Theory of GNSS Radio Occultation - GNSS Remote Sensing: Theory, Methods and Applications - page 115

5.3.3 Ionosphere Retrieval

After the calibration process, the sum of the neutral and the ionospheric delays is
isolated (up to a constant). When the tangent point of the occultation link is in
the ionosphere, the excess phase delay due to the neutral atmosphere is negligible.
There are two types of processing technique for extracting ionospheric delay along
the ray path (Hajj and Romans 1998 ; Schreiner et al. 1999 ): (1) single-frequency
approach, i.e., deriving the ionospheric delay at each carrier frequency (e.g., L1 and
L2) separately; (2) a dual-frequency approach that directly isolates the ionospheric
delay through linear combination by assuming L1 and L2 signals travel along the
same ray path in the ionosphere.
The first approach results in less noisy determination of ionospheric delay but
requires the a-priori calibration processes (Sect. 5.3.1 ) to remove the orbit and clock
errors. The second approach is inherently simpler by eliminating the calibration
process, as the orbit and clocks errors cancel out when forming the L1 and L2 linear
combination. However, the simplicity in the dual-frequency approach is at the cost
of lower precision due to the noise added by L2. Also it assumes L1 and L2 signals
travel along the same ray path in the ionosphere, which could be violated and result
in extra errors in the presence of significant bending in the ionosphere (Hajj and
Romans 1998 ).
By using the single-frequency approach, the bending angle at each signal
frequency can be retrieved from the ionospheric delay or Doppler. Following the
Abel transform in Eq. ( 5.13 ), the vertical profile of refractive index can be derived.
Note that the Abel integral requires knowledge of bending all the way up to the top
of the ionosphere. GPS is above most of the ionosphere, however, the LEO receiver
satellite are generally located inside the ionosphere. Therefore the bending due to
the ionosphere above LEO altitude might not be neglected and needs to be modeled
(e.g., Hajj and Romans 1998 ).
The electron density profile n e (in per cubic meter) can then be derived through
the following relation (Hajj and Romans 1998 ):

n e .r/ D Œ1 n.r/ f 2 =.40:3/: (5.21)

In the ionosphere, the total electron content (TEC in electrons numbers per square
meters) along a ray is related to electron density n e , refractive index n and the excess
phase S (in meters) by

Z n e dl D

40:3 10 16 Z .n 1/ dl D

f 2 f 2 S

40:3 :

D

TEC (5.22)

Due to the dispersive characteristics of the ionosphere, the L1 and L2 signals
propagate on slightly different paths and thus result in slightly different TECs. TEC
may be calculated from excess ionospheric phase delay ( S 1 and S 2 at two carrier
frequencies) after removing the orbit and clock errors through calibration process.