boardsurfr said.. mathew said..
Thus GNSS calculation producing Doppler-speed, also produces the error estimate. ie: implying it has units (m/s, knots, etc) as the speed-value.
xDOP... aka the TDOP, PDOP, GDOP, VDOP, HDOP, etc... are all unit less.
Certainly true for HDOP etc., but not for SDOP.
You left off the previous two paragraphs which say exactly that - are you restating the same thing as a confirmation ?
boardsurfr said..
Two questionable conclusions. A statement by the chip companies what they are trying to give us in the accuracy estimates would be a very good start, but I don't think we'll get that. But we can go and characterize the data that we are getting. That's not really easy, but can be done. Tom Chalko's original work indicated that the error estimates that Sirf chips give are higher than one or two standard deviations; in 81,493 data points, he did not find a single point were SDOP underestimated the actual error. If SDOP was 2 standard deviations, we'd expect about 2,000 points where SDOP is too low, so this points towards SDOP being > 4 SDs (a bit simplified). I have looked into this just a little bit, but my first impression for ublox data was that the ublox speed accuracy estimate is closer to 1 SD or 2 SD. If that is indeed the case, then the numbers are not the same.
Tom's analysis - and thus the Sirf error-values - *are* 4 SD.... the analysis targeted > 99 percentile, so that we could be extremely confident of the error-bounds. Your work here, supports the work Tom and Manfred have done previously regarding the GT-31.
The thread-context was whether the error-value of a given instantaneous speed measurement, is comparative between EHVE and SDOP -> the 2 or 4 SD is irrelevant in that context.... what matters is that the error-value has a scalar-velocity-unit (m/s,knots,kph,etc - ignoring transposing from one to another).
The 2|4 SD difference matters when we try use it to determine accuracy of the specific speed data-point. ie: if we chart all the data, these 2|4 SD's are just error-bars on each value.
... and that is why the GPS-windsurfing community came up with idea of "claimed speed"... that way any GPS hardware irrespective of its age/quality/etc can be used, *provided the hardware can supply an error-value* -> we subtract the worst-case error and thus claim at least that minimum speed.
... thus they *are* the same [ and so allowing for claimed-speed for measuring records ]. To use some other technique, such as blinding trusting the value printed on the screen (....say by using a GPS device which hasn't had this rigour applied) is disingenuous to your friends whom have made the effort to sail fast and claim their speed.
boardsurfr said..
But this analysis is a bit to simplistic. Tom's analysis of stationary (or, more accurately, constant speed) data did not take into account errors that can arise from speed changes at frequencies above the sampling rate (more or less - theory will add a factor of 2 here). Such changes could introduce "aliasing" errors, which is a reason why GPSResults does not use Gaussian error propagation for 1 Hz data (which are presumed to be GT31 data). To what extend that is still justified for 1 Hz GW-52 data is a different question. I am waiting for a few more GW-52s and ublox8 toys to look into this a bit more. Even if we did have a full specification of what SDOP and "Speed accuracy estimate" are supposed to be, and even if we did have the entire firmware source code and could understand it, we'd still need to do an empirical validation to see if the data we get are indeed what they are supposed to be.
Tom and Manfred's info specifically describe aliasing - all digital hardware has aliasing... it is an artefact of digital technology [ Gaussian distribution has absolutely nothing to do with digital sampling - one is a function of how your real-world data varies over time, the other is how fast you run your sampling hardware. ]
This is why the GPS-windsurfing community want high-Hz sampling -> so that we can better understand what is really happening sub-second. [ It just so happens analysis like yours, is driving the windsurfing community well ahead of other sports. ]
Gaussian was chosen, because after best-fitting various algorithms over *lots* of data and errors, the distribution of looks Gaussian. The first suggestion was a Sinc function due to its use in Fourier analysis.
