Correntropy based IPKF filter for parameter estimation in presence of non-stationary noise process

Abstract

Existing filtering based structural health monitoring (SHM) algorithms assume constant noise environment which does not always conform to the reality as noise is hardly stationary. Thus to ensure optimal solution even with non-stationary noise processes, the assumed statistical noise models have to be updated periodically. This work incorporates a modification in the existing Interacting Particle-Kalman Filter (IPKF) to enhance its detection capability in presence of non-stationary noise processes. To achieve noise adaptability, the proposed algorithm recursively estimates and updates the current noise statistics using the post-IPKF residual uncertainty in prediction as a measurement which in turn enhances the optimality in the solution as well.Further, this algorithm also attempts to mitigate the ill effects of abrupt change in noise statistics which most often deteriorates/ diverges the estimation. For this, the Kalman filters (KF) within the IPKF have been replaced with a maximum Correntropy criterion (MCC) based KF that, unlike regular KF, takes moments beyond second order into consideration. A Gaussian kernel for MCC criterion is employed to define a correntropy index that controls the update in state and noise estimates in each recursive steps. Numerical experiments on an eight degrees-of-freedom system establish the potential of this algorithm in real field applications.