Initial Orbit Determination (Angles-Only Method)

Angles-only approach applying the Least Squares method

1) In test_AnglesOnly_GEOS3.m, we define global variables: const (astronomical and mathematical constants), CS (unnormalized gravity field coefficients), AuxParam (struct that represents model parameters and time for orbit propagator), eopdata (Earth orientation parameters), PC (planetary coefficients for JPL ephemerides computation).

2) Download Earth orientation parameters from the following link (if it is out of date).

https://celestrak.org/SpaceData/EOP-All.txt

3) Earth orientation parameters are read from EOP-All.txt.

4) Observations are read from GEOS3.txt, and biases from table 4-4 of the book “Fundamentals of Astrodynamics and Applications, 4th Edition, 2013,” are subtracted. Then, measurement noises are set from table 4-4. After that, the station’s ecef position is calculated using Position.m, and three sets of observations are selected to find the initial guess of the satellite state vector utilizing IODmain.m.

5) Parameters for orbit propagator (AuxParam.Mjd_UTC = Mjd_UTC; AuxParam.n = 10; AuxParam.m = 10; AuxParam.sun = 0; AuxParam.moon = 0; AuxParam.planets = 0;) are set, and the initial state vector (Y0_apr) is propagated to the epoch (first measurement’s time). Then, the Least Squares’ initial parameters are set.

6) The epoch’s state vector is propagated to the times of all measurements in an iterative procedure and corrected at each stage. Then, epoch’s state vector is converted from the TOD to the J2000 coordinate system and compared with the true state vector. Finally, the epoch’s state vector is converted to the TEME coordinate system and sv2tle.m is used to produce the TLE.

Please note that numerical integration is done in TOD coordinate system. So, only Earth rotation is considered in Accel.m and VarEqn.m.

References:

O. Montenbruck, E. Gill, "Satellite Orbits: Models, Methods, and Applications," Springer Verlag, Heidelberg, 2005.

D. Vallado, "Fundamentals of Astrodynamics and Applications," 4th Edition, 2013.

https://celestrak.org/software/vallado/matlab.zip

https://sourceforge.net/projects/odtbx/

https://ssd.jpl.nasa.gov/planets/eph_export.html