Finding an Unknown Location with known distances from location Lets say that I have a map and an unknown location. If I have multiple locations in which I know the distance away from the unknown location, can I pinpoint the unknown location?
I am aware of Triangulation, but am looking for something that can be used if the distances from the unknown location are not very precise (i.e only a few decimal digits). Would it be possible to increase the accuracy of the determined unknown location by knowing the distances from the unknown location of many locations?
 A: Absolutely. If you were able to determine the precise distance between the unknown point and a known point, you could picture that the unknown point is somewhere on a circle centered at the known point. With uncertainty, this circle becomes an annulus. By adding more known points, we intersect this annulus with other annuli to narrow it down to a small region. Each data point refines the region a little bit. After three measurements, you will be left with a shape roughly as big across as your error. Further measurements will give annuli which partially overlap this region, giving you even more accuracy. With enough accuracy, and assuming that your error is a random variable in some continuous distribution, you can achieve arbitrary accuracy.
I remember when I was a teenager, I had one of the first smartphones (it was big and slow, but it was hot stuff back then). I had a GPS app that could ping satellites to determine my location. It would tell me how many satellites I was connected to at any given time. I thought it interesting that it could tell my position with just three, but the accuracy kept going up with each additional satellite. This is the same sort of thing.
A: If you can quantify the imprecision it works similar to triangulation. If your known distances are say x km +- y km then you have a region they could be in.
For the first known point you have a ring with a given width. Once you add the second known point you have two regions they could be in. And so forth. Now adding more known points and their distances can help narrow the regions the point can be in assuming your imprecision isn't to large to make the extra information useless.
