  This paper first strictly proved that the growth of the second moment of a
large class of Gaussian processes is not greater than power function and the
covariance matrix is strictly positive definite. Under these two conditions,
the maximum likelihood estimators of the mean and variance of such classes of
drift Gaussian process have strong consistency under broader growth of t_n. At
the same time, the asymptotic normality of binary random vectors and the
Berry-Ess\'{e}en bound of estimators are obtained by using the Stein's method
via Malliavian calculus.
