Online Noise Identification for Joint State and Parameter Estimation of Nonlinear Systems

Abstract

The quality of structural parameter identification in nonlinear systems using Bayesian estimators, such as the unscented Kalman filter (UKF), depends heavily on the assumptions about the state and observation noise processes. In most practical situations though, the noise statistics are not known a priori. While the literature is rich in the area of offline approaches to noise estimation (often as part of model updating in general; the focus is not necessarily on noise parameters), there seems to be shortage of online implementations, which would be useful in structural health monitoring. Assuming that both noises (in the state and observation equations) are additive Gaussian processes, this study investigates how their statistics could be adaptively estimated online during the identification. By introducing certain distributional assumptions for the unknown noise parameters which exploit conjugacy, noise updating is simplified and is suitable for online applications. The proposed method is validated through two illustrative numerical applications. The first, on synthetically generated data where noise is introduced artificially, explores the efficiency of the method in identifying diagonal-only and full noise covariance matrices, as well as sudden changes of the observation noise level. In the second experimental example, the aim is to stabilize the UKF and estimate the parameters of a mathematical model that captures the observed hysteretic behavior in a setting where noise characteristics are indeed unknown. In the latter case, both the noise mean and covariance are adaptive during the identification.