# ISS (ZARYA) TLE to Latitude Longitude Conversion

I am trying to take TLE of ISS (ZARYA) and get the latitude longitude and height. I am aware the TLE is in TEME~(True Equator Mean Equinox) frame. This means that the TLE was generated considering the True Equator as of TLE generation time and X axis pointing to mean equinox. Thus, if I were to calculate instantaneous latitude, longitude and altitude at the TLE generation point I need not worry about the precession and nutation complexity. I am also aware that LLH of ISS is expressed in geodetic coordinates. Now getting the exact sidereal time at the TLE generation time seems to be a little involved process involving UT1 and GMST equations (and UTC!), but I am able to bypass that problem by considering a UT1 time and sidereal time at 1 Jan 2023 12:00PM and then assume them to linearly related for short time. I am assuming within an year deviation will be small enough.

Anyway, I am first trying to attack the latitude problem, which is indepedent of sidereal angle and must come very close to actual number.

I am considering this TLE. Which is for date 2023-05-25 07:49:28.500 I derived the date using tle to date online utility

ISS (ZARYA)
1 25544U 98067A   23145.32602431  .00014206  00000+0  25493-3 0  9994
2 25544  51.6413  81.8570 0005396  18.1967 120.0030 15.50160974398246


Now using historical ISS data I am able to pull the latitude longitude and height at this time ISS Hitorical Data

Lat: 31.581 deg
Lon: -127.093 deg
Ht : 419.88 km


The inertial vectors I derived using the mathematical equations as defined in kep2cart doc are

-3498.170819 -4621.733107  3548.392785     2.785672    -5.551759    -4.477993


Now using this ECEF to LLH online utility I can convert to geodetic lat lon ht:

Latitude  : 31.63493   deg N
Longitude : 232.87807   deg E (forget this for a while)
Height    : 423939.5   m


The two latitudes are off by 0.05 degrees. Why there is this difference? Or I am assuming something about precession and nutation that I cannot?

Another issue is the altitude, using WGS84 system altitude should also come exact. Why is there difference in altitude?