声学与深度辅助惯性导航系统的等变滤波器设计
Equivariant Filter Design for Acoustic and Depth Aided Inertial Navigation Systems
浏览论文内容
中文总结 AI 辅助
针对无GPS的AUV导航，提出基于切群对称性的等变滤波器（TG-EqF），将IMU偏置融入状态空间几何，消除导航状态线性化误差，相比IEKF和MEKF在姿态、速度、位置上误差降低18-25%，且协方差估计更准确。
中文摘要 AI 辅助
在没有GPS导航的自主水下航行器（AUV）中，通常将惯性测量与声学多普勒速度计程仪（DVL）的速度以及由压力推导的深度进行融合。将导航状态置于李群上可以提高精度和一致性。然而，基于不变扩展卡尔曼滤波器（IEKF）的最新滤波器将惯性测量单元（IMU）的偏置作为欧几里得扩展附加，这破坏了精确对数线性误差动力学所需的群仿射结构，导致报告的协方差随估计一起退化。我们应用切群（TG）对称性，将偏置携带在状态空间的几何结构内，为该系统的等变滤波器（EqF）进行推导，使得导航状态中的线性化误差为零，而偏置中仅存在二阶误差。我们为DVL开发了一个等变输出模型，其更新仅产生三阶线性化误差，并配有直接的压力输出。蒙特卡洛模拟将TG-EqF与双帧群IEKF和乘法EKF进行了基准比较。在姿态、速度和位置方面，TG-EqF相比两种替代方案均将误差降低了18%至25%。其主要优势在于其估计的协方差：其平均归一化估计误差平方（ANEES）比其他方法更接近其标称值1。对AUV现场数据的离线分析证实了模拟的结果，展示了减少的位置漂移。
英文摘要
Autonomous Underwater Vehicles (AUVs) navigating without GPS typically fuse inertial measurements with acoustic Doppler Velocity Log (DVL) velocities and pressure-derived depth. Posing the navigation state on a Lie group improves accuracy and consistency. However, state-of-the-art filters based on the Invariant Extended Kalman Filter (IEKF) append the Inertial Measurement Unit (IMU) biases as a Euclidean extension, which breaks the group-affine structure required for exact log-linear error dynamics, causing the reported covariance to degrade alongside the estimate. We apply the Tangent-Group (TG) symmetry, which carries the biases within the geometry of the state space, to derive an Equivariant Filter (EqF) for this system, leaving zero linearization error in the navigation states and second-order error only in the biases. We develop an equivariant output model for the DVL, whose update incurs only third-order linearization error, together with a direct pressure output. Monte Carlo simulations benchmark the TG-EqF against a Two-Frame-Group IEKF and a Multiplicative EKF. The TG-EqF reduces error by 18--25\% against both alternatives in each of attitude, velocity, and position. The main benefit is in the covariance it estimates: its Average Normalized Estimation Error Squared (ANEES) stays closer to its nominal value of one than that of the others. Offline analysis on AUV field data corroborates the findings of the simulations, demonstrating reduced position drift.
发表机构
- The University of Sydney（悉尼大学）
- Georgia Tech（佐治亚理工学院）
机构由 AI 辅助整理，请以论文原文为准。
