The approximate solution of a problem of linear optimal filtration

Abstract

The problem of signal restoration in systems with operator coefficients is considered in the presence of colored (nonwhite) noise in measurements. In this case, the problem of linear filtration is ill-posed. A method for finding an approximate solution to this problem is proposed. The method is based on Tikhonov’s regularization and on the reduction of the linear optimization problem in systems with operator coefficients to that in systems described by ordinary differential equations. The convergence of the algorithm is proved.