Abstract
The article addresses the problem of simultaneous estimation of states and parameters for a class of systems described by nonlinear ordinary differential equations, which model the operation of a counterflow heat exchanger. The augmented vector, which includes both states and parameters, is partially unobservable, and as shown by the analysis of global and local identifiability based on available experimental data, the estimation problem is ill-conditioned and requires regularization. For this purpose, a subset of estimable parameters was selected using an orthogonal method and a D-criterion optimization algorithm. Based on the experimental data, simultaneous estimation of states and parameters was performed using the UKF, with the set of estimated parameters including both the selected subset and competing parameter sets. Experimental-statistical modeling demonstrated that regularizing the estimation problem led to better results compared to non-optimal ones, and residual correlation analysis supports the conclusion of their reliability.