TriangulationOut of the three techniques, triangulation is the only one that measures angles rather than distance, and it is a preferred technique by the surveyors.
Figure 1: Basics of TriangulationThe surveyors fix two points (point 1 and point 2) with a known distance between them, which is established as the baseline. From these two points, the surveyors measure the angle made by lines from distant points intersecting with the base line using a device called Theodolite. These angles are then used to determine the unknown distances and thus locate the distant points. So, if the known points are replaced with anchors, at least 2 anchors are required to determine a location in a 2D space and at least three anchors would be required to determine a location in a 3D space. Today, triangulation mostly finds its use in Surveying, Navigation, Metrology, Astrometry, Binocular Vision, Model Rocketry, and Gun Direction of Weapons. Triangulation is usually the preferred option when surveying a hilly area due to the ease of establishing stations at appropriate distances and ascertaining the line of sight. In cities and crowded areas, the line of sight is hugely impacted and can only be overcome by the use of towers, which escalates the cost to a high degree.
Using Triangulation to survey a narrow strip of terrainThe entire area to be surveyed is covered with a framework of triangles, each formed with a baseline that is derived from the previous triangle. The complete framework is known as the Triangulation system or triangulation figure. An image will make it clearer.
Figure 2: A triangulation system used in narrow terrain surveyingThe internal angles of each triangle shouldn’t be less than 300 or more than 1200. For a narrow strip of terrain, a chain of triangles provides a quick and economical solution. For a larger area, however, the triangles have to be replaced by quadrilaterals or polygons.
TrilaterationTrilateration is a more popular technique that is also used by GPS. Trilateration pinpoints a location by measuring distance. In order to understand this, let’s understand the basic localization technique used by GPS.
Figure 3: Trilateration used by GPSWhat a satellite does is broadcast a signal for a GPS receiver to pick up. This is how the distance between a satellite and a GPS receiver is known. At this point, the GPS receiver can be anywhere along the radius of the circle (or sphere in a real-world scenario). Similarly, when 3 such satellites come into contact with the GPS receiver, the exact location is determined. In the above diagram, it can be seen that each satellite is at the center of a circle. The intersection of the circles gives the location of the GPS receiver. As the GPS receiver moves, so does the point of intersection of the circles. In real-world scenario, the circles become spheres, and thus 4 satellites are required to pinpoint the location with sharp accuracy. When we think this in terms of positioning, at least three non-collinear anchors are needed in a 2D space and at least four non-coplanar anchors are needed in three-dimensional space.