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I'm testing the capabilities of radio strength for inhouse, small-object localisation. I'm not here to discuss this (altough any recommandations are always welcome).

For this localisation I'd use about 5 radio nodes each set up in corners of a room. Known are the exact xy coordinates of these nodes and the size of the room.

The robot has to determine only by the signal strength of the nodes where it is, such as illustrated here; Where the dots are the nodes and the robot is inside the sector in which all circle are adjacent to one and other.

The problem is as follows: How do I algebraically determine the xy position of the robot?

In a rectangle this is mathematically not a big problem, but I need a method that will work with an unspecified number of nodes (atleast more than 4) and in different settups.

Any help is greatly appreciated! (and excuse my english; i'm tired and in a bit of hurry)

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    Why is this more di$f$ficult not in a rectangle? Also, does signal strength translate directly to distance? Note, you only need to know 3 nodes to find the robot, if exact distances are provided.2012-12-06

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You have a set of equations $(x_i - x)^2 + (y_i - y)^2 = r_i^2$ where $(x_i, y_i)$ is the position of i'th node, $(x, y)$ is the position of robot and $r_i$ is the distance between them.
Take any two nodes and compute the difference of their equations: $2(x_i - x_j)x + 2(y_i - y_j)y = x_i^2 - x_j^2 + y_i^2 - y_j^2 + r_j^2 - r_i^2$ Here is a line equation. I suggest that you compute several such lines and get their intersections (should I elaborate on that?), then possibly take an average of some sort in case of errors in measurements.

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    Yes off course! I can work it out from here. Thanks a lot!2012-12-09