A least squares estimator is derived for the state transition matrix phi of a linear, stationary sampled data system operating in a stochastic environment. The estimator is shown to be unbiased and minimum variance under the condition of full observability of the state vector of the system. The estimator is also shown to be the Maximum Likelihood Estimator for the case of the stochastic environment having Gaussian statistics. The estimation scheme is compared with two other recently published estimation schemes, both of which are shown to be special cases of the scheme herein presented.