🤖 AI Summary
Long-standing inconsistencies in symmetry modeling hinder unified filter design for inertial navigation systems (INS).
Method: This work proposes a systematic reconstruction framework grounded in equivariant symmetry. It introduces, for the first time in INS, two novel classes of Lie group equivariant symmetries, establishes a comprehensive taxonomy encompassing all admissible symmetry choices, and integrates equivariant filtering (EqF), matrix Lie group theory, and nonlinear stochastic observer design to achieve a unified modeling framework for both the extended Kalman filter (EKF) and its modern Lie group variants.
Contribution/Results: The framework reveals the fundamental mechanisms underlying performance differences among existing filters, precisely delineates their applicability boundaries and intrinsic accuracy limits, and delivers an interpretable, scalable paradigm for designing high-precision, real-time navigation filters—thereby laying a rigorous theoretical foundation for enhancing robustness and consistency in IMU/GNSS integrated navigation.
📝 Abstract
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.
