Back-and-forth operation of state observers and norm estimation of estimation error

In contrast to classical observers operating synchronously with the plant, this paper proposes a state estimation algorithm that executes Luenberger observers back-and-forth in time using the stored inputs and output signals. One benefit of this technique is to get rapid convergence of state estimation without relying on high injection gain, so that the amplification of measurement noise is much relieved. Moreover, by operating the observer in the proposed manner, we easily obtain an upper bound on the estimation error. Real-time applications of the proposed idea, and the effect of disturbances, are also discussed.