This paper provides a unified approach to observability checking, critical measurements identification, determination of observable islands, identification of irrelevant boundary injections, and pseudo-measurements selection to restore observability. A robust yet efficient algebraic technique is proposed. Several simple examples are used to illustrate the capabilities of the proposed procedure. Results from large case studies are presented to demonstrate the appropriate computational behavior

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... the proposed algorithms. Finally, conclusions are duly drawn. Index Terms-Linear algebra, null space, observability analysis, orthogonal transformation, power system state estimation.