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SP3 files provide satellite positions for every 15 minutes. How would you find the satellite position at a time between two logged positions, i.e. 7 minutes after the last logged position?

I can think of several ways to do this: 1. Just use the position at the closest interval. 2. Linear interpolation between the intervals on either side. 3. passing a polynomial through several consecutive points and using the polynomial to estimate any satellite position within the time frame.

I don't think the overall effect on the accuracy of the estimates would vary much between all three of these (but I don't know this as a fact). Is this the case? Is there a "standard" way for dealing with it?

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Lagrangian polynomial are used for sure. I do not know if I would call it a standard. See for instance http://www.navipedia.net/index.php/Precise_GNSS_Satellite_Coordinates_Computation.

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