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We study a finite-horizon robust minimax filtering problem for time-varying discrete-time stochastic uncertain systems. The uncertainty in the system is characterized by a set of probability measures under which the stochastic noises, driving the system, are defined. The optimal minimax filter has been found by applying techniques of risk-sensitive linear-quadratic exponential Gaussian (LEQG) control. The structure and properties of the resulting filter are analyzed and compared to H∞ and Kalman filters.