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This paper addresses the problem of input and state joint estimation for linear discrete-time stochastic systems without direct feedthrough from unknown input to output.The input estimate is obtained from the multi-step innovation by least square estimation while the state estimate is obtained from the input estimate and the standard Kalman filter.This method still performs well when the dimension of the unknown input vector is equal to that of the state vector.The effectiveness of the proposed method is demonstrated through the numerical example.Finally,the method is applied to an anaerobic digestion process to estimate the concentration of the dissolved methane and the carbon dioxide in the anaerobic digestion reactor.