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I am trying to estimate the relative positions of many points based on the distances between them, but no known points. This is for a project where I have 5-10 or more devices which are using ultrawideband to communicate and measure the distances between themselves.

I know about triangulation but that requires a set of three or more stationary known points. For my project we would know the distance between our point and every other point, as well at the distance between every other point and all the points which surround it. Theoretically the only point we would know the location of would be ourselves as we would be at 0,0.

Is there any way to get an estimation or even an exact location of some or all of the points with this information?

I have looked around and I can't even find where to start with this so I was hoping someone could point me in the right direction.

sss89
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Spencer Brennessel
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If you have a set of $n = 5$ to $10$ points in the plane and you know the distances between each pair then the (abstract) graph formed by those points and the edges between them is a rigid structure in the plane (except in very unusual circumstances). That means the structure is determined up to rotations and translations. So if you know one point (yourself, at the origin) and one direction from that point to another then you know all the locations (perhaps up to a reflection).

All the pairwise distances is much more information than you need. That would be $n(n-1)/2$ numbers to find the $2(n-1)$ unknown coordinates.

Try searching for "rigid graph".

Ethan Bolker
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