# How does the radius work in Trilateration

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
• 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? Aug 11 '14 at 2:50
• 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. 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. Jul 22 '14 at 23:02
• 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
• 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) Jul 23 '14 at 0:19