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The paper proposes a new tool for real-time assessment of measurement sets in the context of power-system-state estimation. This tool incorporates many functions including observability analysis and restoration, as well as identification of critical measurements and critical sets. Using only network-topology data, the proposed methodology updates the qualitative characteristics of the current available measurement set in real time. The identification of critical measurements and sets is done using only network topology and is completed before running any state estimation. Mapping the system states and using information concepts, a new state space is obtained where the relationship (information) between measurements and states is straightforward. This map is easily found via triangular factorisation of the Jacobian matrix. Starting from a base-case measurement set, every time a snapshot of measurements has to be analysed, only refactorisation has to be carried out. Sparse-matrix techniques speed up the process. The method was tested in the IEEE-14-bus system as well as in the Brazilian 383-bus system, proving to be reliable, fast, easy to implement and suitable for real-time operation.