An improved extended Kalman filter for parameters and loads identification without collocated measurements

As well-known, the extended Kalman filter (EKF) is a powerful tool for parameter identification with limited measurements. However, traditional EKF is not applicable when the external excitation is unknown. By using least-squares estimation (LSE) for force identification, an EKF with unknown input (EKF-UI) approach was recently proposed by the authors. In this approach, to ensure the influence matrix be of full column rank, the sensors have to be deployed at all the degrees-of -freedom (DOFs) corresponding to the unknown excitation, saying collocated measurements are required. However, it is not easy to guarantee that the sensors can be installed at all these locations. To circumvent this limitation, based on the idea of first-order -holder discretization (FOHD), an improved EKF with unknown input (IEKF-UI) approach is proposed in this study for the simultaneous identification of structural parameters and unknown excitation. By using projection matrix, an improved observation equation is obtained. Few displacement measurements are fused into the observation equation to avoid the so-called low-frequency drift. To avoid the ill-conditioning problem for force identification without collocated measurements, the idea of FOHD is employed. The recursive solution of the structural states and unknown loads is then analytically derived. The effectiveness of the proposed approach is validated via several numerical examples. Results show that the proposed approach is capable of satisfactorily identifying the parameters of linear and nonlinear structures and the unknown excitation applied to them.