Analysis of the effect of precession and nutation motions on ECI - ECEF transformation

In Global Positioning Satellite Systems (GNSS), the position of satellites must be defined in a coordinate system that is independent of the movement of the Earth (fixed in space), while a point on the Earth must be defined in a coordinate system that has axes exhibits the same movement of the Earth (Earth-fixed). To define the positions of satellites in geodesy, Cartesian coordinate systems called ECI (Earth Centered Inertial) are used, and to define the position of a point on the Earth, another Cartesian coordinate system called ECEF (Earth Centered Earth Fixed) is used. The relationship between the two coordinate systems is established through the mathematical definition of the Earth's movements, including precession, nutation, Earth's rotation, and polar motion. The International Astronomical Union (IAU) mathematically defined precession in 1976 and nutation in 1980. IERS publishes the polar coordinates and the time difference used to calculate the true angular rotation of the Earth at regular intervals. In this thesis, a program called "Eci2ecef" was designed to perform the conversion between ECI and ECEF coordinate systems for multiple epochs in a short time. The IAU 1976 precession and 1980 nutation models and the IERS EOP 14 C04 series were used in the design of the program to perform the conversion. To examine the effect of precession, nutation, polar motion, and Earth's rotation parameters on the transformation between the two coordinate systems and to track the periodic motion of precession and nutation, the transformation matrices from the ECEF system to the ECI system for each day from January 1, 2000 to August 31, 2022 were calculated, and the impact of parameters on GPS-SVN 43 ve 63 satellites, and IGS NABG00NOR and SYOG00ATA stations were investigated. Within the scope of the study, the effect of the parameters used in the conversion on the transformation was determined for each epoch over an approximately 23-years period, and their maximum and minimum effects, three-dimensional graphics, and absolute time-variable effect graphics were presented. The data obtained from the numerical application were consistent with the periods defined for precession and nutation in the literature, and they were examined in detail with the created graphs.