Input reconstruction problem is usually encountered in the areas such as virtual sensing, image restoration, sensor linearization, and communications. The input reconstruction problem can be seen as an inverse problem. Given a nominal system, two types of approaches are commonly used for solving the inverse problem. The first one is to directly invert the nominal system, and the second one is to derive an inversion of the nominal system in an indirect way. However, for the first type of approaches, system inversion cannot be directly conducted under some conditions such as there exist nonminimum-phase zeros in the nominal system, while for the second type of approaches, simultaneously guaranteeing stability and causality of the obtained inversion is still not solved well. In order to avoid the drawbacks existing in the two types of approaches, an alternative approach is proposed for input reconstruction. In this approach, the input signal is first modeled as the output of a state-space model, afterwards two Kalman filters for the model resulted by combining the input signal model and the nominal system model are implemented alternatively such that the input signal can be sequentially reconstructed in an infinite horizon. The proposed input reconstruction approach is applied in two examples, and simulation results can illustrate the effectiveness of the proposed approach.
