How can I snap irregular GPS point data to regular points of a route?

I have irregular GPS points in several shapefiles with meteorological parameters of a mobile measurement campaign.
In order to compare the different shapefiles I would like to snap the irregular GPS points to predefined waypoints (e.g. regular with 1m distance) of the route.

I was able to prepare the regular points with 1m distance. But how can I assign the values of the irregular GPS points to my artificially created points? The number of GPS points is larger compared to the regular points.

I thought about buffering the regular points and take all GPS points within the buffer to calculate the mean of the measured values. What do you think about this idea?