With all the recent discussion regarding GPS accuracy, I have had a bit of a closer look at what Real Speed actually shows when looking at SBN files from the GW60.

I have a few questions
What are the units of HDOP?
What are the units of SDOP?
I assume the Doppler error is in knots, but what exactly does this mean? If my speed is say 30kt and my doppler error is 0.3, What is the level of certainty that the true speed was between 29.7 and 30.3?

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tbwonder said..
With all the recent discussion regarding GPS accuracy, I have had a bit of a closer look at what Real Speed actually shows when looking at SBN files from the GW60.

I have a few questions
What are the units of HDOP?
What are the units of SDOP?
I assume the Doppler error is in knots, but what exactly does this mean? If my speed is say 30kt and my doppler error is 0.3, What is the level of certainty that the true speed was between 29.7 and 30.3?

HDOPis unit-less (check en.wikipedia.org/wiki/Dilution_of_precision(navigation)). It's a bit an antiquated measure that rarely, if ever, plays a role when windsurfing.

Short answer for SDoP: in knots if speed is in knots, certainty somewhere around 95% (probably 90-99% for typical windsurfing data).

Long answer for SDoP:
SDOP is a poorly chosen name, since it's completely different from HDOP - it's an error estimate for the speed, so the units are the same as the units used for the speed. The one other GPS chip manufacturer (u-blox) that includes speed error estimates used the term "sAcc", speed accuracy. I have never seen a definition of what probability level SDoP or sAcc refer to. Tom Chalko did some stationary tests, but there are a few questions to how this applies to non-zero speeds, especially for GW-52s and GW-60s.

Empirically, the certainly for the range as you describe it (+- error estimate) seems to be somewhere around 95%, give or take a few percent, for single points. That is for low SDoP/sAcc averages (averages less than 1.5). The error distribution does not appear to be even close to a normal distribution for higher error values, there are way more outliers than expected. For the categories (2 sec etc.), GPSResults uses "Gaussian error propagation" by default for 5 Hz+ data, and calculates 2-sigma values. That seems appropriate given the the observed error distribution, and should result in 95% confidence if both average and max SDoP/sAcc values are reasonably low. Note that GPSResults only filters single points, so regions with higher error averages can slip through (see boardsurfr.blogspot.com/2017/06/ducks-fly-fast.html for an example).

There's a difference between the way Realspeed and GPSResults show the accuracy numbers.
I'll give a 2s example from one of my files last month.
GPSResults gives the +/- numbers, (0.301kts), and the mSDoP numbers (0.583)

Real speed has SDOP Max (0.583) and doppler error (.47)

So it looks like realspeeds SDOP MAX is the same as GPSResults's mSDoP. what realspeed's doppler error is I have no idea

In Real Speed often the SDOP Max and Doppler error are the same, but not always.

What about GPSActionReplay, I have just installed the trial version, but I don't see any way of viewing the error data? Is it there somewhere?

So in order to see the accuracy of the tracks I am posting to GPSTC which number from which analysis program should I be using?

GPSAction Replay only shows the SDOP numbers in the "Trackpoints Table". Click on the "Tracks toolbox" button in the button row on the top, then click on the "Trackpoints Table" button at the bottom of the "Tracks Panel" window. SDoP is shown as "+/-" column.

However, GPSAR does not try to calculate the error for 2 second runs etc., like GPSResults does.

Correction: GPSActionReplay also has a graph for the SDOP data, which can be useful. To see it, move the mouse to a window with data, click on the "Change View" button (visible only if the mouse is in the window!), and select "Sdop-graph".

While we're talking about GPSAR Pro, and decrepit is reading: last time I checked, GPSAR did not read accuracy data from .ubx files correctly, so this won't work for u-blox prototypes.

Thanks boardsurfr, I have just studied my 2 sec PB track in GPSAR in the track points table I can see the SDOP numbers shown in the (+/-) columun. When I view the sdop graph it is possible to highlight the 10 track points of my 2 sec peak and it then shows the average SDOP over the 2 secs as 0.49.

RealSpeed shows a SDOP max of 0.622 this is the highest error recorded over the 10 points which correlates exactly with the high one in GPSAR track points list. It looks as if the "Doppler Error" Shown in Realspeed is actually the average sDOP as this value is 0.49.

If looking at GT31 data in Realspeed the SDOPmax and Doppler error are often the same as only two points are being averaged.

So my understanding now is that the accuracy of a track can be judged by:
HDOPmax - around 1 or less, which relates to number of Satelites : 7 ok, 8 or more good
SDOP Average from GPSAR (which is the same as Doppler Error from Real speed) - should be as low as possible (Typical appears to be 0.3 to 0.6 kts)
Or is the SDOPmax more important?

Next question how does the software that calculates 2 sec peak speeds use this data? Does it exclude track points that are outside certain parameters?


