Improve the autonomy of the SE2(3) group based Extended Kalman Filter for Integrated Navigation: Theoretical Analysis

2026-01-22

AI Summary

This work addresses the challenge of maintaining model autonomy in high-precision integrated navigation under the conventional SE2(3) Lie group framework, where Earth’s rotation and inertial sensor biases introduce Coriolis terms in non-inertial frames, complicating error propagation. The study systematically analyzes error propagation characteristics of SE2(3) across inertial, Earth-fixed, and world reference frames, identifying velocity-dependent coupling terms as the primary obstacle to autonomy. To overcome this limitation, an improved multi-reference-frame modeling approach is proposed. Theoretical error analysis and an SE2(3)-based extended Kalman filter demonstrate that the method significantly approximates fully autonomous navigation, offering a more robust theoretical foundation and practical implementation pathway for high-precision applications.

Technology Category

• Intelligent Robots: State Estimation
• Reasoning under Uncertainty: Other Foundations of Reasoning under Uncertainty
• Planning, Routing, and Scheduling: Model-Based Reasoning

Application Category

• Graph Algorithms and Modeling for the Web: Efficient manipulation of static and dynamic Web-related graphs
• Systems and Infrastructure for Web, Mobile and WoT: Location- and context-aware Web and WoT applications and services
• Security and Privacy: Large-scale security measurements

Abstract

One of core advantages of the SE2(3) Lie group framework for navigation modeling lies in the autonomy of error propagation. Current research on Lie group based extended Kalman filters has demonstrated that error propagation autonomy holds in low-precision applications, such as in micro electromechanical system (MEMS) based integrated navigation without considering earth rotation and inertial device biases. However, in high-precision navigation state estimation, maintaining autonomy is extremely difficult when considering with earth rotation and inertial device biases. This paper presents the theoretical analysis on the autonomy of SE2(3) group based high-precision navigation models under inertial, earth and world frame respectively. Through theoretical analysis, we find that the limitation of the traditional, trivial SE2(3) group navigation modeling method is that the presence of Coriolis force terms introduced by velocity in non-inertial frame. Therefore, a construction method for SE2(3) group navigation models is proposed, which brings the navigation models closer to full autonomy.

Problem

• SE2(3)
• autonomy
• high-precision navigation
• error propagation
• inertial navigation

Innovation

• SE2(3) Lie group
• autonomous error propagation
• high-precision navigation
• Coriolis force
• Extended Kalman Filter