A Greedy Algorithm for Observability Analysis

This letter presents a numerical algorithm for observability analysis. The proposed algorithm is based on a greedy strategy combined with a Gram-Schmidt orthonormalization procedure of the rows of the measurement Jacobian matrix. The algorithm outputs the system is observable with the available measurements, and if not, it looks for the best candidate measurements to restore observability. Also, an efficient calculation of the null space of the Jacobian matrix can be obtained. The algorithm is an improvement with respect to other existing algorithms that calculate a factorization of the Jacobian matrix. Throughout the process it is not necessary to invert matrices, nor select pivots and the errors caused when dividing by values close to zero are avoided. Four examples are given to illustrate the effectiveness of the proposed method.