If anyone is interested my 2sec PB is on KA72, 14-Jan-18

Great to see someone interested in their accuracy! I think the +\- numbers give the accuracy for any result, so that would be the average rather than the maximum. Peter I stick with gpsresults whenlooking at .ubx files, but I'll keep that in mind if I'm tempted to try something else

Decrepit, which program are you referring to?
The +/- column in GPSAR are given for each recorded point, The average is visible when you select multiple points

You lost me at Hello ??????

sorry TB I haven't used gpsarpro for a while, it runs a bit slow on this machine. GPSResults, shows the +/- for each result along with mSDoP, which I guess is the maximum error.

I'll try GPSARPro, and see if I can match up the numbers with GPSResults, (Peter I'll use an .SBP file not .UBX)

No that's a real pain, I still haven't managed to get an average, but the max looks the same

The 'SDOP' average for mutiple points from 5Hz units is a 'least squares'* average. (GPS-Results only take the straight 'average' error for 1Hz data.)

*As I understand it, the more points you have, the lower the average error as high and low error tend to cancel each other out.

Boardsurfr argues this is not exact as there are other sources of potential error, and I agree to some extent, but for our intents and purposes, it is close enough.

Here is a comparison of a GW-60 and GW-52 from the same session. Note that the error is higher with the watch worn on the wrist and this is due to a smaller antenna and less ideal view of the sky, especially when sailing with under grip on altenate tacks. The GW-52 was worn on the head and has a larger antenna and better, more consistent 'view' of the satellites.

The +/- refers to each result. i.e 30 knots, +/- 0.100 would mean that the speed is 99% probability to be within the range 29.9 to 30.1 knots.

In practice, the actual error difference I see when comparing exactly the same GPS types (GW-52 with GW-52 or GT-31 with GT-31) side by side is pretty much always well within the possible error range reported. (For 10 data points or more).

When comparing different models with the GW-60, it is sometimes slightly outside the smallest number, as seen here in some results.
You will also notice that some results are in a different rank order between devices when they are very close and within the error margin, as is to be expected.
Also note that the 5 X 10 results are within 0.03 knots, which is a big reason why this category is considered a really good competition comparison.
Note also that the single 2 second results error could be are up to almost 0.4 kts, and the actual difference between the two GPS is almost .19 knots. This illustrates why the 2 second is considered a less reliablely accurate result. (The max and 1 second are even worse).

(results from GPS-Results)



As far as RealSpeed goes, I think from memory the Doppler Error figure is the average for the points selected in the division, but I would have to check with Mal, or do some calculations to be certain.

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sailquik said..
The 'SDOP' average for mutiple points from 5Hz units is a 'least squares'* average. (GPS-Results only take the straight 'average' error for 1Hz data.)

*As I understand it, the more points you have, the lower the average error as high and low error tend to cancel each other out.

Boardsurfr argues this is not exact as there are other sources of potential error, and I agree to some extent, but for our intents and purposes, it is close enough.

Here is a comparison of a GW-60 and GW-52 from the same session. Note that the error is higher with the watch worn on the wrist and this is due to a smaller antenna and less ideal view of the sky, especially when sailing with under grip on altenate tacks. The GW-52 was worn on the head and has a larger antenna and better, more consistent 'view' of the satellites.

The +/- refers to each result. i.e 30 knots, +/- 0.100 would mean that the speed is 99% probability to be within the range 29.9 to 30.1 knots.

In practice, the actual error difference I see when comparing exactly the same GPS types (GW-52 with GW-52 or GT-31 with GT-31) side by side is pretty much always well within the possible error range reported. (For 10 data points or more).

When comparing different models with the GW-60, it is sometimes slightly outside the smallest number, as seen here in some results.
You will also notice that some results are in a different rank order between devices when they are very close and within the error margin, as is to be expected.
Also note that the 5 X 10 results are within 0.03 knots, which is a big reason why this category is considered a really good competition comparison.
Note also that the single 2 second results error could be are up to almost 0.4 kts, and the actual difference between the two GPS is almost .19 knots. This illustrates why the 2 second is considered a less reliablely accurate result. (The max and 1 second are even worse).

(results from GPS-Results)



As far as RealSpeed goes, I think from memory the Doppler Error figure is the average for the points selected in the division, but I would have to check with Mal, or do some calculations to be certain.

So as there is no documented way to check data in GPSTC what SDOP error is acceptable to post numbers?
Is there a minimum number of Satellites that are required???

The min number of satellites and Doppler speed error figures are easly seen in the properties and settings windows of the various stand alone speed analysis programs. KA72 uses the same figures as I understand it.
In the case of min satellites it is 5. (A minimum of 4 sats is required to actually get a 'valid' positional fix)
The max Doppler speed error figure can vary depending on the Hz of the data. It is lower in 1Hz data (around 0.8) and higher in 5hz and 10Hz data (up to 3) to account to higher individual point error in higher Hz devices and whether the filter is done just on individual points or on an average over a number of points.

There was seen to be no need to document this specifically on the GPS-TC website as the figures are set by default in the various analysis programs and the authours of all those programs have cooperated, and if the SDOP limits are exceeded, the analysis program will flag the results as invalid. i.e. it wont appear in the results list.