Power system state estimation is heavily subjected to measurement error, which comes from the noise of measuring instruments, communication noise, and some unclear randomness. Traditional weighted least square (WLS), as the most universal state estimation method, attempts to minimize the residual between measurements and the estimation of measured variables, but it is unable to handle the measurement error. To solve this problem, based on random matrix theory, this paper proposes a data-driven approach to clean measurement error in matrix-level. Our method significantly reduces the negative effect of measurement error, and conducts a two-stage state estimation scheme combined with WLS. In this method, a Hermitian matrix is constructed to establish an invertible relationship between the eigenvalues of measurements and their covariance matrix. Random matrix tools, combined with an optimization scheme, are used to clean measurement error by shrinking the eigenvalues of the covariance matrix. With great robustness and generality, our approach is particularly suitable for large interconnected power grids. Our method has been numerically evaluated using different testing systems, multiple models of measured noise and matrix size ratios.
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