[Talk-GB] accurate GPS

Simon Ritchie simonritchie.uk at gmail.com
Wed Oct 9 10:05:36 UTC 2019


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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