Alas, you need some variant of differential GPS to be able to cancel out the fast and slow errors.

Without a reference signal used for cancelling errors, you will always have huge problems. Driving a car 60mph/100kpm will give a reasonably distance for a 100m section but if doing the plotting Andy suggested you will be able to see the GPS move of itself at 3-5km/h or maybe even more. That should give an indication of errors in relation to your transport time between point A and B.

One type of correction in existence is a GPS that also listens to a stationary transmitter on the ground, who picks up the GPS error and transmits a correction.

Another type of correction is a fixed GPS on the ground who sends up correctional information to a satellite who then sends it back again, removing the need for a special radio frequency for a ground-based transmitter.

But without corrections, your GPS will suffer from lens effects in the atmosphere and errors in actual locations of satellites.