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How to use Wolfram Alpha to calculate location of three overlapping Circles

Posted 2 years ago

I have three sensors, and each sensor provides the distance to a person. The distance sensed provides a Radius for the person in a circle around the sensor. But the distances sensed are not exact, only approximate. It may be off by several feet. So the Radii of the three circles may not overlap, or they may intersect at one point, or the circles may overlap without intersecting exactly at one point. This may be corrected, if necessary, by increasing the radii proportionally until the three circles overlap each other. Once the circles overlap each other, the person's approximate location can be found by calculating the center of the overlapped area.

How can Wolfram Alpha give the person's location from the distance reported by three sensors? What are the methods to do this?

POSTED BY: Don Baechtel
7 Replies
Posted 2 years ago
POSTED BY: Werner Geiger
Posted 2 years ago

Looks Good.

Great Job !!

POSTED BY: Don Baechtel

You may try intersecting three annuli, each given by inequalities.

POSTED BY: Gianluca Gorni
Posted 2 years ago

You may try intersecting three annuli, each given by inequalities.

How do I use the intersection of three annuli to find the location of the person?

How do I do this in Wolfram?

POSTED BY: Don Baechtel
Posted 2 years ago
POSTED BY: Werner Geiger
Posted 2 years ago

Can you provide more details? I do not quite follow your method.

POSTED BY: Don Baechtel
Posted 2 years ago

Minimize the sum of the squared error? Can you think how to write an expression for that?

For one sensor that will be the square of the distance from the unknown x,y point to the circle given by the center and the sensor's estimated radius.

Sum the three squared errors and ask WolframAlpha to find the x,y that minimizes that sum.

Do you have an example of the three sensor positions and three distances estimated?

POSTED BY: Bill Nelson
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