Novel recursive optimal filter for the joint input-state estimation in linear discrete-time systems

This paper presents a new recursive optimal filter structure for joint input and state estimation of linear time-varying discrete systems in the presence of unknown inputs. The method is concerned with the direct feedthrough matrix which has an arbitrary rank. The resulting filter is optimal in the sense of the unbiased minimum-variance (UMV) criteria. The paper extends the existing results, in particular the ones of Hsieh in 2009. A numerical example is given in order to make a comparison between the proposed filter and the Hsieh filter developed by [7].