Parameter estimation with multiple sources and levels of uncertainties

Least-squares designs are sensitive to errors in the data, which can be due to several factors including the approximation of complex models by simpler ones, the presence of unavoidable experimental errors when collecting data, or even due to unknown or unmodeled effects. In this paper, we formulate a new design criterion that treats multiple sources of uncertainties in the data with possibly varied degrees of intensity. We show that the solution has a regularized form, with one regularization parameter for each source of uncertainty. The parameters turn out to be model dependent and can be determined optimally as the nonnegative roots of certain coupled equations. Applications in array signal processing and image processing are considered.