Abstract
The study presents a robust methodology for simultaneous state and parameter estimation in nonlinear thermal systems, demonstrated on a counter-current heat exchanger model operating with nitrogen under industrial conditions. To address challenges of ill-conditioning and parameter correlation, local sensitivity analysis is combined with regularization through optimal parameter subset selection using orthogonalization and D-optimal experimental design. The Unscented Kalman Filter (UKF) is employed to jointly estimate the augmented state vector in real time, leveraging high-fidelity dynamic simulations generated in Unisim Design with the Peng–Robinson equation of state. The proposed framework achieves high estimation accuracy and numerical stability, even under limited sensor availability and measurement noise. Monte Carlo simulations confirm robustness to ±2.5% uncertainty in initial conditions, while residual autocorrelation analysis validates estimator optimality. The approach provides a practical solution for real-time monitoring and model-based control in industrial heat exchangers and offers a generalizable strategy for building identifiable, noise-resilient models of complex nonlinear systems.