Equivariant IMU Preintegration With Biases: A Galilean Group Approach

2024-11-08

IEEE Robotics and Automation Letters

AI Summary

To address inconsistent sensor error modeling and large linearization errors in IMU preintegration—leading to degraded navigation state estimation accuracy—this paper proposes an equivariant preintegration method grounded in the left-trivialized tangent group $mathrm{Gal}(3) ltimes mathfrak{gal}(3)$ of the Galilean group. It is the first work to embed IMU preintegration within the Galilean geometric framework, enabling unified geometric modeling and coupled updates of navigation states and sensor biases. This formulation substantially reduces linearization errors inherent in conventional SE(3)- or $mathbb{R}^n$-based models. The method integrates differential geometry, Lie group theory, Lie algebra, and equivariance principles, operating on a discrete-time system model and implemented via the Lie++ library. Evaluations on both synthetic and real-world IMU datasets demonstrate that our approach achieves 23–37% average reduction in orientation and position estimation errors compared to state-of-the-art methods (e.g., IMU-Preint, LIO-SAM), with markedly improved estimation consistency. The source code is open-sourced and integrated into Lie++.

Technology Category

• Intelligent Robots: State Estimation
• Machine Learning: Calibration & Uncertainty Quantification
• Search and Optimization: Sampling/Simulation-based Search

Application Category

• Semantics and Knowledge: Methods to enhance, augment, integrate or synergize semantic models such as knowledge graphs and LLMs
• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• User Modeling, Personalization and Recommendation: On-Device user modeling, personalization, and recommendation

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><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><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.

Problem

• Inertial Measurement Unit
• Navigation System
• Sensor Error

Innovation

• Galilean Group Theory
• IMU Data Processing
• Sensor Error Handling