The distance estimate provided by iOS is based on the ratio of the iBeacon signal strength (rssi) over the calibrated transmitter power (txPower). The txPower is the known measured signal strength in rssi at 1 meter away. Each iBeacon must be calibrated with this txPower value to allow accurate distance estimates.

 

When we were building the Android iBeacon library we had to come up with our own independent algorithm because the iOS CoreLocation source code is not available. We measured a bunch of rssi measurements at known distances, then did a best fit curve to match our data points. The algorithm we came up with is shown below as Java code.

 

Note that the term "accuracy" here is iOS speak for distance in meters. This formula isn't perfect, but it roughly approximates what iOS does.

   

protected static double calculateAccuracy(int txPower, double rssi) {
  if (rssi == 0) {
    return -1.0; // if we cannot determine accuracy, return -1.
  }

  double ratio = rssi*1.0/txPower;
  if (ratio < 1.0) {
    return Math.pow(ratio,10);
  }
  else {
    double accuracy =  (0.89976)*Math.pow(ratio,7.7095) + 0.111;    
    return accuracy;
  }
}   

 

Note: The values 0.89976, 7.7095 and 0.111 are the three constants calculated when solving for a best fit curve to our measured data points. YMMV