A unified extension of the robust two-stage Kalman filter and its application to functional filtering

This paper extends previous work on robust two-stage Kalman filter (RTSKF) for systems with unknown inputs affecting both the system state and the output. By making use of an augmented known input model, an augmented unknown input model, an unknown input error dynamics model, and the previously proposed RTSKF, a unified extension of the RTSKF is further proposed to enhance the unknown input filtering performance. Through the global optimality analysis technique, the conditions under which the unknown input filter and the system state estimator of the RTSKF can both achieve the globally optimal filtering performances are provided. An application of this new RTSKF to functional filtering problem is addressed.