The tracks show that the GPS points from the phone are not accurate here. I was going straight - I did not suddenly go upwind and accelerate 5 knots within one second. The jibe in the lower right corner also shows that the GT-31 is much more accurate: the blue curve from the GT-31 shows a nice curve; in contrast, the red curve from the phone GPS wiggles all over the place.
I have seen spikes in GT-31 data, too, but they tend to be rare (as long as you look at the Doppler results), and are usually very easy to identify. Most of the time, it's just a single value that's wrong, which gives a very sharp peak. Also, GT-31 spikes tend to be linked to crashes (although that's not always the case). Either way, they are easy to see and remove.
The 4-second, 5-knot spike shown above it the worst in the 2-hour recording, but there are a number of other spikes, too. Many of the other spikes affect only one point, which seems to be off by 1-2 knots (an example is in the track before the jibe). More than 98% of the time, the speed values from the GT-31 and the phone are very close.
So using an Android phone with the GPS Speed Talker app can be helpful, although one has to take the announced speeds with a bit of skepticism. Perhaps other phones are more accurate, although the only thing I have seen was a description that some other phones have less accurate GPS units. Posting results from Android phones to sites like GPS-speedsurfing.com or the GPS Team Challenge is, at best, questionable. The standard filters in GPS action replay did NOT remove the spike above, and my 2-second speed for the day would have been 4 knots to high. There are obviously good reasons why these sites suggest to use GT-31 units.
If you want to hear how fast you are going while sailing with the highest possible accuracy, you can always use a bluetooth-enabled GT-31 (a BGT-31), and have the GPS Speed Talker app use the BGT-31 data for the announcements.