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arXiv 2607.03211cs.ROcs.SYeess.SY
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适用于全球的辅助惯性导航系统的误差状态卡尔曼滤波器运动学推导

Derivations of Error-State Kalman Filter Kinematics for Globally Applicable Aided Inertial Navigation Systems

Airbus Central Research and Technology(空客中央研究与技术部);Department of Engineering Cybernetics, Norwegian University of Science and Technology(挪威科技大学工程控制论系)

Antonia Hager, Torleiv H. Bryne

AI总结:

研究全球导航系统中处理地球曲率等因素的状态估计算法,通过不变误差状态卡尔曼滤波器利用李群对称性,给出四种经典和不变的误差状态卡尔曼滤波器数学公式供比较与实现。

摘要:

全球导航系统需要能处理地球曲率、地球自转和引力变化的状态估计算法。在经典误差状态卡尔曼滤波中,误差状态动力学依赖轨迹。不变误差状态卡尔曼滤波器利用李群对称性表示误差,选择标准、左不变或右不变滤波器取决于系统动力学和传感器配置。本文给出了适用于全球的辅助惯性导航系统的四种经典和不变误差状态卡尔曼滤波器的数学公式。

英文摘要:

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.

机构、总结、中文摘要均由AI分析而来,可能存在错误,请以论文正文为准。

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