An iterative augmented unscented Kalman filter for simultaneous state-parameter-input estimation for systems with/without direct feedthrough

Abstract

A few unscented Kalman filters (UKFs) have been developed for simultaneous state-parameter-input estimation, however, these UKFs often have at least one of these limitations: requiring ad hoc procedures; requiring displacement measurements, which may be inconvenient to obtain, to fuse with acceleration measurements to avoid the “drift phenomenon” in the estimated displacement responses and unknown inputs; requiring a (full-rank) feedthrough matrix; and undesirable computational efficiency. To overcome these limitations, a novel iterative augmented unscented Kalman filter (IAUKF) for simultaneous state-parameter-input estimation for systems either with or without direct feedthrough is developed and examined in this study. The IAUKF closely follows the Bayes’ theorem with no ad hoc procedure, featuring theoretical simplicity. An iterative strategy is introduced to improve the accuracy of the unknown input estimation at each time step, so that the “drift phenomenon” encountered by the existing augmented Kalman filter is avoided. Further, the IAUKF requires no prior models for the time histories of the unknown inputs and applies to systems with/without direct feedthrough. With realistic assumptions, the steps for computationally efficient implementations of the IAUKF are proposed. Numerical examples of nonlinear structural systems with/without direct feedthrough of the unknown inputs are adopted to examine the effectiveness and the computational efficiency of the IAUKF.