Trilateration vs. Triangulation for Indoor Positioning Systems

Indoor asset tracking is all the rage. But when talking about indoor asset tracking as a whole, it's important to keep in mind that it's made up of a loosely woven group of technologies, each of which can calculate position using one of two methods: triangulation or trilateration. The two are distinct in important ways even though both can theoretically contribute to a single indoor positioning solution.

What Is Triangulation?

Triangulation is a method for calculating a position that relies on a known distance between two measuring apparatuses and the measured angles from those two points to an object. This works using the angle-side-angle triangle congruency theorem to the find the location of an object.

What Is Trilateration?

Trilateration is the more common method for position calculations. Trilateration uses the known distance from at least three fixed points in 2D space or four fixed points in 3D space (as if on the surface of the Earth) to calculate the position of an object. Trilateration works by finding the intersection of a series of circles (imagine in a Venn diagram).

Triangulation and Trilateration in Practice

In the asset tracking space, trilateration is currently much more common. Most companies that use BLE or Ultrasonic technologies rely on trilateration because of how easy it is to implement. Take for example a BLE tracking solution. All a solution needs is three (the "tri" of trilateration) regular beacons and a BLE tag. When the tag starts reporting RSSI values, those values can be converted to distances and used to locate the tag. This is not perfectly accurate, having roughly 1-2m accuracy, but it's relatively simple since it uses common hardware and requires relatively simple math.

On the other hand, triangulation is hard. It requires knowledge of not just the location of BLE beacons but also their spatial rotation. The calculations aren't much more complex than trilateration, but the measurements themselves are significantly more sensitive due to how they are measured. While trilateration relies on signal strength as an analog for distance, triangulation relies on timing differences in the reception of tags' signals. Because these signals travel at the speed of light, the time differences in transmission are very small. This makes measuring instruments more expensive.

Combining Triangulation and Trilateration

As hard as it is, triangulation is likely to catch up to trilateration over time, and ultimately, the two will likely be used in tandem for many applications for added accuracy and redundancy. As mentioned, trilateration taps out at ~1-2m accuracy, but triangulation shows promise of reaching accuracies of ~0.5m. Their combined power holds potential for even higher accuracy applications, specifically when higher costs aren't an issue.