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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.
SHORAN was later used for off-shore oil exploration and for aerial surveying. The Australian Aerodist aerial survey system utilized 2-D Cartesian true-range multilateration. [7] This 2-D scenario is sufficiently important that the term trilateration is often applied to all applications involving a known baseline and two range measurements.
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 .
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.
Let (x, y, z) be the standard Cartesian coordinates, and (ρ, θ, φ) the spherical coordinates, with θ the angle measured away from the +Z axis (as , see conventions in spherical coordinates). As φ has a range of 360° the same considerations as in polar (2 dimensional) coordinates apply whenever an arctangent of it is taken. θ has a range ...
An xy-Cartesian coordinate system rotated through an angle to an x′y′-Cartesian coordinate system 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 ...
If a left-handed Cartesian coordinate system is used, with x directed to the right but y directed down, R(θ) is clockwise. Such non-standard orientations are rarely used in mathematics but are common in 2D computer graphics, which often have the origin in the top left corner and the y-axis down the screen or page. [2]
Two-dimensional spaces can also be curved, for example the sphere and hyperbolic plane, sufficiently small portions of which appear like the flat plane, but on which straight lines which are locally parallel do not stay equidistant from each-other but eventually converge or diverge, respectively.