Guaranteed recovery of unknown data from indirect noisy observations of their solutions on a finite system of points and intervals
We consider the Cauchy problem for the first-order linear systems of ordinary differential equations with unknown right-hand sides and initial conditions that are supposed to be subjected to some quadratic restrictions. From indirect noisy observations of their solutions on a finite system of points and intervals, we obtain the linear guaranteed mean square estimates of linear functionals on unknown data of the above-mentioned problems. It is established that if the correlation functions of observational errors are not known and belong to special sets, such estimates are expressed via so