My layman understanding of the Uncertainty Principle is that you can’t determine the both the position and momentum of a particle at the same point in time, because measuring one variable changes the other, and both cannot be measured at once.
But what happens if I measure a charged particle with any number of detectors over a period of time? Can I use a multitude of measurements to infer these properties for some point in the past? If not, how close can we get? That is, how precise can our estimate be?