Trilateration is the use of distances (or "ranges") for determining the unknown position coordinates of a point of interest, often around Earth ( geopositioning). When more than three distances are involved, it may be called multilateration, for emphasis. The distances or ranges might be ordinary

Euclidean distance In mathematics, the Euclidean distance between two points in Euclidean space is the length of the line segment between them. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, and therefore is o ...

s ( slant ranges) or spherical distances (scaled central angles), as in '' true-range multilateration''; or biased distances ( pseudo-ranges), as in ''

pseudo-range multilateration Pseudo-range multilateration, often simply multilateration (MLAT) when in context, is a technique for geopositioning, determining the position of an unknown point, such as a vehicle, based on measurement of biased ''time of flight, times of flig ...

''. Trilateration or multilateration should not be confused with ''

triangulation In trigonometry and geometry, triangulation is the process of determining the location of a point by forming triangles to the point from known points. Applications In surveying Specifically in surveying, triangulation involves only angle m ...

'', which uses

angle In Euclidean geometry, an angle can refer to a number of concepts relating to the intersection of two straight Line (geometry), lines at a Point (geometry), point. Formally, an angle is a figure lying in a Euclidean plane, plane formed by two R ...

s for positioning; and '' direction finding'', which determines the line of sight direction to a target without determining the radial distance.

Terminology

Multiple, sometimes overlapping and conflicting terms are employed for similar concepts – e.g., ''multilateration'' without modification has been used for aviation systems employing both true-ranges and pseudo-ranges."Multilateration (MLAT) Concept of use", International Civil Aviation Organization, 2007"Radar Basics"
Christian Wolff, undated Moreover, different fields of endeavor may employ different terms. In

geometry Geometry (; ) is a branch of mathematics concerned with properties of space such as the distance, shape, size, and relative position of figures. Geometry is, along with arithmetic, one of the oldest branches of mathematics. A mathematician w ...

, ''trilateration'' is defined as the process of determining absolute or relative locations of points by measurement of distances, using the geometry of

circle A circle is a shape consisting of all point (geometry), points in a plane (mathematics), plane that are at a given distance from a given point, the Centre (geometry), centre. The distance between any point of the circle and the centre is cal ...

sphere A sphere (from Ancient Greek, Greek , ) is a surface (mathematics), surface analogous to the circle, a curve. In solid geometry, a sphere is the Locus (mathematics), set of points that are all at the same distance from a given point in three ...

s or

triangle A triangle is a polygon with three corners and three sides, one of the basic shapes in geometry. The corners, also called ''vertices'', are zero-dimensional points while the sides connecting them, also called ''edges'', are one-dimension ...

s. In surveying, ''trilateration'' is a specific technique.free dictionary
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True-range multilateration

Pseudo-range multilateration

References

{{reflist Geometry Geopositioning