I would like to determine the equation describing the trajectory of an object using data from 2 distance sensors. I figured out how to do this if the sensors take simultaneous measurements but this cannot be done without generating crass talk between the sensors. The object moves too far when the sensors are set to their fastest sequential measurements, so I cannot assume that the measurements are simultaneous. Here's the givens:(adsbygoogle = window.adsbygoogle || []).push({});

The whole problem can be done in 2 dimensions (XY coordinates).

The path of the object is that of a projectile without air resistance so it follows a parabolic path so we that the equation for the object path is quadratic and the object follows all rules for a falling object.

Both sensors are on the y (vertical) axis and the lower one is on the origin.

I am only interested in the path when the object is in "positive" space (both x and y positions are positive).

The sensors return both distance to object and time of measurement but cannot measure simultaneously.

The sensors measure the nearest object within a 20 degree cone, so they cannot be "aimed" parallel to each other, making the problem fairly simple but only uses 2 measurements to determine the path.

The minimum time between measurements is about 5 ms and the object is moving around 5 m/s, so each sensor can take multiple readings.

Maximum range is about 2 meters.

The object is falling and will not pass through the origin, but I see no reason why the problem can't be done in reverse by just reversing the timeline.

What I am really after is the angle of the object path as it passes through the X-axis, but this is easy to obtain if the trajectory equation is known. I can deal with the error in sensor measurements if I know the path equation, so what I need is a theoretical way to determine the path from the distance measurements. Any thoughts on how to approach this problem would be greatly appreciated!

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# Trajectory Path from 2 Distance Sensors

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