Locating a Point Using 3 Beacons

Beacons can be used to track the movement of object on a given space like in our example, is perhaps a Fashion Store with a regular  rectangular shape. Assuming the object is a smartphone with a beacon app installed and has stable internet connection to transmit data back to the shop owner's back end app. These data will be the rssi(received signal strength) of each beacons received every 1 second.

The back end app by default, knows exactly the position of the three beacons.

So with these sets of data available, the location of the smartphone can be traced every second using trilateration algorithm which is a process of finding the location of the point using the geometry of circles, spheres and triangle. More information about trilateration is in wikipedia.

Using the rssi transmitted by the smartphone, and since we know the distance of each beacon from each other(d and e), we have a lot of data to use in determining the exact location of the point. We will also assume that all points of interest in the scenario lie on the same plane. The formula for computing distance in meters from  rssi is as follows:

RSSI = -20 * log10(distance in meters) + RssiAtOneMeter
distance in meters = pow(10, (RssiAtOneMeter - ReceivedRSSI) / 20)

source: Evaluation of the Reliability of RSSI for Indoor Localization

In the above picture, we can easily determine the value of x and y by Trigonometry's Pythagorian Theorem:

Using the eaquation:

x2+y2=b2