Unknown Input Kalman Filtering for Linear Discrete-Time Fractional Order Systems With Direct Feedthrough

This paper presents an algorithm for a joint estimation of pseudo states and unknown inputs of a fractional order system. The special case where the unknown inputs have direct feedthrough to the outputs is considered. Necessary and sufficient conditions are given under which an unbiased pseudo state and input estimation is possible. The prediction step of the fractional Kalman filter uses an approximation as it can not be calculated exactly in practice. Therefore, the estimation procedure is suboptimal. Nevertheless, the method yields accurate estimates of pseudo states and unknown inputs which is illustrated by means of an academic example.