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?
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?
minimize the sum of the distance from p to p1 and the distance from p to p2 and the distance from p to p3 with p1 = (1,0) and p2 = (0,2) and p3 = (-1,0) and p = (x,y)
should do. But in my WolframAlpha Android App this query is not understood.
**Postscript: **
Sorry. This is not what you need. It will give the center of gravity, i.e. mean, of the three sensor locations. Anyway, you’d better handle that problem directly within Wolfram Language, not WolframAlpha. The latter’s natural language queries are a nightmare concerning mathematics. Most of the time they are not understood and it’s and endless trial and error game to achieve results.
Assuming I understood what you meant, I wrote a solution notebook in Wolfram Language. I don’t think you can solve it in WolframAlpha (maybe with the desktop version, which I don’t have).