I have a problem which can be boiled down to the following simplification: An irregular target is moving on a 2d plane in a non-random but unknown way. I have a number of snapshots of the target in the 2d plane, so I have N samples of the targets location. The movement is back-and-forth / circular in nature, so it does not move across the plane but on the plane.
I want to shoot the plane in such a way that I hit >99% of the targets surface, while minimizing misses while the target is moving and minimizing the amount of hits needed. I cannot observe the target while shooting it, so I have to base my hits on previous observations. I also don't know the starting or current position of the target, just the location of the plane it moves upon.
The assumption is that the N samples I have will sufficiently 'predict' the possible locations of the target in the future (it's all I have). I also assume I can hit the plane with 100% accuracy.
One of the methods I came up with is create a probability distribution of the targets location over time, then hitting the plane with an intensity related to the probability the target is at that location. This way I cannot ensure however I hit enough of the targets surface. I can simulate hits, misses, and target coverage, but I don't know how to calculate these.
Are there any other ways I can calculate this? Simulate it? Are there any real-world examples that already do something similar?
I have an analogy to further simplify it: I have a video snapshot of a moving target, and I want to paint the target using a paintball gun. I don't want to hit the background, and I have to shoot at it blindly. My paintball gun has a 100% accuracy.
Thanks for any suggestions!