Ionospheric Propagation Effects on GNSS Signals and New Correction Approaches - Global Navigation Satellite Systems: Signal,Theory and Applications - page 390

In case of cycle slips (a jump in carrier-phase ambiguity constant due to loss of signal
tracking results in discontinuous arcs of phase data) in the phase data, the wide-lane
combination method of Blewitt (1987) can be applied for the correction. While the TEC
estimated by the carrier-phase difference Eq. (28) is precise and smooth but biased by an
unknown phase ambiguity constant, the TEC estimated by the code pseudorange difference
Eq. (27) is noisy and less precise but not ambiguous. In order to obtain an absolute and
precise estimate of TEC, the accurate phase measurements needs to be levelled to the
calibrated absolute code measurements by a least square method.

To derive an elevation independent vertical TEC from a slant TEC measurement, the
ionosphere is assumed to be composed of a single thin layer at a representative height of
about 350, 400 or 450 km from the earth's surface. The intersection point between a slant ray
path and the thin layer is called an ionospheric piercing point (IPP). A mapping function is
used to convert the slant STEC to vertical VTEC at the IPP or vice versa (details of the
derivation is given in Hoque & Jakowski, 2008).

( )

hR +

mE

STEC / VTEC ≈ (29)

2 2

( ) ( )

2

hR + − RR + cos β

mE h E

where h m is the height of maximum electron density (varies between 250 -450 km), R E is the
earth's mean radius (~ 6371 km), R h is the receiver height above the earth's surface and β is
the elevation angle.

Based on similar techniques using observation from more than hundred worldwide GNSS
ground stations, German Aerospace Center (DLR) Neustrelitz computes vertical TEC
estimates at numerous IPPs worldwide. Thus, TEC maps are produced by assigning IPP
measurements to homogeneous latitude and longitude grid points as shown in Fig. 1.
European and global TEC maps and 1-hour-ahead forecasts are distributed via the
operational space-weather and ionosphere data service SWACI (Space Weather Application
Center Ionosphere, http://swaciweb.dlr.de, see also Jakowski et al., 2011) to the
international community with an update rate of 5 minutes. The advantage of such services is
that single frequency GNSS users can correct the ionospheric propagation effect in near real
time.

3. Estimation of ionospheric effects
3.1 First- and higher-order ionospheric terms

Equations (12) and (13) indicate that the signal delay caused by the first order term is equal
in magnitude but opposite in sign on GNSS carrier-phase and code pseudoranges, i.e., the
carrier-phase pseudorange is advanced while code pseudorange is retarded. The first order
term is directly proportional to the TEC encountered by the satellite signal during its travel
through the ionosphere and inversely proportional to the square of the signal frequency.
The first order term includes about 99% of the total ionospheric effect. Therefore, if the
frequency and link related slant TEC are known, the first order propagation effect can
easily be computed and corrected. If the TEC map is available, the slant TEC can be
computed simply multiplying the vertical TEC at the IPP by the mapping function (e.g., Eq.
29).