noisy observations

We consider boundary value problems with periodic boundary conditions for first-order linear systems of impulsive ordinary differential equations with unknown right-hand sides and jumps of solutions at the impulse points entering into the statement of these problems which are assumed to be subjected to some quadratic restrictions.  From indirect noisy observations of their solutions on a finite system of intervals, we obtain the optimal, in certain sense, estimates of images of their right-hand sides under linear continuous operators.  Under the condition that the unknown correlation functi

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