迭代等变滤波器
The Iterative Equivariant Filter
- The University of Sydney（悉尼大学）
- McGill University（麦吉尔大学）
机构由 AI 辅助整理，请以论文原文为准。
中文总结 AI 辅助
本文提出迭代等变滤波器（IterEqF），结合迭代扩展卡尔曼滤波与等变滤波的优点，通过迭代更新和协方差重置提升移动机器人距离定位的精度，尤其在瞬态收敛阶段表现更优。
中文摘要 AI 辅助
本文提出了迭代等变滤波器（IterEqF）。迭代扩展卡尔曼滤波器（IterEKF）用迭代校正步骤替代了标准EKF的校正步骤，该迭代校正步骤是非线性加权最小二乘问题的高斯-牛顿解。标准等变滤波器（EqF）利用并尊重在齐次空间和李群上提出的状态估计问题的底层对称性。IterEqF的动机在于结合IterEKF和EqF两者的特点，从而产生一种非常适合导航问题的高性能状态估计解决方案。本文推导了IterEqF更新步骤的迭代过程，并展示了该方法的内在非线性如何自然地导致滤波器协方差“重置”到新坐标中。针对移动机器人基于距离的定位的蒙特卡洛模拟表明，与标准EqF相比，性能有所提升，尤其是在瞬态收敛期间。
英文摘要
This paper presents the iterative equivariant filter (IterEqF). The iterative extended Kalman filter (IterEKF) replaces the standard EKF correction step with an iterative correction step that is the Gauss-Newton solution to a nonlinear weighted least squares problem. The standard equivariant filter (EqF) exploits and respects the underlying symmetry of state estimation problems posed on homogeneous spaces and Lie groups. The motivation behind the IterEqF is to combine the features of both the IterEKF and the EqF, thus leading to a high-performance state estimation solution that is well suited to navigation problems. This paper derives the iteration procedure for the IterEqF update step and shows how the intrinsic nonlinearity of the approach naturally results in a `reset' of the filter's covariance into new coordinates. Monte-Carlo simulations of range-based localisation for a mobile robot demonstrate the improvement in performance relative to a standard EqF, especially during the transient convergence.
