  We consider a reflected Ornstein-Uhlenbeck process $X$ driven by a fractional
Brownian motion with Hurst parameter $H\in (0, \frac12) \cup (\frac12, 1)$. Our
goal is to estimate an unknown drift parameter $\alpha\in (-\infty,\infty)$ on
the basis of continuous observation of the state process. We establish Girsanov
theorem for the process $X$, derive the standard maximum likelihood estimator
of the drift parameter $\alpha$, and prove its strong consistency and
asymptotic normality. As an improved estimator, we obtain the explicit formulas
for the sequential maximum likelihood estimator and its mean squared error by
assuming the process is observed until a certain information reaches a
specified precision level. The estimator is shown to be unbiased, uniformly
normally distributed, and efficient in the mean square error sense.
