Ground GNSS Ionosphere Sounding - GNSS Remote Sensing: Theory, Methods and Applications - page 74

4.3.1.2 Distance-Weighted Method

Ionospheric distance-weighted model is based on the meshing technology. Mesh
VTEC values are computed by distance weighted average method using the
measured VTEC.

X

n

VTEC i
D ij

VTEC j

i D 1

D

n

X

(4.17)

1
D ij

D ij

DR

i D1

where i , j are the number of the grid network. DR is the threshold of distance-
weighted. If the distance between the grid and the ionospheric pierce point is larger
than the threshold, measurement VTEC of this point will not be considered for
distance-weighted average.

4.3.1.3 Hardy Function Interpolation (HFI) Method

In 1977, Hardy developed the Hardy Function Interpolation (HFI) method. We here
apply the HFI method to establish GPS grid ionospheric model over a small local
region. For the GPS site coordinates (B i ,L j ), the VTEC of fitting model can be
written as (Jin et al. 2004 ):

X

n

VTEC .B; L/ D a i Q .B; L; B i ;L i / (4.18)

i D1

where VTEC(B,L) is the VTEC of the measurement points in a single plane, (B i and
L i ) is the coordinate of grid node, and a i is the vector of the VTEC value at the grid
point. The corresponding core function can be expressed as follows:

h .B B i / 2

C " 2 i ˇ C .L L i / 2 Q.B; L; B i ;L i / D (4.19)

where © 2 and “ are the smooth factor, whose empirical values are 0.01 and 0.5
respectively. If there are m measurement points (B j ,L j ) and n grid nodes (B i ,L i ),
and let n grid nodes (B i ,L i ) as central sites of core function Q . Thus, the VTEC of
each GPS epoch in the Eq. ( 4.18 ) can be written as follows:

v . VTEC / D Qa (4.20)