arXiv:2603.24130cs.ROcs.SY2026-03

提出一种统一的视觉惯性导航滤波方法,提升精度与效率。

Equivariant Filter Transformations for Consistent and Efficient Visual--Inertial Navigation

  • 通过等变滤波器间的数学映射,实现状态一致性设计。
  • 在真实数据和模拟中验证,精度高且计算更快。
  • 适合需要高可靠性的自动驾驶与机器人定位系统。

本文提出一种用于视觉-惯性导航的等变滤波器(EqF)变换方法。通过建立具有不同对称性的EqFs之间的解析联系,该方法实现了系统性的一致性设计与高效实现。首先,我们形式化了从全局系统状态到局部误差状态的映射,并证明其在任意两个EqF的误差状态间诱导出非奇异线性变换。其次,推导了相关线性化误差状态系统及不可观测子空间的变换规律。这些结果给出通用一致性设计原则:对于任意不可观测系统,可通过变换局部坐标图,合成具有状态无关不可观测子空间的一致性EqF,从而避免繁琐的对称性分析。第三,为缓解一致性所需非分块对角雅可比矩阵带来的计算负担,提出两种高效实现策略。这些策略利用结构更简单的分块对角式EqF的雅可比矩阵加速协方差运算,同时保持一致性。大量蒙特卡洛仿真与真实世界实验验证了该方法在精度与运行时间上的优越性。

原文摘要 · Abstract (English)

This paper presents an equivariant filter (EqF) transformation approach for visual--inertial navigation. By establishing analytical links between EqFs with different symmetries, the proposed approach enables systematic consistency design and efficient implementation. First, we formalize the mapping from the global system state to the local error-state and prove that it induces a nonsingular linear transformation between the error-states of any two EqFs. Second, we derive transformation laws for the associated linearized error-state systems and unobservable subspaces. These results yield a general consistency design principle: for any unobservable system, a consistent EqF with a state-independent unobservable subspace can be synthesized by transforming the local coordinate chart, thereby avoiding ad hoc symmetry analysis. Third, to mitigate the computational burden arising from the non-block-diagonal Jacobians required for consistency, we propose two efficient implementation strategies. These strategies exploit the Jacobians of a simpler EqF with block-diagonal structure to accelerate covariance operations while preserving consistency. Extensive Monte Carlo simulations and real-world experiments validate the proposed approach in terms of both accuracy and runtime.

导航滤波器视觉惯性

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