MikeRSpencer's comment is the key to choose the best method among possible options QGIS can offer.
- Sample at each GPS point
- Sample at a regular interval along the line
Without additional information from OP (well...not yet), remaining option would be:
- Sample all the cells along the line
In QGIS Processing Toolbox, there is a SAGA Tool Profiles from lines (in
SAGA | Terrain Analysis - Profiles).
The output table shows 1 record (row) per each cell on which the line overlays. Depend on how we want to sample out from this table, we can use
DIST (distance from the start point) or
X,Y coordinates to refer the location.
Positive point is that we can choose sampling method afterwords. Negative point is the data size, unnecessarily large, if we have already decided how we want to measure the profile.