グローバル対応補助慣性航法システムのための誤差状態カルマンフィルタ運動学の導出
Derivations of Error-State Kalman Filter Kinematics for Globally Applicable Aided Inertial Navigation Systems
地球の曲率や自転、重力変化を考慮したグローバル航法システム向けに、古典的および不変誤差状態カルマンフィルタ（ESKF）の数式を体系的に整理し、比較・実装のためのリファレンスを提供する論文。
著者: Antonia Hager, Torleiv H. Bryne
分類: cs.RO, eess.SY
原文アブストラクト
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.