Chapter 2 Radio Occultation Theory and Constellation Deployment Principle. 11
2.2 The GNSS Radio Occultation Theory
2.2.1 The Global Navigation Satellite System
The GPS developed by United States, is the only fully functional GNSS in the world. It consists of 24 satellites, with a few more satellites for backup, distributed in six circular orbit planes about the globe with an inclination angle of ~55o, a period of 12 hours and an altitude of 20,200 km. Although originally designed as a navigation aid by the U.S. Air Forces, the ground-based and the space-based applications of the GNSS remote sensing have shown positive impacts on climate monitoring, global and regional weather prediction, ionospheric research, and space weather forecasting.
Each GPS satellite continuously transmits right-hand circularly polarized signals at L1 and L2 band frequencies. The L1 and L2 signals received from each GPS satellite can be written as [3]:
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2.2.2 GNSS Radio Occultation Retrieval Theory
In Figure 2-1 a GNSS RO operation concept and data set for an occultation event are shown. By measuring the phase delay of radio waves from GNSS satellites as they are occulted by the Earth’s atmosphere, accurate and precise vertical profiles of the bending angles of radio wave trajectories in the ionosphere, stratosphere and troposphere are obtained.
A complete GNSS RO data set for an RO event includes (1) Occultation data: signal from an occulting GNSS satellite to occulting LEO satellite with 20 msec data rate (see link 1 marked in Figure 2-1); (2) Referencing data: signal from a non-occulted GNSS satellite with 20 msec data rate (see link 2 marked in Figure 2-1); (3) Precision orbit determination (POD) data: signals from other three non-occulted GNSS satellites with 10 sec data rate; and (4) Fiducial IGS (International GNSS Service) data: GNSS navigation data from ground fiducial network sites with 1sec data rate from occulting GNSS satellite (see link 3 and link 4 marked in Figure 2-1) [39]-[40].
A basic GNSS RO measurements and processing flow is presented in Figure 2-2. We derive the single path GNSS RO theory in this Section. From the calculus of variation the ray path from the GNSS satellite to the LEO satellite, in a geometric optics context, is by definition a path of stationary path and satisfies Fermat’s principle globally and Snell’s law locally [5], [42]. Figure 2-2 we show a ray path geometry from a occulted GNSS satellite (point G) to a LEO satellite (point L) in the plane of propagation and illustrating radio occultation of GNSS signals. This ray must satisfy the requirement
=
whereΔρis the ray delay, Δφ is the phase delay, n(r) is the real part of the refractive index, r is the geocentric position vector of any point on the ray, s is the arc length along the
ray path, rL is the geocentric position vector to the LEO satellite, r is the geocentric G position vector to the occulting GNSS satellite, and r is the geometric straight line distance LG between the LEO satellite and the occulted GNSS satellite.
From Figure 2-2, the excess Doppler from the intervening medium can be derived as
LG refraction at the LEO and occulted GNSS satellites and is equal to unity, respectively; TL and TG are the ray path tangent vectors of the LEO and occulted GNSS satellites, respectively; and VL and VG are the velocity of the LEO and occulted GNSS satellites, respectively. The triangle OLG defines the instantaneous plane of propagation of the ray from the occulted GNSS satellite to the LEO satellite. The interior angles of this triangle OLG and its sides are completely determined from the precision orbit determination (POD) information about the orbits of the LEO and occulted GNSS satellite. The refraction-related quantities, which are the bending angleα =δL +δG, can be determined from the excess Doppler measurement of Eq. (4) by applying a=nr×T =constant, which is Bouguer’s law, essentially a Snell’s law for a spherical symmetric medium.
As the ionosphere is considered as a source of concentration of electrons and the frequency of electromagnetic wave, the L1 and L2 GNSS signals can be combined to significantly reduce the effect of the ionosphere. The atmospheric bending angle can be calculated using Eq. (5) below
From the bending angles, profiles of atmospheric index of refraction are obtained through the equation of Abel transformation as [3], [42]:
⎥⎥
In the atmosphere, the index of refraction, n, is very close to unity such that it is usually discussed in terms of the refractivity, N. By using Eq. (7) N is a function of temperature (T in K), pressure (P in hPa), water vapor pressure (Pw in hPa), electron density (ne in number of electrons per cubic meter), and frequency of the GPS carrier signal (f in Hz) as
2
The refractivity profiles can be used to derive profiles of electron density in the ionosphere, temperature in the stratosphere, and temperature and water vapor in the troposphere by using Eq. (7).
For problems from multipath, there have been several data processing methods for RO data inversion to retrieve atmospheric parameters from a wave optics theory treatment [5], As for the F3 mission, Kuo et al. develop a RO data processing procedures used to obtain stratospheric and tropospheric bending angle and refractivity profiles from the raw phase and amplitude data [23], [37]. The Phase Lock Loop (PLL) technique employed in earlier RO missions was replaced by a novel open loop technique for the F3 mission [43]-[45]. There are other data processing procedures or algorithms developed by other methods [5], such as the geometrical optics method (GOM) [46]-[47], the back-propagation method (BPM) [48]-[49], the radio holographic method (RHM) [50]-[51], the amplitude-retrieval method (ARM) [52], the full-spectrum-inversion method (FSIM) [53], the canonical transformation
method (CTM) [54], the sliding spectral (or radio optics) method (SSM) [44]-[45] and National Central University Radio Occultation (NCURO) algorithms [55]-[56].
The F3 RO processing includes four radio holographic algorithms: BPM, SSM, CTM, and FSIM. Detailed description and derivations of F3 RO data processing procedure could refer to Kuo et al. in [23]. The RO data processing procedure and steps currently used for F3 mission are listed as follows:
1. Input (Phase, amplitude, LEO/GPS position and velocity);
2. Open-loop data processing GNSS navigation data messages (NDM) removal and phase correction;
3 Detection of L1 phase locked loop tracking errors and truncation of the signal;
4: Filtering of raw L1 and L2 Doppler;
5. Estimation of the “occultation point”
6. Transfer of the reference frame to the local center of Earth’s curvature;
7. Calculation of L1 and L2 bending angles from the filtered Doppler;
8. Calculation of the bending angles from L1 raw complex signal;
9. Combining (sewing) L1 bending angle profiles from steps 7 and 8;
10. Ionospheric calibration of the bending angle;
11. Optimal estimation of the bending angle;
12. Retrieval of refractivity by Abel inversion;
13. Retrieval of pressure and temperature;
14. Output (bending angle, refractivity, pressure, temperature, moisture).