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Trilateration uses distance measurements to determine position using spheres, circles or triangles. GPS and land surveys use this method for precise locations. In 2D, circles can be used to find a point’s location. In 3D, spheres are used, as in GPS systems. GPS calculates distance to satellites and uses trilateration to determine position on Earth’s surface.
Trilateration is a type of measurement used to determine the position of a point using the geometry of spheres, circles or triangles. Unlike triangulation, which uses angle measurements to determine location, trilateration uses distance measurements. Global Positioning Systems (GPS) and land surveys apply this method to provide precise geographic locations on the earth’s surface.
In two-dimensional geometry, the radii of circles can sometimes be used to find the location of a point. For example, if an unknown point X is 3 units away from point A, it could be anywhere in a radius of 3 units around point A. When viewed, you can see that the set of possible locations for X forms a circle around point A. If it is also known that point X is 4 units from point B, however, a second circle of possible locations is formed around B with a radius of 4 units. These two circles overlap, intersecting at two points, one of which must be X.
A third measurement allows us to find X. If we know that X is 5 units from point C, we form a third circle with radius 5. This circle will intersect with the other two only in one of the two points, which we then know is X.
The example above can be applied to situations where you need to find an approximate geographic location. For example, if a person was trying to find his location on the ground, he might be able to infer it by finding three distances from known landmarks or cities. In most cases, however, accurate navigation requires the use of a three-dimensional trilateration method.
The main difference between two-dimensional and three-dimensional trilateration is that spheres are used instead of circles in the three-dimensional method. The radii of four spheres are measured and the position is determined from the points of intersection. This is displayed through one of the most common applications of trilateration: a GPS system.
GPS systems work by calculating their distance to satellites orbiting the Earth. If the GPS user is on the surface of the Earth, we already have a sphere with a known radius – the planet itself. GPS sends precise signals to satellites and receives messages which it uses to determine the transit time and, by extension, its distance from each satellite. The distances of three satellites form three spheres, which overlap in two possible positions, one on the earth’s surface and one in space. For GPS users on land, the coordinate on the surface is the correct location.
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