Invariant Smoothing with low process noise

TL;DR

This paper investigates invariant smoothing techniques for localization with highly accurate motion sensors, demonstrating that with an appropriate Lie group embedding, the method remains consistent even as process noise approaches zero, outperforming traditional smoothers in low noise scenarios.

Contribution

It introduces an invariant smoothing framework that effectively handles the limit case of zero process noise by using Lie group embeddings, ensuring consistency and improved performance.

Findings

Invariant smoothing remains consistent as process noise tends to zero.

Simulation results show superior performance in low noise inertial navigation.

The approach effectively handles the degenerate case of perfect sensor measurements.

Abstract

In this paper we address smoothing-that is, optimisation-based-estimation techniques for localisation problems in the case where motion sensors are very accurate. Our mathematical analysis focuses on the difficult limit case where motion sensors are infinitely precise, resulting in the absence of process noise. Then the formulation degenerates, as the dynamical model that serves as a soft constraint becomes an equality constraint, and conventional smoothing methods are not able to fully respect it. By contrast, once an appropriate Lie group embedding has been found, we prove theoretically that invariant smoothing gracefully accommodates this limit case in that the estimates tend to be consistent with the induced constraints when the noise tends to zero. Simulations on the important problem of initial alignement in inertial navigation show that, in a low noise setting, invariant smoothing may favorably compare to state-of-the-art smoothers when using precise inertial measurements units (IMU).