Optimal estimation of a signal perturbed by a fractional Brownian noise

We consider the problem of optimal estimation of the value of a vector parameter $\text{thetavector}=({\theta }_0,\dots ,{\theta }_n{)}^{\mathrm{\top }}$ of the drift term in a fractional Brownian motion represented by the finite sum ${\sum }_{i=0}^n{\theta }_i{\phi }_i(t)$ over known functions ${\phi }_i(t)$, $\text{alli}$. For the value of parameter $\text{thetavector}$, we obtain a maximum likelihood estimate as well as Bayesian estimates for normal and uniform a priori distributions.