# Formula to calculate a position given three 2D locations and distance

I am doing a project for my final year computer science and normally post on stack-overflow but this question seems more suited for here. I need a formula to calculate my position from three 2D points and signal strength. I am pretty bad at maths and need a shove in the right direction.

An example of input would be,

Signal / Distance = -60 ([dBm][1]) , Co-ordinates [1.0,1.0]
Signal / Distance = -40 ([dBm][1]) , Co-ordinates [4.0,3.0]
Signal / Distance = -90 ([dBm][1]) , Co-ordinates [7.0,1.0]


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Can you convert signal strength to an absolute distance, or only to a relative one? You might look at the references in math.stackexchange.com/questions/39561/… – Ross Millikan Mar 4 '13 at 19:28
I'm using the Recieved Signal Strength Indicator (RSSI) which can vary due to obstacles. This question says more about getting the distance from RSSI. stackoverflow.com/questions/13705647/… I can only convert assuming there's nothing in the way.. – Tom celic Mar 4 '13 at 19:50

In a perfect world, you could translate your signal strengths into distances. Two distances would describe two circles on the plane, and the third distance could serve to select one of the two resulting points of intersection.

But as your comment indicates, this is not a perfect world. So you might be looking for the point which minimizes the difference between the measured and the computed distances. That's an optimization problem, and a non-linear one at that. A lot more difficult than simply intersecting circles.

So you'll have to decide whether you want to hope for a good enough world, or research deeply into the topic of non-linear optimization.

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