  This paper discusses the problem of determining optimal designs for
regression models, when the observations are dependent and taken on an
interval. A complete solution of this challenging optimal design problem is
given for a broad class of regression models and covariance kernels.
  We propose a class of estimators which are only slightly more complicated
than the ordinary least-squares estimators. We then demonstrate that we can
design the experiments, such that asymptotically the new estimators achieve the
same precision as the best linear unbiased estimator computed for the whole
trajectory of the process. As a by-product we derive explicit expressions for
the BLUE in the continuous time model and analytic expressions for the optimal
designs in a wide class of regression models. We also demonstrate that for a
finite number of observations the precision of the proposed procedure, which
includes the estimator and design, is very close to the best achievable. The
results are illustrated on a few numerical examples.
