Generalization of a Parameter Set Selection Procedure based upon Orthogonal Projections and the D-Optimality Criterion

Many models derived from first principles contain more parameters than can be reliably estimated from data. Selecting a subset of the parameters for estimation is one common approach to deal with this problem. One popular method sequentially selects parameters based upon orthogonalization of the sensitivity vectors, however, it has the drawback that only one parameter is added at each step of the iteration and that no correlations of not yet chosen parameters can be taken into account. In order to address this drawback, a generalization of the parameter set selection procedure based upon orthogonalization is presented in this work. The procedure can add any number of parameters at each iteration such that correlations among the parameters that will be added to the set of estimated parameters can be taken into account. It is shown that two existing parameter set selection techniques form special cases of the presented method.