This paper describes the theoretical basis and some applications of a identifiability/observability test for state-space models based on the recursive calculation of the numerical condition of the observability matrix. This test evaluates the possibility of estimating the unknown states and parameters of a mathematical model under defined experimental conditions and available information. The numerical value of the proposed “observability parameter” is also an index of uncertainty propagation through the model. As examples of the utility of the proposed test, the paper presents the analysis of a reduced-order model for two wastewater treatment plant configurations (D-N and Alpha process), evaluating the on-line information that is theoretically indispensable in distinguishing each one of the unknown states and parameters under steady or dynamic conditions.

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