Simultaneous input and state estimation with a delay

In this paper, we present recursive algorithms for linear discrete-time stochastic systems that simultaneously estimate the states and unknown inputs in an unbiased minimum-variance sense with a delay. By allowing potential delays in state estimation, the stricter assumptions in a previous work [1] can be relaxed. Moreover, we show that a system property known as strong detectability plays a key role in the existence and stability of the asymptotic estimator with a delay we propose.