Unbiased Minimum-Variance Input and State Estimation for Systems with Unknown Inputs: An Online Solution

It is well-known that the optimal MSDISE (multi-step delayed input and state estimation) solution is a smoothed result, which may not be practical for online estimation. In this paper, an online MSDISE, which is obtained by using a linear line segment prediction of the optimal MSDISE solutions, is proposed to solve the inherent time-delay problem of the MSDISE. To facilitate the design, the optimal MSDISE is derived by using the recently proposed time-distributed unknown input filtering technique. It is shown that the filtering performance of the online MSDISE can approximate to that of the optimal MSDISE. A simulation example is given to show the effectiveness of the proposed results.