# Trilateration with error account or lack of precision

I am developing a node.js/javascript application where I would have dozens of beacons in a row (positions known), which gives me their distances to specific object (3 or 4 distances per object). The idea is to trilaterate those distances to infer the coordinates of this object.

I have technical background but I am not an expert in geometry nor cartography. I have check a lot of articles about trilateration. Most interesting:

With the distances involved (hundreds of meters), instead of 3D problem, I can simplify to 2D problem, but I am not sure which would be best approach to tackle it. I would need a fast algorithm, since I can have around 12 different position calculations (different objects) every second.

I have different ideas:

1. Using wikipedia's article is the easiest way. I have a pair of javascript libraries that perform this algorithm (cannot put links due to constraints in stackexchange). Problem: does not take into account error in measurements, so many times equation does not give you a solution (approximate value would be enough...)
2. Using Mathematica: cannot do that. Is there any other C++ or javascript/nodejs library that performs those calculations?
3. Using postgis: I think I can create a circular stripe (donut) per beacon distance, using ST_BuildArea. Then intersect those areas and calculate the centroid. Do you think this would be a proper approach using geometry - not geography-? Fast enough for 12 positions/second?
• Hi, what is your thoughts on this question 3 years after? Have you found robust algorithm for your application? – evilive Nov 4 '18 at 8:47