The growing importance of electric energy for survival and societal development has led to larger energy supply systems, posing challenges in maintaining a reliable power supply. Phasor measurement units (PMUs) are used to monitor and analyze these systems, but it is not feasible to install measuring units at every endpoint due to their size and cost. State estimation (SE) techniques are employed to filter redundant or incorrect measurements to produce reliable estimations. This paper proposes a Linear Robust Static State Estimation (LRSSE) technique using the Generalized Maximum Likelihood (G-M) estimator combined with a Linear Static Estimation (LSSE) algorithm for estimating power system states, comprising voltage magnitudes and phase angles, are assessed while accounting for unidentified noise statistics in a linear measurement model obtained from PMUs. The algorithm incorporates a mixture of Gaussian and non-Gaussian noise to simulate unknown noise statistics and also a Recursive Covariance Estimation (RCE) approach is employed to estimate the covariance matrix. The efficacy of the algorithm against the bad data is evaluated on both the IEEE 57 Bus test System and the IEEE 118 Bus test System. The outcomes are juxtaposed with the prevalent LSSE technique under outlier scenarios, employing diverse performance metrics and statistical parameters.