Robust Extended Kalman Filter for Transient Tracking and Outlier Suppression

A new filter is proposed that achieves reliable state estimation in nonlinear systems with multiple equilibrium points. The latter may exhibit strong nonlinearity and sudden transient behavior triggered by either system process noise, or observation noise, or outliers. Our filter is able to output the correct qualitative state over time quickly and reliably when the system dynamics experience switch-like transitions. It yields robust performance through two key features: (a) existence of observation redundancy in the filter equations and (b) application of generalized maximum likelihood (GM-) estimators when solving for the system states in an extended Kalman filter (EKF) methodology. Our filter, which we call the GM-EKF, is formulated in a batch-mode regression form to process the observations and predictions together. This observation redundancy allows the GM-EKF to track system transitions from one equilibrium point to another one much more reliably and in a faster way than the conventional EKF, even when the observation noise variances are much larger than the system process noise variances. As for the GM-estimator, it enables the filter to bound the influence of outliers while maintaining a high statistical efficiency when the system is resident around a stable equilibrium point. Results are presented from simulations applying the EKF and GMEKF on the Langevin model, which is commonly used to model climate transitions. These simulations reveal the improvements in estimation efficiency, robustness, and reduced time delay when tracking the transitions.