A Novel Methodology for Combined Parameter and Function Estimation Problems

This article presents a novel methodology, which is highly efficient and simple to implement, for simultaneous retrieval of a complete set of thermal coefficients in combined parameter and function estimation problems. Moreover, the effect of correlated unknown variables on convergence performance is examined. The present methodology is a combination of two different classical methods: The conjugate gradient method with adjoint problem (CGMAP) and Box–Kanemasu method (BKM). The methodology uses the benefit of CGMAP in handling function estimation problems and BKM for parameter estimation problems. One of the unique features about the present method is that the correlation among the separate unknowns does not disrupt the convergence of the problem. Numerical experiments using measurement errors are performed to verify the efficiency of the proposed method in solving the combined parameter and function estimation problems. The results obtained by the present approach show that the combined procedure can efficiently and reliably estimate the values of the unknown thermal coefficients.