Estimation of Multi-Parameter Models by Least Squares and Adaptive Filters

Parameter estimation is based upon a comparison of predicted deterministic model responses to data. The models are often numerical, e.g., finite volume, with intrinsic inaccuracies. In addition, the models typically assume a full knowledge of the physical processes. By using the concept of state variables and employing the Kalman filter approach it is possible to include undetermined effects in the model. This paper describes such an approach to the estimation of thermal conductivity in a transiently heated and cooled one dimensional system and shows that it leads to a resolution of questions about the time behavior of the residuals previously observed in an estimation based upon the least squares analysis.