Global Positioning - Point Return Error

conZ

Afraid this isin't about Sat Nav's or Geo cacheing, this is actually about the Global Positioning System and the level of accuracy.

This was put to me recently, but I can't remember the exact calcs, only the general idea which was put to me as the "point return error".

For instance...
I am required to map Point A to 1m accuracy (red dot in image below).
I go along and map Point A using a GPS device (X and Y only).

Someone else then comes along and maps Point A using a similar device, but has a different coordinate, and argues that my point A is incorrect.

As my point is to 1m accuracy, any point within that 1m radius of point A can be chosen as my point. Therefore, if point A is exactly at the edge of the 1m radius, and it is to 1m accuracy, I now have a situation where I have 2m radius accuracy from my original position (see attachment).

Therefore, if I choose my point to be at the edge of the 2m radius, I can put my point 4m from my original point.

You can go on and on with this, but when it comes down too it, my point could be 100m away from the other guys reading, but I would still be correct.


Can anyone clarify this or am I in the wrong forum altogether?

eirlink

"if point A is exactly at the edge of the 1m radius"

point A is NOT at the edge of this 1m radius...its in the middle AND it never moves. Only thing that moves is YOU / your friend with the other device...

this example is all based on "if's" and moving points.

conZ

But if your point can be accurate to 1m, technically it can be anywhere within that 1m circle in relation to the point (we'll say a TBM) when checked.

Therefore, if you take any point within that circle, and set it as (0,0), and that has an accuracy to 1m, you now have a second circle with a 1m radius, and potential to have the point anywhere within this ~5m2 area.

So if someone comes along to map this TBM, and finds that you're coordinates are inaccurate, you can argue that based on this point return error, I can technically have my coordinates a fair distance from the TBM and I'd be correct.

This has been proven, i'm just trying to get it correct in my head.
Gotta run.

coylemj

conZ wrote: »

Therefore, if point A is exactly at the edge of the 1m radius, and it is to 1m accuracy, I now have a situation where I have 2m radius accuracy from my original position (see attachment).

If point A is exactly at the edge of the 1m then that's where it is, it cannot have a '1m accuracy', it's at that point exactly so the original proposition is correct i.e. the exact position is within 1m metre of the original fix.

You can't say that it's exactly at a given position to 1m accuracy, it's either exact or it isn't.

robinph

coylemj wrote: »

You can't say that it's exactly at a given position to 1m accuracy, it's either exact or it isn't.

Yep, if the actual real point is not within that first 1m radius area then the initial claim of it being to 1m accuracy is bogus.

If someone else then comes along and obtains a different location, but also to 1m accuracy, then that is really now narrowing down where the real point that you are trying to locate is. In your second diagram the real point can only be within the area covered by both your 1m accuracy circle and the second persons 1m accuracy circle.

Venn diagrams or something I thing they were called back in maths class, that was a long time ago though so I could be thinking of something different.

conZ

Ok... Unconvincing.

I'll be meeting him again within the next week, and i'll get it down properly, and post here again...

robinph

Independently each point that you've found to 1m accuracy could contain the real point anywhere within each radius. When the two are taken together though you are increasing the overall chances of locating the real point as it still has to be within the 1m range from each point you've mapped, so can then only be within the area covered by where each of those radius lines overlap.

The third image in your diagram could not happen, it would be perfectly possibly for another survey point to be taken though that was not centered around a point within either of your first two circles as long as some part of it overlaps with the already overlapping radius of the two already taken.

http://upload.wikimedia.org/wikipedia/commons/7/7a/Venn_diagram_cmyk.svg*
In this image, stolen from the one on Wikipedia due to my crappy drawing skilz, the center point of circle C is not going to be within the 1m range of either of circles A or B. The area in which they overlap though is where the real point that you are trying to locate must be though.

* Wikipedia doesn't seem to allow inlining of their image files by the looks of it, so you'll have to click the link.