Estimating Velocity from Fuzzy Position Data with Known Uncertainty

Question

I was wondering if someone could maybe clarify or direct me to the best answer for this question. I want to estimate velocities from position data. However, the position data is fuzzy but I have an idea of its uncertainty. My initial sense is that one is supposed to use some iteration of a Kalman filter, but from my limited understanding of it, you need to know at least one parameter with some certainty, i.e., the position data. So to summarize, my questions are:

1. Is it possible to estimate velocity values given fuzzy position data?
2. If so, what are some available techniques for doing so?

Answer 1

1. Yes it is. That what's Kalman filter is all about. Your measurement includes position data, and there is a hidden velocity parameter. You will need some kind of model, like constant-velocity. You can input your idea of uncertainty into Kalman noise matrixes to improve results.

2. You can use Kalman filter, which is good to predict the future. If you just want to estimate the velocity in post-processing step (after you have all data), you can use something simpler, like estimating the derivative. This will have the advantage of being smoother and more accurate.