A Gram Matrix-Based Method for Observability Restoration

This letter presents an improved numerical algorithm for observability restoration of unobservable systems. The algorithm provides a minimal set of measurements to render the system observable, by checking the pivots in the triangular factors of a Gram matrix associated with a Jacobian matrix corresponding to a reduced network and measurement set. The dimension of the Gram matrix is equal to the number of existing and candidate boundary measurements at observable islands, that is relatively low even for very large systems. That makes the proposed method fast and computationally efficient. An example is given to illustrate the details of the proposed method.