New dual-IMU method achieves global convergence for relative pose estimation

Researchers from the University of Salerno and Institut Universitaire de France have published a new method for estimating the relative pose (position and orientation) and velocity between a vehicle and a moving target using only onboard Inertial Measurement Units (IMUs) and relative position or bearing sensors. The approach, detailed in arXiv:2605.13031, addresses a critical challenge in autonomous navigation: how to maintain accurate relative localization without GPS or external infrastructure. The key innovation lies in formulating the body-target relative dynamics on the Lie group SE2(3) and then recasting them into a linear time-varying (LTV) model in the ambient space R^15. This enables the use of a deterministic Riccati observer, which achieves global exponential convergence of the estimation error provided certain uniform observability (UO) conditions are met.

The authors rigorously analyze the observability conditions for two sensor configurations. For relative position measurements, UO requires only a persistence-of-excitation condition on the target's acceleration—a relatively mild requirement. For bearing-only measurements, additional conditions on the relative geometry are needed. Building on the observer, they design a nonlinear complementary filter on the special orthogonal group SO(3) to extract smooth orientation estimates with almost global asymptotic stability. Simulation results confirm that the estimator converges quickly and robustly, even under noisy IMU data and moderate maneuvers.

This work has significant practical implications for multi-vehicle coordination, aerial swarms, and robotic manipulation where precise relative navigation is essential. By eliminating dependency on external positioning systems, the method enhances robustness in GPS-denied environments such as indoor factories, underground mines, or urban canyons. The theoretical guarantees of global convergence are particularly valuable for safety-critical applications.