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I have an object that is moving towards target points and I want to determine when it will reach or pass through them. I receive points in real time, which represent the current position of the object. The position is a 6-D vector. The data can be download from here

Initial approach

For each received point:

  • Calculate distance between current and target points.
  • As the object approaches the target, the distance decreases. If current distance is greater than previous distance, I consider that it has reached the target. It's good enough for me.

Problem

The problem is that the point can sometimes fluctuate a bit. It can increase and then decrease again (noise), even if it has not yet reached the target. But because of this fluctuation, my algorithm detects a false positive because the current distance is greater than the previous one.

The image shows false positives and true positives. When a real upward trend begins, I know that the object has reached the target point. My simple idea to start with is to get rid of false positives by using a smoothing filter and fit a curve. After that I can find when positive slope begins which tells me when object reached target.

I wonder if I should try this approach or any other recommendations including smoothing filters, fitting a curve, etc?

enter image description here

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  • $\begingroup$ Please confirm if this is a 1D problem. (In 2D, the distance can form a minimum while being far from the origin.) $\endgroup$ Commented Jun 26, 2023 at 8:59
  • $\begingroup$ If 1D, why don't you just compare the distance to $0$ ? Or detect a change of sign ? $\endgroup$ Commented Jun 26, 2023 at 9:00
  • $\begingroup$ I suggest you show us one or two examples of real data: a plot of the sequence of points (connected by lines) in 1D, 2D, or 3D; a plot of the distance from the origin, as a function of time. Also, what do you know about the movement of the object? Does it tend to move in a straight line? Is it a physical object, with acceleration typically bounded (e.g., a car, a plane, etc.)? I don't think we can answer whether you should use noise filters; that will depend on the specific situation where this arises, and is beyond the scope of this site. $\endgroup$ Commented Jun 26, 2023 at 16:42
  • $\begingroup$ @D.W., I added an update in my post $\endgroup$ Commented Jun 27, 2023 at 5:39
  • $\begingroup$ Please don't use "UPDATE". Instead, revise your question so it reads well for someone who encounters it for the first time. See cs.meta.stackexchange.com/questions/657/… $\endgroup$ Commented Jun 27, 2023 at 7:50

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No one can tell you what will be best; you'll have to try different approaches and see what works best in your setting.

I think one reasonable approach worth trying is to filter the data using a Kalman filter, then find the filtered point that is closest to the origin (or target) (without trying to look for upward/downward trends).

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