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This paper introduces backtracking and trust region methods into power system state estimation. The traditional Newton (Gauss-Newton) method is not always reliable particularly in the presence of bad data, topological or parameter errors. The motivation was to enhance convergence properties of the state estimator under those conditions, and together with QR factorization to make a globally convergent and reliable algorithm. The trust region formulation shows that such a model is more robust than the traditional Newton (Gauss-Newton) or Backtracking (line search) algorithm. Both algorithms have been programmed and applied to representative power networks, and the computational requirement has been found.