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This paper presents a numerical method for observability analysis and restoration in power system state estimation based on Gram matrix factorization. A method to identify observable islands based on minimum norm solutions is also presented. The method has the advantage of being easy to implement because all information used for the new formulation can be extracted or adapted from operations that are present in conventional state estimation. The observability analysis and restoration are performed in a single step in which measurements and pseudo-measurements are processed. If the system is nonobservable, minimum norm solutions obtained with nonredundant measurements are used to identify observable islands and, in the sequel, with the results of Gram matrix factorization, a set of nonredundant injection measurements that restore the global observability of the system is obtained. This approach is an alternative to the classical observability analysis and results in methods that are robust and suitable to be used in real-time applications. Numerical examples to show the performance of the methods are presented.