A numerical identifiability test for state-space models application to optimal experimental design

This paper describes a mathematical tool for identifiability analysis. easi ly applicable to high order non-linear systems modelled in state-space and implementable in simulators with a time-discrete approach. This procedure a lso permits a rigorous analysis of the expected estimation errors (average and maximum) in calibration experiments. The methodology is based on the re cursive numerical evaluation of the information matrix during the simulatio n of a calibration experiment and in the setting-up of a group of informati on parameters based on geometric interpretations of this matrix. As an exam ple of the utility of the proposed test, the paper presents its application to an optimal experimental design of ASM Model No.1 calibration, in order to estimate the maximum specific growth rate mu (H) and the concentration o f heterotrophic biomass X-BH.