However, the results looked a lot worse when I changed one analysis parameter by selecting the "Doppler" checkbox, and re-computing the results. Here is a direct comparison:
Let me start by quickly reviewing the difference between "positional" and "doppler" analysis (not all my readers are GPS speedsurfers - if you are, perhaps just skip to the next paragraph). All GPS units, regardless if you use them for directions in your car or for measuring your speed while windsurfing, determine your position from the measured distance to several GPS satellites (typically 6-8). The accuracy of the position is limited by a number of factors to about 3 meters. My GPS, the Navi GT-31, measures the position once a second; the difference in two positions gives you the speed. When windsurfing at 20 knots, you move about 10 meters in one second. An error of 3 meters would then give you a 30% error in the speed, a rather large error! But fortunately, there is another way top measure the speed using the "Doppler Effect". Doppler-based measurements tend to be much more accurate, with reported speed accuracies of 0.1 knots. This is why GPS-based speed events generally require the use of a GPS that logs Doppler speed, like the GT-31 that I used.
So, if Doppler speeds are much more accurate, does this also mean that the Doppler-based jibe analysis is more accurate? Not so fast! Let's look at the GoPro video of the jibe #1, where the position-based speed was 13.8 knots, but the Doppler-analysis thinks it's just 6.2 knots:
The jibe was nicely planed through, which typically requires a minimum speed of more than 10 knots. For comparison, here is a section from the same session where I was moving at about 7 knots (and positional and doppler speeds were very close):
Nina was also wearing a GPS, so I could use her tracks together with mine to accurately define this 8-second period where I was sailing at 7 knots (I was slightly slower at the very beginning and end of the movie).
Obviously, the board speed during the jibe was significantly higher than 7 knots, so the Doppler-based jibe analysis does not seem to be accurate. Let's take a close look at the track and speeds for another jibe (#12 in the table above):
This jibe (#12) was a bit wider than jibe #1, and the discrepancy between positional and Doppler-based minimum speed was smaller. This was a recurring theme in all the jibes I looked at: the tighter the jibe, the more the minimum speed would drop in the Doppler analysis. I was working on laydown jibes, so I was cranking them relatively tight; Nina's jibes that day were wider, and the speed differences between Doppler and non-Doppler analysis were much smaller.
To some extend, the 1 Hz sampling rate will cause an underestimate of the speed when the board changes direction rapidly. Even in the positional analysis, we measure the distance along a straight line, but the board had sailed a longer arc. In the Doppler analysis, a similar error would occur; however, it should also be of similar magnitude, and not substantially larger. But we need to keep in mind that even the binary data files do not contain "raw" data, but rather the result of a complex mathematical analysis. From the time difference in the speed curves, it appears that the Doppler data include a filter with something like a 3-4 second time constant. In 4 seconds, the board changes direction by perhaps 120 degrees in the jibes - that's very far away from a straight line! I think this could explain why the Doppler speeds in the jibes appear to be too low, and that things get worse the tighter the turns are.
This entire thing is not just a theoretical thing. If I want to know how good my jibe was, it makes a big difference if I kept 70% or just 44% of my speed. Keep in mind that the Doppler-based analysis keeps estimating lower speeds for several seconds in a row, without ever "compensating" for it with higher speeds. If you'd draw two tracks, one based on positional and one based on Doppler data, the "Doppler surfer" would fall behind in every jibe!
This has a significant effect on alpha 500 results. For the top jibes in the tables above, the lower mid-jibe Doppler speeds added about 2 seconds to the time to reach 500 meters, dropping the alpha speed by 1-2 knots! Since alpha team rankings are usually quite tight, even just one knot would make a significant difference. However, I do not think that going to non-Doppler alphas is the solution, since the non-Doppler data errors add up over the 45-50 seconds that a 20-knot alpha 500 run requires.
For now, the solution for alpha rankings is to go with wider jibes with a very even carve. In the future, we can only hope that better GPS units with a higher sampling frequency become available. Several 10 Hz GPS trackers are commercially available already, but it is not clear if any of them provide the Doppler data required for highly accurate speed measurements - and if such Doppler data do not suffer the same shortcomings shown here for the GT-31.
----
Added July 25, 2014:
I recently learned why the position-based speed and the doppler speeds were so different, especially during jibes: I had my GT-31 set to "low power" mode. In low power mode, the GT-31 tracks fewer satellites (at most 6), which leads to much lower accuracy. Simply setting the power mode back to "normal" resulted in a much better agreement between doppler and regular speed data. The tracks also seem much more accurate in "normal" power mode, where the GT-31 typically tracks 8-10 satellites.