Learning uncertainty in state estimation with applications for robotic systems

State estimation is crucial for accurate operations of robotic systems. Traditional state estimation methods often assume fixed noise models, which can lead to suboptimal performance when the system dynamics or the environment introduces varying levels of uncertainty. This thesis proposes novel approaches to learning uncertainty in state estimation, focusing on dynamic uncertainty that evolves with the system’s state. By incorporating variational inference methods, we present estimation frameworks capable of adapting the uncertainty model based on real-time data, ensuring more accurate and reliable state estimates. The proposed approaches are evaluated through several applications in robotic systems, including wind estimation by small unmanned aerial vehicles (sUAVs), where inaccuracies in the drag force modeling introduce significant uncertainty in the system. We introduce three novel Variational Wishart Process (VWP) algorithms to learn state-dependent uncertainties and leverage these VWP algorithms to develop a novel Variational Bayesian Adaptive Kalman Filter (VB-AKF) that jointly estimates system states and their associated uncertainties, including state-dependent covariances. Results from both simulated and experimental datasets demonstrate strong performance of the proposed algorithms and show that incorporating dynamic uncertainty improves state estimation accuracy and yields reliable confidence bounds.