Robust optimal experimental design for identifiability using the overall mean squared estimation error

Mathematical modeling is essential for understanding and controlling physical systems, particularly in scientific and engineering contexts. Accurate parameter estimation is critical for model reliability but often constrained by the cost and complexity of experiments. Optimal Experimental Design (OED) addresses this challenge by identifying experimental conditions that maximize information gain. Traditional OED approaches rely on the Fisher Information Matrix (FIM) and scalar optimality criteria, yet they are sensitive to unknown parameter values. To mitigate this, robust OED methods incorporate prior uncertainty, using strategies such as maximin and expectation-based criteria. In this work, we introduce a novel robust OED framework that unifies prior parameter uncertainty and measurement noise into an Overall Mean Squared estimation Error (OMSE) matrix. This formulation enables the use of standard optimality criteria while inherently accounting for both sources of uncertainty/noise. We demonstrate the effectiveness of our method through two case studies involving dynamical systems of varying complexity and discuss practical considerations for its implementation.