Triangulation: Locate Point with 3 Sensors

[geolej]

I have 3 sensors I know the distance between. They report to me 0.58V when no change is found and when a change is found they report .64V .79V .66V for example. Would it be possible to locate the point where the item is?

 

[HallsofIvy]

Not without knowing how the reported value is connected to the distance from the sensor to the point of "change". If you can use the reported value to determine the distance, then you can imagine three circles with the sensors as center and the determined distances as radii. For example, if you sensors are at $(x_a, y_a)$, (x_b,y_b)[/itex], and $(x_c,,y_c)$ and the distances are determined to be $R_a$, $R_b$, and $R_c$, respectively, the the point to be determined must satisfy $(x-x_a)^2+ (y-y_a)^2= R_a^2$, $(x-x_b)^2+ (y-y_b)^2= R_b^2$, and $(x-x_c)^2+ (y-y_c)^2= R_c^2$. IF those circles all intersect, then they will, generally, intersect in one point- but there are special cases in which they will intersect in more than one point. Solve those equationsw for x, y, and z.

I have assumed that you are talking about points in a plane. In three dimensions, you would need four sensors to specify a point.

 

[geolej]

The sensors report a higher value when the item is closer, and lower value when further away. They are hall-effect sensors. Can you provide me with more info into triangulation?