Breaking the Gaussian Barrier: Leveraging ReGVAMP to Extend EKF and IEKF

In the non-linear hidden Markov chain (HMC) model, commonly employed in robotics, navigation, signal processing, and control systems, various variants of Kalman filter (KF) like the Extended Kalman Filter (EKF) and Iterated Extended Kalman Filter (IEKF) have been developed for different scenarios, with their limitations and advantages. However, their effectiveness can diminish in the presence of non-Gaussian noise, which is prevalent in many real-world situations. This paper presents a novel approach to tackle non-Gaussian noise leveraging the revisited Generalized Vector Approximate Message Passing (ReGVAMP) within the context of EKF and IEKF. ReGVAMP extends these KF variants to break the Gaussian barrier, thereby enhancing the accuracy of state estimation. A tracking simulation validated the feasibility of our proposed algorithms.