Triangulation: Locate Point with 3 Sensors

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SUMMARY

This discussion focuses on triangulation using three hall-effect sensors to locate a point based on voltage readings. The sensors report a baseline voltage of 0.58V when no change is detected and higher voltages (e.g., 0.64V, 0.79V, 0.66V) when an object is present. To determine the object's location, the distances derived from these voltage readings must be converted into radii for circles centered at the sensor coordinates. The intersection of these circles will yield the object's position, although special cases may result in multiple intersection points. In three-dimensional space, four sensors are necessary for accurate triangulation.

PREREQUISITES
  • Understanding of hall-effect sensors and their voltage output
  • Knowledge of basic geometry and circle equations
  • Familiarity with coordinate systems (2D and 3D)
  • Ability to solve systems of equations
NEXT STEPS
  • Research how to convert voltage readings to distance measurements for hall-effect sensors
  • Learn about solving nonlinear equations for intersection points of circles
  • Explore triangulation algorithms in both 2D and 3D contexts
  • Investigate the use of additional sensors for improved accuracy in three-dimensional triangulation
USEFUL FOR

This discussion is beneficial for engineers, robotics developers, and anyone involved in sensor-based location tracking and triangulation techniques.

geolej
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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?
 
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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.
 
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?
 

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