Optimal Estimation of a Signal Perturbed by a Fractional Brownian Noise

Abstract

We consider the problem of optimal estimation of the value of a vector parameter $\thetavector=(\theta_0,\ldots,\theta_n)^{\top}$ of the drift term in a fractional Brownian motion represented by the finite sum $\sum_{i=0}^{n}\theta_{i}\varphi_{i}(t)$ over known functions $\varphi_i(t)$, $\alli$. For the value of parameter $\thetavector$, we obtain a maximum likelihood estimate as well as Bayesian estimates for normal and uniform a priori distributions.