Global Positioning System Reference
In-Depth Information
Figure 5 shows that the third order term on code observables can be as big as 50 mm at low
elevation angles during times of high TEC.
3.2 Estimate of LoS propagation assumption error
Due to the ray path bending satellite signals propagate through curvature paths instead of
straight line of sight paths. However, a curvature path length and the corresponding LoS
path length are not equal rather the curvature path is slightly longer than the LoS one. The
difference between them is defined as the excess path length and it can be computed by the
following formula given by Jakowski et al. (1994).
b
1
len
I
2
1
4
d
=
1
TEC
(33)
(
)
1/2
f
2
1c s
b
β
2
where b 1 = 2.495×10 8 , b 2 = 0.8592 and β is the elevation angle. The excess path length d I len will
be estimated in millimeters when β is measured in radians, f is in MHz and TEC is in TEC
units. The frequency dependence of the excess path length has been plotted in Fig. 6.
Fig. 6. Frequency dependence of the excess path length at different levels of ionospheric
ionization and elevation angles
Figure 6 shows that at the L2 frequency, the excess path length can be as big as 100 mm at
low elevation angles during times of high TEC such as VTEC = 250 TECU.
3.3 Estimates of residual terms in the ionosphere-free solution
Although residual terms in ionosphere-free solutions are less than 1% of the first order
ionospheric effect, they cannot be ignored if centimeter / millimeter level accuracy is
required in GNSS positioning and timing applications. A plot showing comparison of dual-
frequency GPS L1-L2 residual terms is given in Fig. 7 for better understanding of their
relative influences on precise range estimation. For this, the ray tracing tool has been used in
which the ionosphere is modelled by a Chapman layer with a peak density of 7.75×10 12 m -3
at 350 km altitude and scale height of 78 km, and corresponding VTEC = 250 TECU.
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