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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:

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    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 differences?), but neither the Wikipedia entry nor this question have helped.

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Rezzie
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  • How is this a programming question? – John Saunders Nov 09 '10 at 20:14
  • I'm looking for help with implementing the described model? There was a related question already on StackOverflow (linked in the original question), but if there's a more relevant place I should have posted this please let me know... – Rezzie Nov 09 '10 at 22:46
  • Localization tag refers to Software Localization (process of adapting software to local market demands). What you are looking for is algorithm. Let me re-tag it for you. – Paweł Dyda Nov 10 '10 at 08:49

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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
guruslan
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    Throwing away all receivers except for the three closest seems a bit of a shame. – Gareth Rees Nov 10 '10 at 13:33
  • So by rewriting the power degradation formula I can estimate the distance from the respective base stations (r1, r2, r3?). What do i, j and d in your posted formulae represent? – Rezzie Nov 10 '10 at 18:11