Backward-in-time input reconstruction

Input reconstruction is the problem of reconstructing unknown inputs to the system, be it deterministic or stochastic or a combination of both, from knowledge of plant model and the output measurements alone. Being a fundamental and long-standing problem, the literature on this topic is extensive, but is also somewhat fragmented. Furthermore, connections between feasibility of input reconstruction and zeros of the system have been established in the literature. In this paper, we explore possible methods to reconstruct inputs for systems with non-minimum phase zeros. Although the existing literature suggests that in the presence of non-minimum phase zeros, any estimator will yield an error that grows in time, we are able to overcome this problem by developing an estimator that goes backward in time.