This paper investigates the problem of inertial navigation system (INS) filter design through the lens of symmetry. The extended Kalman filter (EKF) and its variants, have been the staple of INS filtering for 50 years; however, recent advances in inertial navigation systems have exploited matrix Lie group structure to design stochastic filters and state observers that have been shown to display superior performance compared to classical solutions. In this work we consider the case where a vehicle has an inertial measurement unit (IMU) and a global navigation satellite system (GNSS) receiver. We show that all the modern variants of the EKF for these sensors can be interpreted as the recently proposed Equivariant Filter (EqF) design methodology applied to different choices of symmetry group for the INS problem. This leads us to propose two new symmetries for the INS problem that have not been considered in the prior literature, and provide a discussion of the relative strengths and weaknesses of all the different algorithms. We believe the collection of symmetries that we present here capture all the sensible choices of symmetry for this problem and sensor suite, and that the analysis provided is indicative of the relative real-world performance potential of the different algorithms.

翻译：本文通过对称性视角研究惯性导航系统（INS）滤波器设计问题。扩展卡尔曼滤波（EKF）及其变体在五十年间一直是INS滤波的支柱方法，然而近年来惯性导航系统的进展利用矩阵李群结构设计的随机滤波器和状态观测器，已被证明具有优于经典解法的性能表现。本研究考虑装备惯性测量单元（IMU）与全球导航卫星系统（GNSS）接收器的运载体场景。我们证明，针对这些传感器设计的全部现代EKF变体均可解释为最近提出的等变滤波器（EqF）设计方法论在INS问题不同对称群选择上的应用。这一发现促使我们提出两项先前文献未考虑的INS问题新型对称性，并全面探讨各类算法的相对优势与局限性。我们认为，本文提出的对称性集合完整覆盖了本研究问题及其传感器组合理想的对称性选择，所开展的分析能够反映不同算法在实际环境中的相对性能潜力。