To prove a speed based on a video is easy. use the same cam, go at a static speed. such as
10, 20, 30, 40, 50, 60, 70, 80, 90, 100. in the same car, in the same stretch of the road.
Now take each footage and compare it to the video footage speed, simply time how fast the objects are moving in the actual footage vs their speed in the test footage. You will have an approximation already.
to narrow it down further, repeat the video capture again in between the zones noted and you will get a very accurate time frame by time frame traveling speed.
And in all reality, GPS speed are usually lagged behind by a few seconds...