Equivariant IMU Preintegration With Biases: A Galilean Group Approach

Abstract

This letter proposes a new approach for Inertial Measurement Unit (IMU) preintegration, a fundamental building block that can be leveraged in different optimization-based Inertial Navigation System (INS) localization solutions. Inspired by recent advances in equivariant theory applied to biased INSs, we derive a discrete-time formulation of the IMU preintegration on <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">${\mathbf {Gal}(3) \ltimes \mathfrak {gal}(3)}$</tex-math></inline-formula>, the left-trivialization of the tangent group of the Galilean group <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$\mathbf {Gal}(3)$</tex-math></inline-formula>. We define a novel preintegration error that geometrically couples the navigation states and the bias leading to lower linearization error. Our method improves in consistency compared to existing preintegration approaches which treat IMU biases as a separate state-space. Extensive validation against state-of-the-art methods, both in simulation and with real-world IMU data, implementation in the Lie++ library, and open-source code are provided.