Define Trilateration.

Trilateration is a geometric technique used in navigation, surveying, and positioning systems to determine the precise location of a point in space by measuring the distances from that point to three known reference points, called anchors or base stations. Unlike triangulation, which involves measuring angles, trilateration relies on distance measurements to determine the position of the target point.

The basic principle of trilateration involves creating a series of circles or spheres around each reference point with radii equal to the measured distances to the unknown point. The point of intersection of these circles or spheres represents the possible locations of the target point. By using three reference points, trilateration narrows down the potential positions to two points, and the addition of a fourth reference point resolves the ambiguity, providing a unique solution for the target point's coordinates.

The mathematical formulation of trilateration involves solving a system of equations based on the distances between the unknown point and the reference points. The equations represent the geometric relationships among the points and are typically derived from the Pythagorean theorem for three-dimensional space.

Trilateration finds widespread applications in various fields:

1. Global Navigation Satellite Systems (GNSS):
   GPS (Global Positioning System) and other GNSS systems use trilateration to determine the position of GPS receivers on Earth's surface by calculating distances from satellites with known positions.

2. Indoor Positioning Systems:
   Trilateration is employed in indoor positioning systems using technologies such as Bluetooth beacons, Wi-Fi access points, or RFID (Radio-Frequency Identification) tags. These systems enable accurate positioning within buildings where satellite signals may be limited.

3. Surveying and Geolocation:
   Trilateration is used in land surveying and geolocation applications to determine the coordinates of points on the Earth's surface based on distance measurements from known control points.

4. Wireless Communication Networks:
   Trilateration is applied in cellular networks to estimate the location of mobile devices. By measuring the distances between a mobile device and multiple cell towers, the device's location can be determined.

Trilateration provides a practical and effective method for precise positioning, especially in scenarios where line-of-sight measurements may be obstructed or where accurate angle measurements are challenging to obtain. Its versatility makes it a fundamental technique in various navigation and positioning technologies.