A robust algorithm to test the observability of large linear systems with unknown parameters

This work proposes a robust algorithm to examine the observability of linear systems whose dynamic states and parameters are to be identified. The observability of a dynamical system plays a fundamental role in predicting whether it would be successful to use system identification methods to estimate the dynamic states and parameters of the system from a given set of input-output measurements. The motivation of the development of the suggested algorithm arises from the need to address the significant physical memory requirements of the standard implementation of the Observability Rank Condition (ORC). The high computational cost of the ORC substantially limits its applicability to real-world engineering systems, even when the underlying dynamics can be reasonably approximated as linear. The framework of the algorithm is obtained through the derivation of a recursive formula for the computation of the observability matrix of linear systems with unknown parameters. To further improve the efficiency, robust numerical implementations of the algorithm are achieved through random realizations of the dynamic states and parameters and the use of modular operations. The superior performance of the algorithm is demonstrated using several examples of large linear dynamical models of engineering systems containing up to thousands of dynamic states and parameters