Whist researching Doppler velocity error calculations and sources, i was reminded of the ground breaking work that Tom Chalko and Manfred Fuchs did in establishing the prodigious superiority of Doppler speed measurement over Positional measurement calculations.
These two scholarly works from around 2007 say it all really, and they were written before we had access to the GPS system 'SDOP' calculations from the Sirf Binary and Ublox ubx output.
Highly recommended fireside reading! 
bioresonant.com/dl/dl.htm?name=HighAccuracySpeed.pdfhttp://www.gps-results.com/GPS_Speed.pdf
Very interesting article.
I suggest one more very simple experiment we could perform.
Lets take GPS on your next ride on carousel coming into our town.
Our GPS is travelling with us on a exact circle and with constant speed .
We know that rotating speed and diameter will not change very fast so lets see how our recording may looks now on the GPS Results graph.
The test will show us :
Are there any sudden peaks or not ? If that path is more exact circle or not really ?
We are shown in article that Doppler method present much better accuracy , but there will be interesting to see ( in this carousel experiment ) how well is handle changes in direction.
Another interesting question could be how well our GPS handle change from one set of satellites to another set : For example lets imagine that results are calculated from 3 actually visible satellites and that set is constantly changed from one to another (?)
That test would have some serious problems.
First, you would need to sit on the top of the roof with a clear view to the horizon in all directions to be sure you get good satellite geometry, no multi path and do not cause the GPS to constantly switch satellites.
None of these problems exist in windsurfing if the GPS is worn properly.
Also, you can get the same accuracy spread test figures if you use geo stationary testing and this eliminates multiple sources of errors, which is what the Authors of both articles did. Remember, we are not testing positional accuracy, we know that is highly inaccurate in comparison. But such a test may be useful in properly controlled conditions to test if the speed graph is constant, and that may be useful to gain insight into Alpha accuracy. If you used the Doppler heading info to draw your Mapview, you will be disappointed with the pattern. We have already determined that Doppler derived heading data is highly unreliable during 180 degree turns in Alphas, which is why we use the Doppler speed for Alphas, but use the positional data for drawing the proximity circle. (Yes, we use potentially inaccurate positioning for it but it is the choice less prone to error in this case, especially in the very short term). If you study some Alphas carefully in GPS.Results or RealSpeed, you will see this discrepancy quite clearly at times, where the Doppler derived heading goes off way outside (or sometimes inside) the actual proximity circle track. The issue with Doppler derived headings and trying to derive position from them is that any very small error persists and more errors accumulate which takes the resultant position off on a divergent tangent. In roughly straight line sailing which we normally do, this is not a source of error as actual position is irrelevant.
The GPS system needs to have a minimum of 4 satellites locked to make meaningful calculations. More satellites locked means more accurate calculations. If you only have 4 satellites being used you will get meaningless results if one drops out before another is gained. The advantage of many satellites locked is that now there is far less detrimental effect (or virtually none) as one drops out and another is acquired. generally, experience had shown we need to have a minimum of 5 satellites and preferably 6 to 8 (or more), depending on their position in the sky, for reliable results. This is where Multi GNSS (Global Navigation Satellite System) receivers like the latest Ublox M8 should have a big advantage with their ability to use acquire if to 14 or more satellites at the same time.
Here is another Paper that explains the accuracy error 'SDOP':http://webcache.googleusercontent.com/search?q=cache:uX0--iNZczAJ:bioresonant.com/dl/dl.htm%3Fname%3DSDOP.pdf+&cd=1&hl=en&ct=clnk&gl=au&client=safari
We could modify carousel experiment with long line, hobby model or airplane doing rounds with constant speed.I am interested in variances in speeds shown by our gps and the path it show.I am convinced that our GPS's are very accurate, but interesting will be to know how often that system introduce errors such nicely camouflaged that are not later detected and removed by software.
Eventually the system may be 99.99 accurate but during 4 hours session those remaining % may introduce extraordinary results.
So lets hang our GPS one day on electric motor with rotating long line for 4 hours and see what variation in results our GPS come with.
BTW .I strongly suspect that result with proposing stationery GPS as opposing to my traveling on constant radius say 20 m, may come with different accuracy numbers.
This is hidden in the definition of Doppler effect itself and if we think about 5 traveling at speed satellites then our GPS also traveling at different direction 40 knots linear speed . The computation errors may multiply.
BTW we are talking here about cheap $100 technology for everyday user but apparently SpaceX have similar problems with accuracy when landing their space rockets on floating on the ocean barge. No need to mention that their budget, expertise and experience is much better .
Select to expand quoteMacroscien said..]
Eventually the system may be 99.99 accurate but during 4 hours session those remaining % may introduce extraordinary results.
