Trilateration

Trilateration is a method of determining the relative position of objects using the geometry of triangles in a similar fashion as triangulation. Unlike triangulation, which uses both distances and angles to calculate the subject's location, trilateration uses the known distances between two or more reference points, and the measured distance between the subject and each reference point. To accurately determine the relative location of a point on a 2D plane using trilateration alone, at least 3 reference points are needed.

The reason for this lies in the geometry of circles. If you know the distance of a subject point from some fixed reference point, then that point could exist anywhere on a circle of that radius from the reference. If you know that it is also a certain distance from a second reference point, then it also exists somewhere on a circle of that radius from the second reference point. These two circles intersect at precisely two points, and the subject could be at either point. The distance between the subject and a third reference point introduces a third circle into the diagram, and all three circles intersect at one point only: the position of the subject, relative to the three reference points.

Of course, this assumes that the subject and the reference points all exist on the one plane, meaning that there are only 2 dimensions involved. For 3D space, 4 reference points are needed and the subject point exists on the surface of spheres instead of circles. Apart from those differences, the technique is still the same.

In practical use, the minimum number of reference points may not be required to disambiguate the subject's location. For example, if the subject is known to be on land, or on the surface of the Earth, and one of the candidate locations is at sea or in space, that point may be disregarded.