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This paper presents a very fast power system state estimating algorithm to solve the power system state estimation problem. Conventional techniques of state estimation, which are based on the Weighted Least Square (WLS) method, face many issues, including lack of observability, high sensitivity to model parameters and long calculation time in large power systems. The main objective of conventional WLS methods is to minimize a linear objective function, while the aim of the presented method is to improve the results of conventional algorithms and obtain the least minimum possible value of the linear objective function alongside solving the problems mentioned above, by means of an iterative method. The proposed approach is tested on IEEE 14, 30 and 57 bus test systems using MATLAB software. The results reflect the considerable performance of the proposed method. [ABSTRACT FROM AUTHOR]