Ground GNSS Atmospheric Sensing - GNSS Remote Sensing: Theory, Methods and Applications - page 37

combination (LC) equation of double-differenced (DD) phase and code observations
can be expressed as:

f 1 L1 i kl f 2 L2 i kl

1

LC i kl

D

f 1 f 2

D i kl C ZTD k .t / .m. z i k / m. z j

k // ZTD l .t / .m. z l / m. z j

//

l

f 1 N1 ij

kl

c

kl f 2 N2 ij

C " ij
kl

C (3.3)

f 1 f 2

where ZTD is the zenith tropospheric delay, m is the mapping function, f i is the
frequency ( i D 1,2), Li and Ni are the double-differenced phase and ambiguity
of the frequency f i , respectively, kl ij is the double-differenced pseudorange, c is
the velocity of light in vacuum, and " kl ij is noise. Using the least square, the
unknown parameters can be estimated, including ZTD, coordinate and ambiguity,
etc. (Jin et al. 2010 ).

3.2.1.2 Non-difference Observation

With the double difference GNSS processing technique, tropospheric delays can be
derived with a high accuracy, but some information are removed. Nowadays, the
emerging Precise Point Positioning (PPP), high accuracy tropospheric delay can be
estimated too, while the precise orbit and clock are provided by an external network
such as IGS products.

3.2.2 Mapping Functions

The GNSS slant tropospheric delay (STD) is the total delay along the signal path
from the satellite to the receiver throughout the neutral atmosphere. The Zenith Total
Delay (ZTD) along the zenith direction can be obtained through mapping function
related to the satellite zenith angle E , i.e.,

ZTD D STD:m. z /

D ZHD m h . z / C ZWD m w . z / (3.4)

where STD is slant tropospheric delay, z is the corresponding elevation angle, m ( z )
is general mapping function, m h ( z ) and m w ( z ) are dry and wet component mapping
functions, respectively, ZHD and ZWD are Zenith Hydrostatic Delay and Zenith
Wet Delay, respectively. Over the past 30 years or more, a number of mapping
functions have been developed by geodesists and meteorologists.