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I have TLE and RINEX navigation file for GPS satellite PRN 20, for 01.04.17r. 19:56:56 and 20:00:00 respectively. See also The Receiver Independent Exchange Format Version 3.03.

It seems that the value of longitude of the ascending node (Ω0) differs for both while all the other parameters are relatively similar.

RINEX file:

M0 = -0.41907076212790001
e  =  0.0044262305600569997
ω  =  1.5754052384999999
i  =  0.92697366533970005
Ω0 = -0.4446281969834

TLE file:

M0 =  5.8389169820721856
e  =  0.0042077
ω  =  1.5770882387483363
i  =  0.92682044735729674
Ω0 =  2.7589292150900362

What can be the reason for this?

While the values for M0 are close modulo 2π, the values for Ω0 seem to differ by only π, or about 180°.

Checking also other datasets the result is similar, although the difference between values differs.

TLE:

GPS BIIR-4  (PRN 20)    
1 26360U 00025A   17091.83120691 -.00000002  00000-0  00000-0 0  9995
2 26360  53.1029 158.0750 0042077  90.3605 334.5453  2.00565359123815

RINEX:

20 17  4  1 20  0  0.0 4.665344022214D-04 1.591615728103D-12 0.000000000000D+00
5.600000000000D+01-1.231250000000D+01 5.538802141913D-09-4.190707621279D-01
-5.606561899185D-07 4.426230560057D-03 6.150454282761D-06 5.153646507263D+03
 5.904000000000D+05-6.705522537231D-08-4.446281969834D-01 3.725290298462D-08
 9.269736653397D-01 2.442500000000D+02 1.575405238500D+00-8.669646839876D-09
 2.714398779890D-11 0.000000000000D+00 1.942000000000D+03 0.000000000000D+00
 2.000000000000D+00 0.000000000000D+00-8.381903171539D-09 5.600000000000D+01
 5.899500000000D+05 4.000000000000D+00
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    $\begingroup$ As a suggestion, have you checked that PRN20 of TLE and RINEX are the same satellite?. The offset of $M_0$ and $\Omega_0$ that you are reporting are typical between different satellites of a constellation. Also, your shortcut of TLE and RINEX shoes PRN20 while you started the question asking about PRN1 (a typo error maybe?) $\endgroup$ – Julio Nov 3 '17 at 10:48
  • $\begingroup$ Where did you get the RINEX file? $\endgroup$ – pericynthion Nov 3 '17 at 19:36
  • $\begingroup$ The rinex file is from garner.ucsd.edu, TLE from celestrak.com/NORAD/elements/gps-ops.txt. @Julio how can I check whether PRN20 is the same satellite for both files? I know the satellite numbers are different for glonass rinex and tle files but I thought for GPS it's the same. Yes PRN1 is a typo. $\endgroup$ – kas Nov 13 '17 at 20:34
  • $\begingroup$ @MartynaKasyr, if I were you I will search for another satellite in your TLE that matches the current orbital elements values of your RINEX file to barely confirm (or not) the discrepancy of PRN numbers between TLE and RINEX. There is also an open question about this topic here space.stackexchange.com/questions/20887/… $\endgroup$ – Julio Nov 15 '17 at 10:56
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They are in different reference frames. The TLE element set is defined relative to the True Equator, Mean Equinox (TEME) reference frame, and the elements in the RINEX Nav message are defined relative to Earth Centered, Earth Fixed (ECEF). Since both frames use the true equator, other elements (such as inclination) don't vary as much as the location of the node.

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