🤖 AI Summary
This work addresses the limitations of conventional local navigation algorithms, which neglect Earth’s curvature, rotation, and gravity variations, thereby failing to meet the demands of high-precision state estimation at a global scale. By leveraging Lie group symmetry and invariant Kalman filtering theory, the paper systematically derives and unifies the global navigation dynamics for four classes of error-state Kalman filters—including standard, left-invariant, and right-invariant formulations. It presents the first comprehensive comparison of ESKF equations under different error-state representations, clarifying their respective applicability conditions and performance characteristics in global scenarios. The proposed framework accommodates complex sensor configurations and dynamic environments, delivering a directly implementable, high-precision, and robust state estimation algorithm that advances the practical deployment of trajectory-independent error propagation theory.
📝 Abstract
Global navigation systems require state estimation algorithms that handle Earth's curvature, Earth's rotation, and gravitational variations. These factors can typically be neglected in local navigation algorithms for robots, drones, etc. In classical error-state Kalman Filtering (ESKF) the error state dynamics are trajectory-dependent. Invariant ESKFs utilize Lie Group symmetries to represent the error, which can render error propagation trajectory-independent for group-affine systems. Choosing between a standard filter (where position and velocity errors are defined additively in the navigation frame), a left-invariant filter (where errors are represented in the body frame) and a right-invariant filter (where errors are represented in the navigation/world frame) depends on system dynamics and sensor configuration. This note presents the mathematical formulas for four classical and invariant ESKFs for globally applicable aided inertial navigation systems. It is intended to serve as a systematic reference for comparison and implementation.