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Trilateration in a 2D plane with strong signals

first question to stackoverflow, be careful.

  • I am trying to find the equation (and then the algorithm for) of the center point of three different points on a two-dimensional cartesial plane with a certain value or "signal strength". These strong signal levels are scaled relative to each other, but do not have to be combined with the circle “radius”.

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

I also checked this topic, but it is a little different than what I need Trilateration using 3 points of latitude and longitude and 3 distances

The general equation is good, but I will give some examples of data for testing:

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

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

Thoughts? TIA

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algorithm geometry computational-geometry trilateration
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3 answers

First, you must normalize the strengths so that their sum is 1 (respectively a constant).

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

Edit: You can calculate this simply by adding vectors scalable to normalized forces. This gives (4243.7344 4393.187) for your example.

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Is it possible to compare the strength of the magnitude / strength of the signal with the mass?

In this case, calculate your center point, such as the center of mass .

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Find the center of the triangle ....

normalize the signal strength, turning them into a percentage of max.

for each point, the shift of the center by a proportional value of the normalized force to the length of the line, the point makes the intersection of the line, the other two do :)

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