You could compute a median of means, where you count clusters as single points by taking the mean of clusters as a single point.
You could compute the emperical distribution function along with a confidence interval. In your case you have a detail which is that your measured speed $V_i$ has some error $\sigma_i$ relative to the actual speed $U_i$, and you want to know the median of $U_i$. You could use a Monte Carlo approach to estimate the error in the estimated median.
Possibly simpler would be to compute mean of means which allows an easier estimation of the error.