• Differences between geocentric and topocentric right ascension and declination:
  • Geocentric RA/Dec are defined as if the observer were at the center of the Earth.
  • Topocentric RA/Dec are defined for a real observer on the Earth’s surface.
  • The coordinate system difference is the slant-range vector $\vec{\rho}_{ECI}$.
• RAZEL algorithm: given the state in ECI/ECEF, compute the Range, Azimuth angle, and Elevation angle.
  • The reverse algorithm is called site-track algorithm.
  • Compute the slant-range vector from the site to the satellite in ECEF:
    • $\vec{\rho}{ECEF}=\vec{r}{ECEF} - \vec{{r}{Site}}{ECEF}$
  • Convert the slant-range vector to the vector in SEZ (South–East–Zenith) coordinate.
  • Compute range, elevation, azimuth angle separately. Details are in Algorithm 27.
• There are many factors that affect the quality of the observation data. The overall process to mitigate that is illustrated in Figure 4-8. Here are some details of the effects:
  • Refraction: including ionosphere (80-300 km) and troposphere (surface - 9km).
    • Ionosphere: free electrons to delay the signal propagation; thus primarily affects range measurements. Use Single Differenced signals can eliminate the effect to first order.
    • Troposphere: hydrostatic (dry) delay and wet delay.
  • Aberration: apparent shift in the observed direction of an object caused by the motion of the observer.
    • Diurnal (Orbital): Caused by Earth’s rotation. Magnitude is around 0.3 arcseconds.
    • Annual: Caused by Earth’s orbital velocity around the Sun. Magnitude is up to 20.5 arcseconds.
    • Secular: Caused by the motion of the solar system.