Trilateration is the use of

distances Distance is a numerical or occasionally qualitative measurement of how far apart objects, points, people, or ideas are. In physics or everyday usage, distance may refer to a physical length or an estimation based on other criteria (e.g. "two co ...

(or "ranges") for determining the unknown position coordinates of a point of interest, often around Earth (

geopositioning Geopositioning is the process of determining or estimating the geographic position of an object or a person. Geopositioning yields a set of geographic coordinates (such as latitude and longitude) in a given map datum. Geographic positions may a ...

). 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 range In radio electronics, especially radar terminology, slant range or slant distance is the distance along the relative direction (geometry), relative direction between two points. If the two points are at the same level (coordinate), level (relati ...

s) or spherical distances (scaled

central angle A central angle is an angle whose apex (vertex) is the center O of a circle and whose legs (sides) are radii intersecting the circle in two distinct points A and B. Central angles are subtended by an arc between those two points, and the arc l ...

s), as in ''

true-range multilateration True-range multilateration (also termed range-range multilateration and spherical multilateration) is a method to determine the location of a movable vehicle or stationary point in space using multiple ranging, ranges (distances) between the veh ...

''; or biased distances (

pseudo-range The pseudorange (from pseudo- and range) is the ''pseudo'' distance between a satellite and a navigation satellite receiver (see GNSS positioning calculation), for instance Global Positioning System (GPS) receivers. To determine its position, a ...

s), 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 Direction finding (DF), radio direction finding (RDF), or radiogoniometry is the use of radio waves to determine the direction to a radio source. The source may be a cooperating radio transmitter or may be an inadvertent source, a naturall ...

'', which determines the line of sight

direction Direction may refer to: *Body relative direction, for instance left, right, forward, backwards, up, and down ** Anatomical terms of location for those used in anatomy ** List of ship directions *Cardinal direction *Bearing (navigation) Mathemat ...

to a target without determining the

radial distance Radial distance, typically denoted or (rho), is the distance from the origin to a point along the radial dimension in a: * Polar coordinate system * Spherical coordinate system * Cylindrical coordinate system A cylindrical coordinate system i ...

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