Simultaneous input and state estimation for uncertain discrete-time stochastic systems

This paper investigates the simultaneous unknown input and state estimation (SUISE) problem for a class of uncertain linear discrete-time stochastic systems with unknown input. First, the augmented system is constructed with the aid of the input model, which is described as a random walk process with finite covariance. Next, a robust filter for the augmented system is proposed. Then, a new SUISE algorithm is obtained from the robust filter as the covariance of the input approaches infinity. Finally, a simulation example illustrates the proposed SUISE algorithm’s effectiveness.