Online updating and uncertainty quantification using nonstationary output-only measurement

• A novel approach is proposed to estimate the noise covariance matrices for extended Kalman filter.
• It is applicable to stationary/nonstationary response of linear/nonlinear systems.
• It provides reliable parametric identification.
• It provides reliable uncertainty quantification.

Extended Kalman filter (EKF) is widely adopted for state estimation and parametric identification of dynamical systems. In this algorithm, it is required to specify the covariance matrices of the process noise and measurement noise based on prior knowledge. However, improper assignment of these noise covariance matrices leads to unreliable estimation and misleading uncertainty estimation on the system state and model parameters. Furthermore, it may induce diverging estimation. To resolve these problems, we propose a Bayesian probabilistic algorithm for online estimation of the noise parameters which are used to characterize the noise covariance matrices. There are three major appealing features of the proposed approach. First, it resolves the divergence problem in the conventional usage of EKF due to improper choice of the noise covariance matrices. Second, the proposed approach ensures the reliability of the uncertainty quantification. Finally, since the noise parameters are allowed to be time-varying, nonstationary process noise and/or measurement noise are explicitly taken into account. Examples using stationary/nonstationary response of linear/nonlinear time-varying dynamical systems are presented to demonstrate the efficacy of the proposed approach. Furthermore, comparison with the conventional usage of EKF will be provided to reveal the necessity of the proposed approach for reliable model updating and uncertainty quantification.