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 distances (
slant range
In radio electronics, especially radar
Radar is a detection system that uses radio waves to determine the distance ('' ranging''), angle, and radial velocity of objects relative to the site. It can be used to detect aircraft, ships, spacec ...
s) or
spherical distances (scaled
central angles), as in ''
true-range multilateration''; or biased distances (
pseudo-ranges), as in ''
pseudo-range multilateration''.
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 ...
'', which uses
angle
In Euclidean geometry, an angle is the figure formed by two rays, called the '' sides'' of the angle, sharing a common endpoint, called the '' vertex'' of the angle.
Angles formed by two rays lie in the plane that contains the rays. Angles ...
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"](_blank)
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 ...
s,
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 edges and three 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, any three points, when non- colli ...
s. In surveying, ''trilateration'' is a specific technique.
free dictionary
/ref>
True-range multilateration
Pseudo-range multilateration
References
{{reflist
Geometry
Geopositioning