Solution of the linear filtration problem for hyperbolic systems

Abstract

The problem of restoring the signals in systems described by hyperbolic equations under colored noises in measurements is considered. It is well known that in this case the filtration problem 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 reduction the filtration problem formulated in terms of systems with operator coefficients to that formulated in terms of systems described by ordinary differential equations. The convergence of the method is proved.