Robust Hybrid EKF approach for state estimation in multi-scale nonlinear singularly perturbed systems

In this paper a general framework is developed for state estimation in a class of nonlinear continuous-time singularly perturbed systems. Our approach is based on the hybrid extended Kalman filter in which observations are originated from discrete measurements. The developed framework is also extended to include linearization error in the observation equation as uncertainty in the estimation filter design. The boundedness of both a priori and a posteriori estimation error covariance matrices is considered as a criterion for the algorithm to have bounded estimation errors. As an approximation method for the estimation covariance matrices in the singularly perturbed system, the matched asymptotic series method is utilized to include the effects of initial conditions by approximating the boundary layer solution in order to attain more accurate filter gain approximation. The developed Hybrid Robust EKF (HREKF) strategy can be used as an estimation method for tracking the effects of hidden damage in a nonlinear system.