Optimal sampling schedule with unknown but bounded measurement errors: Families of linear models

The problem of optimal sampling design for parameter estimation when data are generated by linear models is addressed. The measurements are assumed to be corrupted by unknown-but-bounded additive noise. The sampling design assumes that the samples number is free and no replication is allowed. Two main results are shown: 1) for particular classes of linear models, the optimal measurements number is equal to the parameters number, as in the statistical context; 2) the parameters uncertainty intervals of an actual realization are bounded from above by quantities that can be computed a priori, knowing only the model and the error structure.