[Talk-GB] accurate GPS

Russ Garrett russ at garrett.co.uk
Wed Oct 9 10:47:47 UTC 2019

You are entering an extremely deep rabbit hole here and there are
hundreds of extremely nerdy aspects you have to consider when aiming
for sub-metre precision.

As you correctly point out, the position of trig points is no longer
accurate nor canonical. Errors of half a metre sound absolutely
plausible, as the OS coordinate system has undergone significant
revision since trig points were phased out. You're not going to find a
(publically-accessible) physical location which has better location
error than 1m or so.

I suspect (I may be wrong) that the "conversion errors" you're see are
likely artefacts of the geoid difference between the ETRS and OSGB
coordinate systems. ETRS covers a wider area than OSGB so the OSGB
numbers are likely to be more accurate (even if you've converted them
from ETRS numbers output by your GPS). Different coordinate systems
serve different purposes so this is absolutely normal.

Once you start trying to map things to sub-50cm precision over 10+km
baselines you enter a world where OSGB is not accurate enough either.
You then need to expend a tremendous amount of effort establishing a
custom coordinate system - this is what Crossrail had to do across the
entire London area to provide enough precision for tunnelling

tl;dr: All maps are wrong.


On Wed, 9 Oct 2019 at 11:06, Simon Ritchie <simonritchie.uk at gmail.com> wrote:
> I've been working with some GPS equipment that claims to be accurate to 2cm.  To test it, I've been visiting local OS trig points, taking position measurements and checking if they are correct.
> Unfortunately I've discovered that the data I'm getting from the OS is not nearly as accurate as my equipment claims to be, which is wrecking my testing.
> We tend to assume (well, I do anyway) that OS trig points are very accurate position markers, but compared with modern equipment, that's no longer so.  I thought people might be interested in knowing how accurate they are.
> A related issue is this:  GPS devices don't work in terms of OS map references.  If your tracker device gives you a position in that form, it's done a conversion.  How accurate is that?
> The GPS device in a typical tracker is accurate to maybe three metres, so the position you see on the screen will always be a bit wrong.  If you get it to display your position in OS map reference form, it will need to do a conversion, which introduces an extra error, so the result will be even more wrong.  Not good if you are trying to produce an accurate map.
> The OS published a spreadsheet giving the positions of their trig points in OS map references.  This is available from them as a spreadsheet and Ian Harris has used that data to create the web site:http://trigpointing.uk
> The OS also offer a web page that can convert this to other forms including Cartesian, which is one of the forms that my GPS device gives me:  https://www.ordnancesurvey.co.uk/gps/transformation/
> To test my equipment, I take the OS map ref of a trig point, convert it to Cartesian form,  visit the trig point, get the position in Cartesian form from my device and compare the two.
> The results are typically out by at least half a metre.  Is my equipment faulty, or is the OS data wrong.  How accurate is the published position of the trig point and, when I use the OS web page to convert that to Cartesian form, how accurate is thatt?
> This OS document was very enlightening:  https://www.ordnancesurvey.co.uk/legacy/docs/gps/updated-transformations-uk-ireland-geoid-model.pdf
> It explains how the Cartesian coordinates work, which is useful.  It reminds me that OS maps pretend that the Earth is flat, which introduces an error, but that's tiny, and for my purposes itcan be ignored.  It explains how accurate you can expect the published measurements of trig point positions to be - they can be out by as much as 60 cm!  In general, the document stresses that there is no sure-fire way to convert a position from one system to another.  The result will always be inaccurate.
> So now I know that the published positions of the trig points are a bit wrong, but how accurate is the conversion from OS map ref to Cartesian form?
> OS map references plus height above sea level and Cartesian coordinates both specify a position using a 3D coordinate system.  The origin and the direction of the axes are different in each system so you can't compare thm directly.  However, the distances between two points should be the same regardless of which system you use.  If you have two points in the same coordinate system (a1,b1,c1) and (a2,b2,c2) and the difference along each axis is a,b and c then the distance between them is
>     the square root of (a squared plus b squared plus c squared) by Pythagoras
> If you have two points in a different coordinate system representing the same two positions, the distance between them should be the same.
> So I can test the accuracy of the conversion from OS map references to Cartesian.  In the table below, on the left, we have the trig points at Box Hill and Leith Hill in OS map reference form, the difference along each axis and below that the resulting distance.  On the right we have the same calculation but using the Cartesian coordinates from the OS conversion page.
> Below that I do the same comparison, this time using the trig point at Mickleham Down and the one at Leith Hill.
> In both cases, the distances are out by over two metres.
> So, I'm trying to test equipment which is supposed to be accurate to two cm using data that is out by at least two metres.  That's not going to work.  I need something more accurate to compare my results with.
>                          OS Map Ref                                                          Cartesian
>                 Box Hill Leith Hill   Difference       Box Hill  Leith Hill Difference
> easting        517971.06  513949.28      4021.78   x 4000676.63  4006902.33   -6225.70
> northing       151163.16  143161.71      8001.45   y  -21724.35   -25963.72    4239.37
> height above      171.97     307.00      -135.03   z 4950992.32  4946141.89    4850.43
> sea level
> distance                    8956.35                                 8958.70
>                 Mickleham  Leith  Hill  Difference    Mickleham  Leith  Hill Difference
> easting         517891.74    513949.28     3942.46  x 3998820.07  4006902.33   -8082.26
> northing        153518.13    143161.71    10356.42  y  -21739.43   -25963.72    4224.29
> height above       142.73  307.00  -164.27          z 4952444.39  4946141.89    6302.49
> sea  level
> distance                     11082.66                               11085.53
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Russ Garrett
russ at garrett.co.uk

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