Theory of GNSS Radio Occultation - GNSS Remote Sensing: Theory, Methods and Applications - page 107

the geometric phase of the occultation link is referred as the excess atmospheric
delay , i.e., a combination of the phase delay caused by the neutral atmosphere and
ionosphere. By precisely measuring the excess phase delay and its differential form,
or call Doppler, the bending angle and therefore the vertical structure of atmospheric
refractive index can be derived. In following sections, we will focus on retrieving the
excess atmospheric delay from the RO observations through the calibration process.
The basic observables at a LEO receiver for an occultation event are the occulting
GPS signal amplitude and phase measurements. Specifically for a GPS occultation,
the phase observations consist of L1 (C/A) and L2 (P2) phase measurements
between the LEO receiver satellite and the occulting GPS satellite. These raw
phase measurements L can be modeled (in dimension of distance) as (e.g., Hajj
and Romans 1998 ;Hajjetal. 2002 ):

c
f k

L TR
k

TR
k

D TR C TR

k

C C T C C R D C " k (5.15)

d TEC TR

C O f 2 TR

k

D ne u tral
k

C iono
k

D ne u tral
k

k

C (5.16)

f k

with
k TR the recorded phase in cycles for the signal propagated from transmitter ( T )to
receiver ( R );
c the speed of light in vacuum; k D 1 or 2 for L1 and L2, respectively;
TR the geometric range (distance) between the transmitter and the receiver;
k TR the total excess delay due to neutral atmosphere ( k neutral ) and ionosphere
( k iono );
C T , C R time dependent clock errors of the transmitter and the receiver, respectively;
" k measurement noise due to the receiver's thermal noise and local multipath;
d a constant;
TEC k TR the integrated electron density along the raypath, and
O( f 2 ) the higher order ionospheric terms (order 1/ f

3

or higher).

Subscript k in Eqs. ( 5.15 and 5.16 ) implies the dependency on the frequency. The
ionosphere is dispersive media whereas the neutral atmosphere is non-dispersive at
radio frequencies. However, since the electromagnetic signal has to travel through
the ionosphere before and after it reaches the lower neutral atmosphere, the L1
and L2 signals received at a given time also sense slightly different parts of the
neutral atmosphere. This is why the neutral atmospheric delay term k neutral remains
frequency dependent (Hajj et al. 2002 ).
Here we assume the phase errors caused by the transmitter and receiver antennas'
relative orientation as well as the phase center variations have been modeled
and removed. Also, a constant bias (additive constant) corresponding to a large
integer number (constant) of cycles during an occultation is ignored, since the
derivative of the phase but not the absolute phase delay is of interest for an
occultation measurement. It is worth noting that the high order ionospheric terms