In recent years, Smart Grid was introduced to achieve an environmentally-friendly, adequate, secure and fossil fuel-independent power system. The large scale smart grid studies require accurate state estimation to obtain an acceptable adequacy level. There exist some challenges regarding anomalous power flow studies which motivate grid operators to utilize robust and accurate estimation methods. Therefore, power system state estimators play a pivotal role in real-time grid management. In this paper, a sequential linear minimum mean square error (LMMSE) estimator is utilized to solve the DC power flow problem. First, we introduce the classic linear estimator model which assumes that to-be-estimated parameter values are unknown but deterministic. The LMMSE estimator will be discussed which treats the to-be-estimated parameter as a random variable with a known prior probability density function (pdf). We evaluate the accuracy of the LMMSE estimator by comparing it with maximum likelihood estimator (MLE). Finally, the effect of covariance matrix topology will be studied by defining three scenarios with different noise covariance matrices.