altbeacon - constants for calculating distance

Question

I'm writing my bachelor thesis on indoor navigation using iBeacons. For this i use trilateration to find my position. I've been using the android beacon library, which is now known as the AltBeacon library to detect beacons and calculate the distance. I noticed, that the distances i get aren't that accurate and after some searching here, i came across a post from DavidYoung saying that because most device have different Bluetooth antennas i would have to take that into account when im calculating the distance.
The AltBeacon library calculates the distance like this (taken from DavidYoungs post):

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;
  }
}

My question now is: how do i calculate these values (0.89976, 7.7095, 0.111) for my Lg G2 with RSSI measurements at certain meter intervals from the beacon?
I found this as an example for measurement values with the calculated coefficent.

Nexus 5 Distance Data

Meters RSSI
0.25 -41
0.5 -43
1 -49
2 -65
3 -58
4 -57
5 -67
6 -67
7 -77
8 -70
9 -69
10 -75
12 -72
14 -72
16 -78
18 -83
20 -81
25 -81
30 -75
40 -83

Android device:
version: 4.4.2
build_number: LPV79
model: Nexus 5
manufacturer: LGE

Beacon Info:
RadBeacon Tag
Advertisements per second: 10
Transmit Power: Max

IPhone 5s Average RSSI @1m: -51

Distance formula coefficients calculated for these values:

Intercept: 0.1820634
Multiplier: 0.8229884
Power: 6.6525179

The term intercept suggests linear regression, but when i put the values into a linear regression calculator it gave me results that were nowhere near those values.
I hope you can help me and that my question is clear enough :)

davidgyoung davidgyoung · Accepted Answer · 2015-01-14T12:08:49

There are many kinds of formulas you can use when doing a best-fit regression. For distance calculations, we use a power curve, fitting to which is supported by the free R statistical package. You can read more about how to do this here:

https://github.com/AltBeacon/android-beacon-library/issues/47

While getting a device-specific formula will help you get better distance estimates, much of the error you are seeing from trilateration output is probably from signal noise, attenuating obstructions and multipath. Understand that even with a device-specific formula, beacon ranging is inexact and precision gets worse the further you are away from the device. To mitigate these effects, space your beacons as closely as possible with clear line of sight to the mobile device if possible.

altbeacon - constants for calculating distance

1 Answers