Triangulation vs Trilateration vs Multilateration – for Indoor Positioning Systems

Date: June 6, 2019

Author: Ipshita Biswas

In the world of real-time location systems, a number of loosely woven technologies may be thrown your way. Location tracking is not at all a recent phenomenon, nor is it the outcome of some technological evolution. The need to decipher the location of objects, people, resources has existed from time immemorial. The story of the evolution of positioning systems is nothing less than interesting.

One major aspect of a location tracking system is the basic mathematical computation that determines the exact location. Fortunately, there’s not one but three major ways of determining a location – namely, triangulation, trilateration and multilateration. This article is meant to give an overview of each of these and explore the real-world solutions in which they are used.

Triangulation

Out 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 Triangulation

The 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 terrain

The 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 surveying

The 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 an economical solution. For a larger area, however, the triangles have to be replaced by quadrilaterals or polygons.

Trilateration

Trilateration 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 GPS

What 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 centre 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.

Multilateration

Also known as hyperbolic positioning, multilateration relies on the time difference in the arrival of signals to various base stations or anchors. This is one of the most popular techniques used for indoor and outdoor positioning in confined regions.

The popular positioning methodology known as TDoA uses multilateration in which the anchors need to be synchronized. In this method, the tags send out data packets that are received by the anchors. The difference in the time of reception between the anchors is the basis of the distance calculation and, ultimately, the calculation to locate the object.

The principle behind multilateration is similar to trilateration, except that there’s no circle or sphere here; it’s hyperbolas in the case of 2D and hyperboloids in the case of 3D positioning. Here, too, at least 4 anchors or transmitters are needed to position the tag accurately.

Figure 4: Multilateration in TDoA

TDoA is known as one of the most accurate and power-optimized technique for localization. Our ready-to-use RTLS Solution is TDoA-based, and the combined effect of the intrinsic features of UWB has made it a robust solution for confined area positioning. There are several other technologies beyond UWB that use TDoA for confined area positioning; check out this brief comparison among the leading technologies.

Want to how TDoA compares to the rest of the localization techniques? Read this article on Your ultimate guide to choosing the right UWB methodology.

Conclusion

Each of these techniques has different accuracy, requirements and outputs. Thus, the selection would depend on the use-case. Trilateration and multilateration are gradually becoming more and more popular, but triangulation isn’t lost yet. Some specific use-cases, as pointed out above, still demand it

But, when it comes to confined area positioning or indoor positioning, multilateration is definitely a clear winner.

References:

Triangulation

Trilateration

Multilateration

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