Inertial-Based Integrated Navigation Models on Lie Group Theory: Comparison and Analysis

The inertial-based integrated navigation system based on Lie group is a significant navigation method that overcomes the limitations of the traditional Euclidean spatial based methods by characterizing the navigation parameters (attitude, velocity, and position) using the Lie group theory. This method has been found to be particularly effective in addressing navigation problems under large misalignment angles. It has gained significant traction in inertial-based integrated navigation applications. Lie group-based integrated navigation models have been proposed in different frames in the extant literature. In this paper, a comprehensive summary and analysis of these models are presented. This performance is compared through theoretical analysis and simulation, with a particular emphasis on scenarios involving large misalignment angles. Simulation results indicate that under the large misalignment angles, the Lie group-based integrated navigation models exhibit superior performance compared to the traditional model. Moreover, the Lie group-based integrated navigation models satisfying the group affine property demonstrate further enhance performance.