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This book is about the application of linear filtering theory in vibrations of structure in fluid. The stress is laid on mathmatical models which, in the theory of system, characterize the state of a dynamic system. The models are in the form of linear Ito stochastic differential equations. Discretization of the models which leads to straightforward computer applications is discussed. An approach to nonlinear problems based on the expansion of random functions in a series is presented. Examples of application of Kalman filters are given, which refer to vibrations of cylinders in waves.