A general extended Kalman filter for simultaneous estimation of system and unknown inputs

• An EKF that simultaneously identifies structural parameters and unknown inputs is proposed.
• The EKF method can handle more general measurement scenarios than before.
• Recursive solutions are obtained with least-squares estimation of an extended state vector.
• Decomposition technique is applied to extract the proposed EKF from the recursive solutions.
• The mathematical basis of the EKF method is rigorous based on global optimization.

The traditional Extended Kalman filter (EKF) is a useful tool for structural parameter identification with limited observations. It is, however, not applicable when the excitations on the structure are unknown or the excitation locations are not monitored. A novel Extended Kalman filter approach referred to as the General Extended Kalman filter with unknown inputs (GEKF-UI) is proposed to estimate the structural parameters and the unknown excitations (inputs) simultaneously. The proposed GEKF-UI gives an analytical EKF solution dealing with the more general measurement scenarios with the existing EKF methods as its special cases. Existing constraints on sensor configuration have been removed enabling more general application to complex structures. Simulation results from a 3-storey linear damped shear building, an ASCE benchmark structure and a two-storey planar frame structure are used to validate the proposed method for both time-invariant and time-varying system identification.