) (Jin and Park 2007 ; Jin et al. 2008 ).
This relaxation parameter value is chosen from experience in which the best k
value is identified where the solution converges quickly with a reasonable number
of iterations and the residuals are a minimum. Here k D 0. 01 has been chosen
for all iterations. In addition, it is noted that any iterative algorithm requires an
initial condition before the iteration begins. Due to the poor STEC geometry, the
initialization could be extremely important for the tomographic reconstruction. In
practice, the closer the initial condition is to the true electron density distribution,
the more accurate the reconstruction will be. Here the latest IRI-2007 model ( http://
nssdcftp.gsfc.nasa.gov/models/ionospheric/iri/iri2007 ) is used as an initial guess for
the reconstruction iteration.

4.4.2 Validation of GNSS Ionospheric Tomography

The ionospheric reconstruction algorithm MART can integrate the STEC from
all available GPS receivers to all GPS satellites visible from each site of the
KGN network above a user-specified elevation cut-off angle (usually 15 ı ). The
unknown electron density profile is expressed in 4-D (longitude-latitude-height and
time) voxel basis functions over the following grid: longitude 124E ı -130E ı in 1 ı
increments, latitude 33 N ı -39 N ı in 0.5 ı increments, altitude 100-1,000 km in
25 km increments and time: 1 h increments of linear change in the electron density
per voxel. As there are a sparse number of ions in the ionosphere above 1,000 km,
the effect on the inversion for ionospheric electron density profiles is very small
and the ionosphere is only considered up to an altitude of 1,000 km. Furthermore,
it is faster to invert the unknown ionospheric density parameters because of the
reduced number of unknown variables. In addition, the fewer leaving rays from the
ionospheric space of above defined latitude and longitude range are not used, but