Trilateration is the use of

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

(or "ranges") for determining the unknown

position coordinate A Cartesian coordinate system (, ) in a plane is a coordinate system that specifies each point uniquely by a pair of numerical coordinates, which are the signed distances to the point from two fixed perpendicular oriented lines, measured in ...

s of a

point Point or points may refer to: Places * Point, Lewis, a peninsula in the Outer Hebrides, Scotland * Point, Texas, a city in Rains County, Texas, United States * Point, the NE tip and a ferry terminal of Lismore, Inner Hebrides, Scotland * Point ...

of interest, often around Earth (

geopositioning Geopositioning, also known as geotracking, geolocalization, geolocating, geolocation, or geoposition fixing, is the process of determining or estimating the geographic position of an object. Geopositioning yields a set of geographic coordinates ...

). 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 a line segment between the two points. It can be calculated from the Cartesian coordinates of the points using the Pythagorean theorem, therefor ...

s (

slant range In radio electronics, especially radar terminology, slant range or slant distance is the distance along the relative direction between two points. If the two points are at the same level (relative to a specific datum), the slant distance equals t ...

s) or

spherical distance The great-circle distance, orthodromic distance, or spherical distance is the distance along a great circle. It is the shortest distance between two points on the surface of a sphere, measured along the surface of the sphere (as opposed to a st ...

s (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 le ...

s), as in '' true-range multilateration''; 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 determining the position of an unknown point, such as a vehicle, based on measurement of the '' times of arrival'' (TOAs) of energy waves trav ...

''. 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 me ...

'', which uses

angle In Euclidean geometry, an angle is the figure formed by two Ray (geometry), rays, called the ''Side (plane geometry), sides'' of the angle, sharing a common endpoint, called the ''vertex (geometry), vertex'' of the angle. Angles formed by two ...

s for positioning; and ''

direction finding Direction finding (DF), or radio direction finding (RDF), isin accordance with International Telecommunication Union (ITU)defined as radio location that uses the reception of radio waves to determine the direction in which a radio station ...

'', which determines the line of sight direction to a target without determining the

radial distance In mathematics, the polar coordinate system is a two-dimensional coordinate system in which each point on a plane is determined by a distance from a reference point and an angle from a reference direction. The reference point (analogous to the or ...

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, with arithmetic, one of the oldest branches of mathematics. It is concerned with properties of space such as the distance, shape, size, and relative position of figures. A mathematician who works in the field of geometry is c ...

, ''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 points in a plane that are at a given distance from a given point, the centre. Equivalently, it is the curve traced out by a point that moves in a plane so that its distance from a given point is const ...

sphere A sphere () is a Geometry, geometrical object that is a solid geometry, three-dimensional analogue to a two-dimensional circle. 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 Edge (geometry), edges and three Vertex (geometry), vertices. It is one of the basic shapes in geometry. A triangle with vertices ''A'', ''B'', and ''C'' is denoted \triangle ABC. In Euclidean geometry, an ...

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

Pseudo-range multilateration

References

{{reflist Geometry Geopositioning