New forms of extended Kalman filter via transversal linearization and applications to structural system identification

Abstract

Two novel forms of the extended Kalman filter (EKF) are proposed for parameter estimation in the context of problems of interest in structural mechanics. These filters are based on variants of the derivative-free locally transversal linearization (LTL) and multi-step transversal linearization (MTrL) schemes. Thus, unlike the conventional EKF, the proposed filters do not need computing Jacobian matrices at any stage. While the LTL-based filter provides a single-step procedure, the MTrL-based filter works over multiple time-steps and finds the system transition matrix of the conditionally linearized vector field through Magnus’ expansion. Other major advantages of the new filters over the conventional EKF are in their superior numerical accuracy and considerably less sensitivity to the choice of time-step sizes. A host of numerical illustrations, covering single- as well as multi-degree-of-freedom oscillators with time-invariant parameters and those with discontinuous temporal variations, are presented to confirm the numerical advantages of the novel forms of EKF over the conventional one.