用李群方法统一建模惯性导航，提升融合精度与系统理解。
Tutorial on Aided Inertial Navigation Systems: A Modern Treatment Using Lie-Group Theoretical Methods
- 基于SE_2(3)李群构建几何框架，显式表达对称性与不变性
- 支持高阶状态、同步观测器与等变滤波等现代扩展方法
- 适合需要理论深度与工程实现结合的导航系统开发者
本教程以控制为导向，采用以扩展特殊欧几里得群SE_2(3)为核心的李群形式化方法，介绍辅助惯性导航系统的现代处理方式。重点在于建立清晰、可实现的几何融合框架，将惯性测量与辅助信息融合，并明确展现不变性与对称性的作用。文中还讨论了近期进展，包括高阶状态表示、同步观测器设计及等变滤波方法，这些均为同一基本原理的自然延伸。目标是为读者提供一个连贯的系统理论视角，既有助于理解，也支持现代辅助惯性导航方法的实际应用。
原文摘要 · Abstract (English)
This tutorial presents a control-oriented introduction to aided inertial navigation systems using a Lie-group formulation centered on the extended Special Euclidean group SE_2(3). The focus is on developing a clear and implementation-oriented geometric framework for fusing inertial measurements with aiding information, while making the role of invariance and symmetry explicit. Recent extensions, including higher-order state representations, synchronous observer designs, and equivariant filtering methods, are discussed as natural continuations of the same underlying principles. The goal is to provide readers with a coherent system-theoretic perspective that supports both understanding and practical use of modern aided inertial navigation methods.
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