TLE elements and osculating elements
The page Calculations for the Earth's artificial satellites shows the errors for the IRNSS-1H satellite when the TLE elements are used directly, without SGP4/SDP4 "decoding". Here the errors are shown for 464 satellites and for all the elements.
Let ElementTLE be one element taken directly from the TLE and let ElementKEP be the same osculating element calculated for the TLE epoch with the correct procedure already explained at the page Calculations for the Earth's artificial satellites; in this context, the error is defined as: err = ElementTLE - ElementKEP
For each satellite, the table shows (in degrees and km):
Satellite: the satellite name and the average perigee and apogee altitude over a reference sphere with radius of 6371 km;
the errors for the following elements:
sma: semi-major axis; e: eccentricity; I: inclination with respect to the true equator of the TLE epoch; M: mean anomaly; RAAN: right ascension of the ascending node with respect to the mean equinox of the TLE epoch; AoP: argument of perigee; Rp and Ra: perigee and apogee radius vector.
In the first row there are the mean absolute errors (the sum of the absolute value of err divided by the number of the TLEs); in the second row the are the minimum errors (err is taken with its sign) and in the third row there are the maximum errors (err is taken with its sign).
The number of the TLEs used for the calculations varies from 51 (STARLINK-1084) to 18472 (ISS), the average is 1265 TLEs/satellite, the total number of the used TLEs is 587062.
Let's see an example for the Aqua satellite. We see that if we use the mean motion directly taken from a TLE to calculate the semi-major axis, the absolute error will usually be about 8 km. We also see that, on average, the argument of perigee shown in a TLE is off by 85 degrees from the correct osculating argument of perigee, but the table also shows that the osculating perigee could be in the opposite direction when SGP4 is not used (the maximum possible angular error is ±180 degrees).
That happens, for example, with the following TLE:
1 27424U 02022A 17112.95801317 +.00000217 +00000-0 +58176-4 0 9992
2 27424 098.2007 055.0865 0000509 004.2173 062.1365 14.57117579796188
where the argument of perigee is 4.2173 deg, while the correct procedure gives 184.218591412 deg, almost exactly in the opposite direction!