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The article deals with set-valued estimation of dynamical system state when there is no statistical information about the initial state, disturbances and noises but the sets of their possible values are available. In some cases we can have additional information about disturbance dynamics that can improve the accuracy of the estimates. The article describes set-valued estimation algorithm when disturbance is decomposed as a system of functions with unknown coefficients. The comparison of estimates for the case when the kind of decomposition is known and the case when only a set of possible values is available is performed. [ABSTRACT FROM AUTHOR]