Trilateración

Trilateración is a method for determining the location of a point by using the known distances to three other points. The principle is that if you know the distance from an unknown point to three known points, and you know the coordinates of those three known points, you can pinpoint the location of the unknown point. Imagine three circles, each centered at one of the known points, with radii equal to the measured distances. The unknown point is located where these three circles intersect. In practice, the intersection might not be perfect due to measurement errors, so the location is often estimated as the point closest to all three circles.

This technique is widely used in various fields. Geodesy and surveying employ trilateración to establish precise locations on the Earth's surface. The Global Positioning System (GPS) is a prime example of a system that utilizes the principles of trilateración, although it technically uses multilateración with at least four satellites to account for time synchronization errors. Navigation systems, both terrestrial and marine, also rely on this method. In robotics, trilateración can be used for indoor positioning and localization of autonomous vehicles. The accuracy of the determined location depends heavily on the precision of the distance measurements and the geometric arrangement of the known points.