Summary: The problems of stable solution according to Hadamard to the problem of multidimensional and optimal Wiener filtration, in the mean quadratic sense, at experimentally known input data are discussed. On the basis of the theory, developed by the author, an approach to the synthesis of \(\Omega\)-optimal multidimensional filters is introduced, keeping the natural properties of the initial physical problem. Effective algorithms for stable determination of the weight function of the optimal multidimensional filter and approaches for choosing a vector parameter of the regularization and stabilizing functional for solving the regularized form of the Wiener-Hopf vector-matrix integral equation are proposed.
The algorithm for synthesis of \(\Omega\)-optimal multidimensional filters is stable with respect to approximation errors, rounding and additive disturbances in input data. It can be used in a number of problems with arbitrary dimensions in the optimal filtering and identification of systems.