Trilateration

Please note that the content of this book primarily consists of articles available from Wikipedia or other free sources online. Trilateration is a method for determining the intersections of three sphere surfaces given the centers and radii of the three spheres. A mathematical derivation for the solution of a three-dimensional trilateration problem can be found by taking the formulae for three spheres and setting them equal to each other. To simplify the calculations, we apply three constraints to the centers of these spheres; we assume all three spheres are centered on the z=0 plane, one is at the origin, and one other is on the x-axis. It is possible to transform any set of three points to comply with these constraints, find the solution point, and then reverse the translation to find the solution point in the original coordinate system.

Klappentext

High Quality Content by WIKIPEDIA articles! Trilateration is a method for determining the intersections of three sphere surfaces given the centers and radii of the three spheres. A mathematical derivation for the solution of a three-dimensional trilateration problem can be found by taking the formulae for three spheres and setting them equal to each other. To simplify the calculations, we apply three constraints to the centers of these spheres; we assume all three spheres are centered on the z=0 plane, one is at the origin, and one other is on the x-axis. It is possible to transform any set of three points to comply with these constraints, find the solution point, and then reverse the translation to find the solution point in the original coordinate system.