Robust Measurement Selection Design for Experimental Systems with Input Uncertainty

Input uncertainty in experimental implementation deteriorates data quality for parameter estimation. This work aims to examine the influence of input uncertainty, in particular the inaccurate setting of initial states, to parameter estimation and explore methods to mitigate the effects. First, a Monte-Carlo method is employed to generate input-output data. The input uncertainty is assumed to follow Gaussian distribution. Samples are taken from the uncertainty region and used to produce output through the dynamic system. Statistical characteristics are utilised to quantify uncertainty in outputs. Then a robust experimental design (RED) is proposed, in which the states that are less affected by input uncertainty are selected as measurement state variables. In addition, two different residual functions are used in parameter estimation to compare the estimation robustness against data uncertainty. Simulation studies are conducted using a benchmark enzyme reaction system. Compared to the non-designed experimental settings, improved parameter estimation is achieved via robust design.