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Trilateration in three-dimensional geometry Intersection point of three pseudo-ranges. Trilateration is the use of distances (or "ranges") for determining the unknown position coordinates of a point of interest, often around Earth (geopositioning). [1] When more than three distances are involved, it may be called multilateration, for emphasis.
In mathematics, a rotation of axes in two dimensions is a mapping from an xy-Cartesian coordinate system to an x′y′-Cartesian coordinate system in which the origin is kept fixed and the x′ and y′ axes are obtained by rotating the x and y axes counterclockwise through an angle .
There is no accepted or widely-used general term for what is termed true-range multilateration here . That name is selected because it: (a) is an accurate description and partially familiar terminology (multilateration is often used in this context); (b) avoids specifying the number of ranges involved (as does, e.g., range-range; (c) avoids implying an application (as do, e.g., DME/DME ...
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 biased times of flight (TOFs) of energy waves traveling between the vehicle and multiple stations at known locations.
In mathematics, analytic geometry, also known as coordinate geometry or Cartesian geometry, is the study of geometry using a coordinate system. This contrasts with synthetic geometry . Analytic geometry is used in physics and engineering , and also in aviation , rocketry , space science , and spaceflight .
If a standard right-handed Cartesian coordinate system is used, with the x-axis to the right and the y-axis up, the rotation R(θ) is counterclockwise. If a left-handed Cartesian coordinate system is used, with x directed to the right but y directed down, R(θ) is clockwise.
A useful method, due to Julius Plücker, creates a set of six coordinates as the determinants (<) from the homogeneous coordinates of two points (,,,) and (,,,) on the line. The Plücker embedding is the generalization of this to create homogeneous coordinates of elements of any dimension m {\displaystyle m} in a projective space of dimension n ...
Depiction of Trilateration. The plane, z=0, showing the 3 sphere centers, P1, P2, and P3; the 3 sphere radii, r1, r2, and r3; and the distances, d, i, and j. Only one, the point B, of the 2 intersections is shown. The point A is not an intersection. Date: 4 April 2006: Source: Original PNG by Rossi; SVG version by Braindrain0000: Author: Rossi ...