The sources of error in GPS technology are both well known and well resolved.
The mathematics to model and resolve all the variables of satellite movement for Doppler speed calculations are very well developed.Select to expand quoteMacroscien said..]
BTW we are talking here about cheap $100 technology.........
The cheap devices we use today have computing power vastly superior to those used to put the first men on the moon. It is the miniaturisation of computing power that allows the stupendous level of mathematical computations to take place in this tiny device. The mathematics are incredibly complex but also very mature. We are now seeing $200 RTK chips that can outperform the $100,000 survey grade GPS of 15 years ago. Perhaps the greatest source of error is now related to the tiny size of some antenna and the resulting limitations rather than the GPS engine itself. And them of course there is the big one: The human user introducing all sorts of sub optimal situations to try to hobble it. 
I think that our cheap access to precise GPS technology is byproduct of military.
Smart bomb mean simply GPS with grid fins.
With future development of smart bombs we may expect another improvement coming back to us.
This days smart bomb pointing directly to the target is easy to neutralize with laser or other ballistic.
But if we add this straight line to target less of more regular or random my carousel movement this same bomb or missile will be incredible difficult to intercept.
This way a bomb flying down do also horizontal circles less or more irregular this the very last moment.But if our smart bomb is using the same Doppler technology, this additional movement will add next level of difficulties for calculations and errors..
Select to expand quotesailquik said..
The cheap devices we use today have computing power vastly superior to those used to put the first men on the moon. It is the miniaturisation of computing power that allows the stupendous level of mathematical computations to take place in this tiny device. The mathematics are incredibly complex but also very mature. We are now seeing $200 RTK chips that can outperform the $100,000 survey grade GPS of 15 years ago. Perhaps the greatest source of error is now related to the tiny size of some antenna and the resulting limitations rather than the GPS engine itself. And them of course there is the big one: The human user introducing all sorts of sub optimal situations to try to hobble it.
I am not tracking GPS technology enough to even know where nowadays lay physical border for ultimate GPS precision and what could be theoretical limits in the future.
But I imagine that will be very useful if our everyday smart phone will have GPS with precision in mm rather then meters.
We could use then our Smart phone as a ruler : Mark one position and move 20 cm to read that exact distance on the screen ( calculated automatically by GPS coordinate system) . If we want to measure anything we could use our phone then.
Lets imagine that we will have soon GPS satellite network 150 km above instead of 20,000 km ( now ?) . How it may improve accuracy ?Next possible limitation is precision of the clock, Existing 14ns limit may soon be replaced with optical clocks 10-17 s
Select to expand quoteMacroscien said..
I think that our cheap access to precise GPS technology is byproduct of military.
Smart bomb mean simply GPS with grid fins.
With future development of smart bombs we may expect another improvement coming back to us.
This days smart bomb pointing directly to the target is easy to neutralize with laser or other ballistic.
But if we add this straight line to target less of more regular or random my carousel movement this same bomb or missile will be incredible difficult to intercept.
This way a bomb flying down do also horizontal circles less or more irregular this the very last moment.But if our smart bomb is using the same Doppler technology, this additional movement will add next level of difficulties for calculations and errors..
You cannot instantaneously change direction of flight, as conservation of momentum will be against you. ie: if you can track a missile/bomb at all, you can also track its movements with far faster precision that a flying mass will be able to change trajectory.
Smart bombs of the 90's weren't only GPS with fins - they had inertial navigation... they also didn't use GPS as the primary source of location tracking, as GPS is subject to jamming/interference. Bombs arn't that difficult to intercept, except when they implement active-avoidance of countermeasures -> in the modern era, I would argue that if a Smart bomb cannot avoid a $3 laser, it isn't really all that smart.
Select to expand quoteMacroscien said..
I think that our cheap access to precise GPS technology is byproduct of military.
Smart bomb mean simply GPS with grid fins.
With future development of smart bombs we may expect another improvement coming back to us.
This days smart bomb pointing directly to the target is easy to neutralize with laser or other ballistic.
But if we add this straight line to target less of more regular or random my carousel movement this same bomb or missile will be incredible difficult to intercept.
This way a bomb flying down do also horizontal circles less or more irregular this the very last moment.But if our smart bomb is using the same Doppler technology, this additional movement will add next level of difficulties for calculations and errors..
Geeze Macro. Dunno what you are drinking, but I want some if it!
And remind me never to start a war with you!! 
Yes, GPS was primarily a product of military development. But is have now become vital to the modern technological civilian society and a lot of development is now driven by consumer applications.
Select to expand quotesailquik said..
But is have now become vital to the modern technological civilian society and a lot of development is now driven by consumer applications.
