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I have an UAV which does not give me the raw sensor data (e.g. rinex or ubx). The only format I get is NMEA. Now I want to know how could I use the NMEA-data to get the highest precision of my postitions via postprocessing. Are there any known methods to do this? I thought of something like a virtual sensor at the positions from the NMEA-data to maybe get the rinex-data afterwards from a service like SAPOS.

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It is not possible to do post-processing using NMEA output only, because it only contain final computed positions. And to do post-processing you need the pseudaranges, phases, etc. for each satellite separately.

However, a basic differential correction would be possible if you have the output of a nearby fixed GPS (a base). The key point is that the reference base GPS must use the same set of satellites than your GPS (the rover).

The possible workarounds are as follows:

1.- If the output of the base is RINEX or equivalent (there is many public bases you can download data from), you can compute a kinematic solution for the base using the same satellites reported in the NMEA output of your GPS. Then you can compute the difference between each instantaneous solution of the base and the mean (or known base coordinate), and subtract those differences from the coordinates reported by your GPS (that is the simplest differential correction). However, this won't be possible if your GPS is using a satellite not observed by the base. In the gaps were you have no differential corrections due to this, you can just interpolate from the corrections available before and after the gap. The bigger the gaps the worst will be the effectiveness of the correction.

2.- If your base GPS have only NMEA output, you will have to find moments (epochs) where both GPS happen to be using the same set of satellites. And from those moments, compute and interpolate differential corrections for the whole period of observation. If the view of the sky of the base and rover is too different this last option might become impossible to implement, as there will be too few or no epochs were both GPS used the same satellites.

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To my knowledge there is no way to post-process NMEA data. From my experirence you must have the raw GNSS observations in order to post-process data.

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