Problem Diagnostics and Model Refinement in Dynamic Parameter Estimation

In order to confront the problem of dynamic parameter estimation in face of the many uncertainties involved we propose to carry out an iterative process involving cycles of model specification, solution, analysis and diagnostics, and model modification if necessary. The objective is to suggest a systematic procedure that can ensure arriving at a maximal set of physically feasible parameter values, based on the available data and the suggested model. The proposed procedure is demonstrated using both the sequential and simultaneous approaches, gradient based and direct search minimization methods, and use of scaled compared to non-scaled data. The quality of the resulting model is assessed based on the comparison of the integrated values with the data, residual plots, confidence interval-to-parameter value ratios and the objective function value.