Using mean-variance, I estimate a co-variance matrix $\Sigma$ to obtain the best weights in my portfolio.
However, there are other ways to compute the volatility $\sigma$ than historical standard deviation, for instance using Yang and Zhang estimator.
I don't understand however the link between the vol. estimation and the co-variance matrix. I know that on the diagonals you'll find the volatility, but how do you re-calculate the co-variance matrix after you have obtained more efficient volatility estimates?