Localising a receiver using trilateration of base station signal strengths?

I have a system with a number of base station beacons, each broadcasting an infinitely fast signal describing their position on a 2D Cartesian plane. The signal strength begins with a [unitless] power of 1.0, with the strength degrading over the distance d according to the following formula:

       1
    --------
    4*pi*d*d

Somewhere on that plane is a receiver. It can access the location of the base station and the received signal strength from any base stations in range. I'd like to identify where it is located using this information.

I believe I need to perform trilateration (I'd originally assumed triangulation, but that appears to use timing differ开发者_Python百科ences?), but neither the Wikipedia entry nor this question have helped.

I thought the wikipedia page was self-explanatory. This is a classic case. In the 2D case trilateration you need to have at least three receivers in order to estimate your position. From the given signal strength you can estimate the distance by inverting the formula. I would advise to take three smallest distances in order to reduce the error. Then what you do is apply the formulas from the wikipedia page, but converted for a 2d case.

x = (r1*r1 - r2*r2 + d*d) / 2*d

y = (r1*r1 - r3*r3 + i*i + j*j) / 2*j - (i/j)*x