Exactly. User jurijs.jeshkins has begun what looks to be a promising solution. You can pull a copy of the program from the thread below. I will be running a sample dataset through it later today. As a matter of practice I typically occupy a point for a minimum of 1 minute and most often two minutes regardless of status. More information the better for PPK.
As he also correctly points out in the thread and as you bring up ensure your output file is in the same time format. In my post above it shows output as UTC when it should be GPST as you have shown in red circle.
If inclined to do so in QGIS, one could use the aggregate function based on point time stamps, start and end times, to batch the entire track log into “groups” containing a few hundred observations depending on logging frequency. I am slightly confused on what you mean by midpoint or just two observations. Your corrected log file should have more than two points to interpolate from, unless you occupied the point for 1 second.