Trilatation

Trilateration is a method used to determine the position of a point by measuring distances to known points. Unlike triangulation, which uses angles, trilateration relies solely on distance measurements. The fundamental principle involves intersecting spheres. If a point is at a known distance from a single reference point, its location is confined to the surface of a sphere centered on that reference point. With a second reference point and its distance, the possible locations are narrowed down to the intersection of two spheres, which typically forms a circle. A third reference point and its distance further refine the possible locations to the points where the third sphere intersects the circle, usually resulting in two possible points. In three-dimensional space, this process requires at least four reference points to uniquely determine a position.

The accuracy of trilateration depends on the precision of the distance measurements and the geometric arrangement of the reference points. Errors in distance measurements can lead to significant positional inaccuracies, especially when the reference points are clustered closely together. This technique is widely applied in various fields, including surveying, navigation, and geophysics. For instance, the Global Positioning System (GPS) relies on trilateration, where receivers calculate their position by measuring the time it takes for signals from multiple satellites to arrive. Other applications include determining the location of underground utilities, mapping geological structures, and even tracking animal movements.