I've been trying to understand the trilateration algorithm based on the wikipedia article. As of now, I have a system where I have the distance of 3 sensors wrt my position and i have the exact GPS coordinates of those 3 points.

How do I include the radius?

  • I am trying to conceptually understand what the radius does – raaj Jul 22 '14 at 22:08
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    Based on your latest question on the same issue -- gis.stackexchange.com/questions/110051/… -- you appear possibly to confuse geographic (lat, lon) and projected (N, E) coords. Are you at least clear on those? – Martin F Aug 11 '14 at 2:50
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    If the answer below (including the linked answers) doesn't answer your question, please edit your question to include much more detail on what you understand and don't understand. – Martin F Aug 11 '14 at 2:59

The distance from sensor to target is the radius. That radius defines a sphere around the sensor. The point where three spheres from three sensors intersect is the 3D position of the target.

A somewhat better (less mathematical, more conceptual) explanation of trilateration is at this web page. Some useful GIS.SE questions that also cover the basics and provide additional details:

  • How do i get the sphere for my sensor? I mean, it's just a beacon that I know it's exact 2d coordinates and i know the distance to the beacon via RSSI – raaj Jul 22 '14 at 23:00
  • The distance to the beacon is the radius of the sphere. – Erica Jul 22 '14 at 23:02
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    I was wondering also. I see many explanation on this being done for 3 points. Are there any example on say N number of points? I only saw a matlab example, but I want actual mathematical equations if possible. – raaj Jul 22 '14 at 23:20
  • I can't seem to find any examples. How does this actually work, do i like try all combinations but with trilateration and get an average? Say like Points 1,2,3,4 i do a trilat on 1,2,3..1,3,4..2,1,3..etc. then i get an average? – raaj Jul 22 '14 at 23:26
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    With n > 3 points, it's called multilateration. I believe a least squares approach is most common, but the precise math is getting beyond my knowledge (and the last link above will lead to some good in-depth discussions) – Erica Jul 23 '14 at 0:19

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