三边测量与信号强度的2D平面 [英] Trilateration in a 2D plane with signal strengths

问题描述

第一个问题StackOverflow的，请温柔。

first question to StackOverflow, please be gentle.

• 在我试图找到式（然后算法）三个不同的点上的二维坐标平面的中心点，给予一定的数量或信号强度。这些信号强度都在一个尺度相对于彼此，但不应必要地用半径的圆的混为一谈。

维基百科条目： http://en.wikipedia.org/wiki/Trilateration

我也签出此线程，但它比我需要一点点的不同 <一href="http://stackoverflow.com/questions/2813615/trilateration-using-3-latitude-and-longitude-points-and-3-distances">http://stackoverflow.com/questions/2813615/trilateration-using-3-latitude-and-longitude-points-and-3-distances

I've also checked out this thread, but it's a little different than what I need http://stackoverflow.com/questions/2813615/trilateration-using-3-latitude-and-longitude-points-and-3-distances

一个一般方程是好的，但我会在这里提供一些样本数据点进行测试：

A general equation is nice, but I'll provide some sample data points here for testing:

P1：X，Y = 4153，4550 //幅度或信号强度= 143
P2：X，Y = 4357，4261 //幅度或信号强度= 140
P3：X，Y = 4223，4365 //幅度或信号强度= 139

P1: X,Y = 4153, 4550 // Magnitude or Signal strength = 143
P2: X,Y = 4357, 4261 // Magnitude or Signal strength = 140
P3: X,Y = 4223, 4365 // Magnitude or Signal strength = 139

我的总体感觉是，需要这些点翻译是同等规模（信号强度和分），但我可能是错的。

My general sense is that these points need to be translated to be on the same scale (the signal strengths and the points), but I could be wrong.

思考？ TIA

推荐答案

您必须首先正常化的优势，使它们的和为1（相应的常数）。

You have to first normalize the strengths, so that their sum becomes 1 (resp. a constant).

每个角落点。将所得到的点，如果它们的归一化强度分别为1（因而其他0）。如果此强度为0，另一方面，将所得点将趴在两个人之间的界线。之间，它位于一个平行于与强度的相对距离，该距离线。计算该距离为2的长处，结果点被发现。第三种力量是多余的（它进入通过规范化计算）。

Each of the corner points would be the resulting point if their normalized strength were 1 (and thus the others 0). If this strength were 0, on the other hand, the resulting point would lie on the line between the two others. In between, it lies on a parallel to that line with a relative distance of the strength. Calculate this distance for two of the strengths, and the result point is found. The third strength is redundant (it goes into the calculation through the normalization).

编辑：的你可以简单地通过添加归一化优势缩放向量计算这一点。这给了（4243.7344 4393.187）为你的榜样。

You can calculate this simply by adding the vectors scaled by the normalized strengths. That gives (4243.7344 4393.187) for your example.

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