Foundations and Extensions of Kalman Filtering Beyond Gaussian Noise

Abstract

Kalman filtering remains one of the most influential ideas in modern engineering, underpinning systems that range from autonomous robots and navigation systems to biomedical monitoring and cyber-physical security. This talk presents an overview of my research on Kalman-based state estimation, with an emphasis on how classical theory must be extended to address real-world challenges such as non-Gaussian noise, model mismatch, and systems influenced by unknown external measurement disturbances.

I will begin with an intuition-driven overview of the Kalman filter and its nonlinear variants, revisiting the foundational result that the Kalman filter is the best linear unbiased estimator (BLUE) and is optimal only under zero-mean Gaussian noise assumptions—conditions that are not always guaranteed in practice. I will then present recent advances from my research group that relax these assumptions, including Kalman filter formulations for systems whose measurements are modeled as a doubly stochastic Poisson (Cox) process, as well as systems with state-dependent noise.

I will then transition to recent advances from my research group that incorporate higher-order uncertainty information, adaptive filtering, and robustness to corrupted or incomplete sensor data. The goal of the talk is to connect theory with practice by highlighting the limitations of classical assumptions, presenting principled extensions of Kalman filtering, and providing graduate students with insight into open research problems in modern state estimation.

Bio

Dr. Donald Ebeigbe is an Assistant Professor in the Department of Electrical Engineering at The Pennsylvania State University, where he directs the Control and Autonomous Robotics Lab (CARL). His research focuses on state estimation and controls and their applications to robotics, cyber-physical systems, and biological systems. He received his B.Eng. in Electrical and Electronics Engineering from the Federal University of Technology, Akure, Nigeria, in 2011, and his Ph.D. in Electrical Engineering from Cleveland State University in 2019. He joined Penn State in 2019 as a Postdoctoral Scholar in the Center for Neural Engineering, where he developed estimation and control methods for predictive modeling in biological and health-related systems, and began his appointment as an Assistant Professor in 2022.