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This paper provides a numerical approach to observability analysis, pseudo-measurements selection to restore observability, and identification of critical measurements and critical sets on three-phase state estimation. The approach enables observability analysis and restoration (pseudo-measurements selection) in a straightforward and simple way, without iteration, via triangular factorization of the Jacobian matrix of the weighted least square three-phase state estimator. By analyzing the structure of the matrix resulting from this factorization, the HΔ3φ matrix, the approach enables the identification of critical measurements and critical sets. Numerical examples to show the performance of the approach are presented.