Autonomous platforms require accurate positioning to complete their tasks. To this end, a Kalman filter-based algorithms, such as the extended Kalman filter or invariant Kalman filter, utilizing inertial and external sensor fusion are applied. To cope with real-world scenarios, adaptive noise estimation methods have been developed primarily for classical Euclidean formulations. However, these methods remain largely unexplored in the tangent Lie space, despite it provides a principled geometric framework with favorable error dynamics on Lie groups. To fill this gap, we combine invariant filtering theory with neural-aided adaptive noise estimation in real-world settings. To this end, we derive a novel theoretical extension of classical innovation-based process noise adaptation formulated directly within the Lie-group framework. We further propose a lightweight neural network that estimates the process noise covariance parameters directly from raw inertial data. Trained entirely in a sim2real framework via domain adaptation, the network captures motion-dependent and sensor-dependent noise characteristics without requiring labeled real-world data. To examine our proposed neural-aided adaptive invariant Kalman filter, we focus on the challenging real-world scenario of autonomous underwater navigation. Experimental results demonstrate superior performance compared to existing methods in terms of position root mean square error. These results validate our sim2real pipeline and further confirm that geometric invariance significantly enhances learning-based adaptation and that adaptive noise estimation in the tangent Lie space offers a powerful mechanism for improving navigation accuracy in nonlinear autonomous platforms.
Closed-loop vs. Open-loop Kalman Filter Architectures in Airborne Aided Inertial Navigation
Airbus Central Research and Technology（空客中央研究与技术中心）；Department of Engineering Cybernetics, Norwegian University of Science and Technology（挪威科技大学工程 cybernetics 系）
Neural Network Aided Kalman Filtering with Model Predictive Control Enables Robot-Assisted Drone Recovery on a Wavy Surface
School of Data Science, The Chinese University of Hong Kong, Shenzhen, China（数据科学学院，香港中文大学（深圳））；School of Science and Engineering, The Chinese University of Hong Kong, Shenzhen, China（科学与工程学院，香港中文大学（深圳））；Shenzhen Institute of Artificial Intelligence and Robotics for Society, Shenzhen, China（社会人工智能与机器人研究所，深圳）
School of ECE, Ben-Gurion University of the Negev（本·古里安大学电子工程学院）；Institute for Signal and Information Processing, D-ITET, ETH Zürich（苏黎世联邦理工学院信号与信息处理研究所）；School of EE and CS, KTH Royal Institute of Technology（皇家理工学院电子工程与计算机科学学院）；Faculty of Applied Science, University of West Bohemia（西波维亚大学应用科学学院）；Dept. of CS, University of Massachusetts Boston（马萨诸塞大学波士顿分校计算机科学系）；Dept. of ECE, Northeastern University（东北大学电子工程系）；Math and CS Faculty, Weizmann Institute of Science（魏茨曼科学研究所数学与计算机科学系）
Weak in the NEES?: Auto-tuning Kalman Filters with Bayesian Optimization
Department of Computer Science（计算机科学系）；University of Colorado Boulder（科罗拉多大学博尔德分校）；University College London（伦敦大学学院）；Smead Aerospace Engineering Sciences（Smead航空航天工程科学系）
The Difference between the Left and Right Invariant Extended Kalman Filter
Systems Theory and Robotics Group School of Engineering Australian National University（系统理论与机器人组 工程学院 澳大利亚国立大学）；Control of Networked Systems Group University of Klagenfurt（网络控制系统组 克莱根furt大学）；Hexagon Robotics（Hexagon机器人）；Robotics and Mechatronics (RaM) Group EEMCS Faculty University of Twente（机器人与机电（RaM）组 EEMCS学院 威廉斯堡大学）
