具有信号强度的 2D 平面中的三边测量 [英] Trilateration in a 2D plane with signal strengths

问题描述

StackOverflow 的第一个问题，请温柔.

first question to StackOverflow, please be gentle.

• 在给定一定幅度或信号强度"的情况下，我试图找到二维笛卡尔平面上三个不同点的中心点的方程(然后是算法).这些信号强度都是相互关联的，但不必将其与圆的半径"混为一谈.

关于三边测量的维基百科条目:http://en.wikipedia.org/wiki/Trilateration

Wikipedia entry on trilateration: http://en.wikipedia.org/wiki/Trilateration

我也查看了这个帖子，但它与我需要的有点不同使用3个经纬度点和3个距离的三边测量

I've also checked out this thread, but it's a little different than what I need Trilateration using 3 latitude and longitude points, and 3 distances

一般方程很好，但我将在此处提供一些示例数据点进行测试:

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

我的一般感觉是这些点需要被翻译成相同的比例(信号强度和点)，但我可能错了.

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.

想法?TIA

推荐答案

你必须首先对强度进行归一化，使它们的总和变为 1(分别为常数).

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

如果每个角点的归一化强度为 1(因此其他角点为 0)，则每个角点都是结果点.另一方面，如果该强度为 0，则结​​果点将位于其他两个点之间的线上.在两者之间，它位于与该线平行且具有相对强度的线.计算两个强度的距离，找到结果点.第三个强度是多余的(它通过归一化进入计算).

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).

您可以简单地通过添加由归一化强度缩放的向量来计算它.这给了你的例子 (4243.7344 4393.187).

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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