Synchronous Observer Design for Inertial Navigation Systems with Almost-Global Convergence
Pieter van Goor, Tarek Hamel, Robert Mahony
TL;DR
The paper addresses robust INS state estimation with almost-global convergence guarantees by formulating the INS as dynamics on the Lie group $SE_2(3)$ and introducing the automorphism group $SIM_2(3)$. It then develops a synchronous observer architecture that leverages these symmetries to realize modular, plug-and-play corrections from GNSS position, GNSS velocity, and magnetometer measurements, while ensuring error dynamics of the form $\dot{\bar{E}}=\Gamma\bar{E}-\bar{E}\Gamma-\bar{E}\Delta$. The authors prove almost-global asymptotic stability for the attitude and local exponential stability under persistence of excitation, and demonstrate both simulations with extreme initial errors and real-world UAV data, comparing favorably to ArduPilot's EKF. The work offers a principled geometric framework for INS observers with modular sensor fusion and strong global convergence properties, potentially enabling more robust navigation in space-constrained platforms.
Abstract
An Inertial Navigation System (INS) is a system that integrates acceleration and angular velocity readings from an Inertial Measurement Unit (IMU), along with other sensors such as Global Navigation Satellite Systems (GNSS) position, GNSS velocity, and magnetometer, to estimate the attitude, velocity, and position of a vehicle. This paper shows that the INS problem can be analysed using the automorphism group of the extended special Euclidean group: a group we term the extended similarity group . By exploiting this novel geometric framework, we propose a synchronous observer architecture; that is, an observer architecture for which the observer error is stationary if the correction terms are set to zero. In turn, this enables us to derive a modular, or plug-and-play, observer design for INS that allows different sensors to be added or removed depending on what is available in the vehicle sensor suite. We prove both almost-global asymptotic and local exponential stability of the error dynamics for the common scenario of at least IMU and GNSS position. To the authors' knowledge, this is the first non-linear observer design with almost global convergence guarantees or with plug-and-play modular capability. A simulation with extreme initial error demonstrates the almost-global robustness of the system. Real-world capability is demonstrated on data from a fixed-wing UAV, and the solution is compared to the state-of-the-art ArduPilot INS.