Estimating Velocity from Fuzzy Position Data with Known Uncertainty
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.
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.