Triangulate example for iBeacons

Question

I am looking into the possibility to use multiple iBeacons to do a 'rough' indoor position location. The application is a kind of 'museum' setting, and it would be easier to be able to form a grid with locations for the different objects then individual beacons (although that might not be impossible too).

Are there examples, experiences, with using multiple beacons to triangulate into some kind of location, or some logic to help me on the way to write it myself?

Answer 1

I have been making some experiments to get a precise position using three beacons.

Results of trilateration

Unluckily, the results were very disappointing in terms of quality. There were mainly two issues:

1. In non-controlled environments, where you can find metals, and other objects that affect the signal, the received signal strength of the beacons changes so often that it seems impossible to get error range below 5 meters.
2. Depending on the way that the user is handling the receiver device, the readings can change a lot as well. If the user puts his/her hand over the bluetooth antenna, then the algorithm will have low signals as input, and thus the beacons will supposed to be very far from the device. See this image to see the precise location of the Bluetooth antenna.

Possible solutions

After talking with an Apple engineer who actively discouraged me to go down this way, the option I feel more inclined to use right now is brute force. Try to set up a beacon every X meters (X being the maximum error tolerated in the system) so we can track on this beacons grid the position of a given device by calculating which beacon on the grid is the closest to the device and assuming that the device is on the same position.

Trilateration algorithm

However, for the sake of completeness, I share below the core function of the trilateration algorithm. It's based on the paragraph 3 ("Three distances known") of this article.

- (CGPoint)getCoordinateWithBeaconA:(CGPoint)a beaconB:(CGPoint)b beaconC:(CGPoint)c distanceA:(CGFloat)dA distanceB:(CGFloat)dB distanceC:(CGFloat)dC {
    CGFloat W, Z, x, y, y2;
    W = dA*dA - dB*dB - a.x*a.x - a.y*a.y + b.x*b.x + b.y*b.y;
    Z = dB*dB - dC*dC - b.x*b.x - b.y*b.y + c.x*c.x + c.y*c.y;

    x = (W*(c.y-b.y) - Z*(b.y-a.y)) / (2 * ((b.x-a.x)*(c.y-b.y) - (c.x-b.x)*(b.y-a.y)));
    y = (W - 2*x*(b.x-a.x)) / (2*(b.y-a.y));
    //y2 is a second measure of y to mitigate errors
    y2 = (Z - 2*x*(c.x-b.x)) / (2*(c.y-b.y));

    y = (y + y2) / 2;
    return CGPointMake(x, y);
}