I disagree with Boardsurfr about his use of the term 'Noise' and his contention that is is random in the higher Hz gps tracks. Tests I have done with side by side Mini Motions show surprisingly pretty good correlation of the 'sawtooth' in the speed graph. One in particular shows very clearly, and with great correlation, the change in speed in the fraction of a second when I changed gears during acceleration tests.
I don't think it is entirely random 'noise'. The correlation is not perfect 100% of the time, but it is certainly not random.
My tests were done with the two Mini Motions on my helmet.
It would seem logical to me that when you are sailing the receiver is bouncing or vibrating to some greater or lesser extent. The sawtooth we see could very well be the real manifestation of the micro speed changes that this produces.
Of course, I agree that that movement/vibration is somewhat random, and not a true indication of the horizontal speed one is travelling in that respect. So in
that sense it could be correct to call it 'random noise' (qualified). But I think what the receiver is recording is very, very close to actual receiver micro velocity.
So in that respect, the minimum speed data produced by a 10Hz GPS, worn on the head in particular, during an Alpha should be a very close indication of the true minimum speed. Smoothing it to 1 second would probably be a very poor indicator of actual minimum speed.
Of course, if the GPS is worn on the upper arm, there will be more movement off the path of travel (board and sailor mass) by the GPS during the gybe, and more sudden change of antenna orientation, and I think we can see this in some speed graphs quite clearly. Data from a GPS worn on the wrist is going to show this extra movement and orientation change to a much greater degree again, and is certainly not ideal for the accurate measurement of speeds during the gybe in manoeuvres like the Alpha.
Here is the example of the sub second gear changes from the Motor Bike test:
Acceration test:
The 4 small 'steps' in the speed graph are the gear changes.
Notice that is the speed increases, so does the 'sawtooth'. That would be a logical result of increased vibration at higher speed.
Here is an example of part of a high speed graph:

I noticed that in this test, the red unit data always seemed to be a bit smoother. It could well be that the blue unit was 'rattling' around a bit more in my helmet. But it could be any number of other things as well.