I've got a little further with my research.

My GPS equipment claims to be accurate to two cm. I've now figured out that the data I'm getting from the OS is not nearly as accurate as that, so I can't use it for my testing. That's a tad unfortunate because at present I have nothing else.

Just to answer one question in this thread: why don't I just get my equipment to display OS map references? Firstly, it doesn't, and secondly, if it did, that could be a source of significant error, as shown below.

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, not internally at least. 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. the conversion introduces an extra error, so the result will be even more wrong. As pointed out in another posting, if the extra error is small, it gets lost in the noise. However, errors are additive, so if it's big enough, then yes it does matter.

GPS equipment is improving, which is why I'm doing this work, so in the future you will be able to buy a much more accurate tracker, but if you ask it to display results as OS map references, the conversion may introduce so much error that the extra quality is compromised. To get the most accurate fix you will need to use longitude and latitude or Cartesian coordinates.

Getting back to my investigations: the Trigpointing website gives the map ref of each trig point, which I believe comes from a spreadsheet that the OS publish. They also offer a web page that can convert a map ref to other forms including Cartesian coordinates: 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 that?

This OS document was very enlightening: https://www.ordnancesurvey.co.uk/legacy/docs/gps/updated-transformations-uk-ireland-geoid-model.pdf. It explains how GPS 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 it can 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 them 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 by Pythagoras the distance between them is

the square root of (a squared plus b squared plus c squared)

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. The error introduced by the conversion is much bigger than the error in the original map reference of the trig point.

If you have a GPS tracker and it uses a similar method to convert from its internal format to an OS map reference, the result will not be three metres out, it will be as much as five metres out.

As for my own purposes, 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.

Here are the tables of results. Note that these are purely from OS data and the OS conversion page, not from my equipment:

- Code: Select all
` 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