You are absolutely right and even now we could almost track every person on this planet all movements thanks to smart phones.That is dream for any government comes trough.
But going back to our windsurfing what is the ultimate accuracy required ?
Something like 39.9974 knots looks for me a bit absurd , even if technically possible...
Give the Guy 40, deserve it...
Ahh, that is an easy question.
There is no point going past 100th of a knot as it is a meaningless small amount for all practical purposes. eg. 40.05 Kt
The quest is to know that that figure is correct every time to within a couple of hundredths of a knot for a 10 second run. e.g.. 40.05 (+/- 0.02) That really can be called a 40!!
We can get very close to that now with the newest 18Hz Ublox GPS chips in the right configuration:
eg. 
The point is we need to have accuracy that is verifiable and reliable.
Select to expand quotesailquik said..
Ahh, that is an easy question.
There is no point going past 100th of a knot as it is a meaningless small amount for all practical purposes. eg. 40.05 Kt
The quest is to know that that figure is correct every time to within a couple of hundredths of a knot for a 10 second run. e.g.. 40.05 (+/- 0.02) That really can be called a 40!!
We can get very close to that now with the newest 18Hz Ublox GPS chips in the right configuration:
eg.
The point is we need to have accuracy that is verifiable and reliable.
No wind Daffy..
Select to expand quoteMacroscien said..sailquik said..
But is have now become vital to the modern technological civilian society and a lot of development is now driven by consumer applications.
You are absolutely right and even now we could almost track every person on this planet all movements thanks to smart phones.That is dream for any government comes trough.
But going back to our windsurfing what is the ultimate accuracy required ?
Something like 39.9974 knots looks for me a bit absurd , even if technically possible...
Give the Guy 40, deserve it...
+1
Select to expand quotesailquik said..
Also, you can get the same accuracy spread test figures if you use geo stationary testing and this eliminates multiple sources of errors, which is what the Authors of both articles did.
.. as long as you keep in mind that the authors studied the GT-11 and GT-31. As you point out, newer devices benefit from a lot more computing power in the chips. So they may well apply specific filters only in situations where the speed is near zero. I have seen this with several GPS devices - the first time when I tried to use a car GPS for navigating when walking. Some GPS chips (which we usually do not use in speedsurfing) also have different modes, which adjust the filters depending on the expected speeds.
Therefore, stationary results with new GPS chips and devices should be verified by measurement while moving. We usually do this by comparing tracks to known GPS units (although that creates the problem of sometimes not knowing who is to blame when the results differ). Macroscien's ideas definitely have some merit. The question is how we can get very constant movement, while eliminating potential error sources like changes in reception. Maybe a train with a clear roof or a large ship in calm waters would work. It would be interesting to see, for example, how much of the 5 Hz ripple in the GW-52 data remains.
It's great to have the relevant publications listed here, and to look at them again. For example, Tom Chalko writes:
"Clearly, at least some of these GPS-Doppler speed error components are common for N
<div>consecutive speed errors vke so, strictly speaking, speed errors vke in such sequences may not be statistically independent."
<div>But later when he calculates 99.9% probabilities, he ignores this, and uses math that requires the errors to be statistically independent. As we go to higher data rates, this is important to keep in mind, since errors are more likely to be linked when sampled at a higher rate.
Good point about geostationary testing. The Ublox chips I have been looking at have all sorts of setting in them that device manufacturers can implement. Among them is the ability to stop reporting when the Unit finds itself stationary. All the chip makers would have a version of this and I too have seen it in some implementations.
There is a revised version of Tom's SDOP document which includes and appendix showing the GPS settings in the GT-31 here:
bioresonant.com/dl/dl.htm?name=SDOP.pdf
It is a pity we don't have the same data for the GW-52 implementation.
But I am sure the GW-51 is deliberately set up to continue reporting it's Doppler speed when Geostationary specifically to facilitate geostationary testing.
Interestingly, when I did Geostationary testing with two side by side GW-52's yesterday, the reported speeds were well over 99.9% under 0.019kt. (0.019kt is the resolution of the device records). There were only a handful of values above that and they were mostly during setup and fix and when I picked it up to turn them off. After I deleted the beginning and the end of the 2 hr test, the remaining points above 0.019 numbered less than a dozen, and almost 3/4 of the values were 0.000
I was trying to test an idea that we might be able to do a type of differential post processing to further correct for Doppler errors, but side by side testing produced Doppler speed results that did not exactly match 100% of the time. My conclusion is that my idea will not be valid for post processing. It would be useful to double check on the water validity in a general way and I will do some testing for this as well, although I suspect I may go for many sessions before I see a situation where errors of the magnitude I am looking for may occur!
