Currently, I am trying to determine the position of a GPS satellite from a RINEX navigation file. I am using RINEX 2.11. Tables A3 and A4 describe how navigation files are structured.

In order to calculate the position of said satellites, I am using this appendix containing all needed equations. Right in the beginning, there are two formulas to correct the satellite time to GPS time and one additional formula to calculate the time passed since the reference epoch:

$$ t = t_{SV} - \Delta t_{SV} \tag{1}$$

$$ \Delta t_{SV} = a_0 + a_1 (t - t_{0c}) + a_2 (t - t_{0c})^2 \tag{2}$$

$$ t_k = t - \Delta t_{0e} \tag{3}$$

As you can see, I need multiple time variables for this:

  • $t_{SV}$: time of space vehicle

  • $t_{0c}$: reference time, clock parameters

  • $t_{0e}$: reference time, ephemeris parameters.

I am not sure where to find these three time variables in a RINEX navigation file. I already found this post with a similar question where a comment describes where to find $t_{0c}$ and $t_{0e}$ in a RINEX navigation file (see second answer) but still cant really figure out where $t_{SV}$ comes from. My current guess is that $t_{SV}$ is the time of transmission described in the last column of a data block, is that right?

Edit: After some further reading, I think that $t_{SV}$ is the time of which I want to calculate my satellite position for. So I assume that $t_{SV}$ is basically a time which I wont find in a RINEX file, but rather choose myself. When choosing a value for $t_{SV}$ it should then be no more than half a week away from $t_{0c}$. Is that the right interpretation for $t_{SV}$?

  • 1
    $\begingroup$ $t_{SV}$ is the local time of the SV, while $t$ is the "true" GPS time. So even while $t_{SV}$ is different for each SV, $t_{SV} - \Delta t_{SV}$ yields the same $t$ always. I'm pretty sure that e.g. the time in the TOW counter or the broadcast ephemeris is linked to $t_{SV}$ and not to $t$, but I would have to double check. $\endgroup$
    – Ludo
    Jun 12, 2022 at 11:48
  • $\begingroup$ Thanks for the reply! Im pretty sure that $t$ is not contained in any RINEX file aswell. After even more reading into that topic I found this paper where in section 4.2 it is described how to obtain $t_SV$ from the navigation transmittion time: "To calculate the correct GPS satellite position one needs to use the GPS Time at the NAV-message transmission" and "A normal receiver calculate the GPS Time by comparing the phase displacement of received message with a own code". Any idea what that second part means? $\endgroup$
    – alex05
    Jun 12, 2022 at 13:09
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    $\begingroup$ I can only imagine that the remark is referencing solving the Navigation Equation, where "time" is the fourth variable solved for via the pseudo ranges. A bit cryptic though. $\endgroup$
    – Ludo
    Jun 12, 2022 at 16:35


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