Accuracy Evaluation of INS/ZUPT Filtering Methods Based on Different Geometric Error Definitions

2026-09-25

AI Summary

This study addresses the impact of geometric error definitions on the accuracy and consistency of INS/ZUPT filtering by systematically deriving multiple geometric filtering models and proposing a novel group operation based on left-tangent-group equivariant errors. By comparing the performance of invariant filters, two-frame group filters, equivariant filters, and the conventional extended Kalman filter (EKF), the filtering characteristics under different geometric frameworks are revealed. The results demonstrate that, under small initial errors, the EKF position error remains below 0.1% of the distance traveled, with geometric filters achieving comparable accuracy. Although no significant consistency advantage is observed, this work provides a systematic theoretical framework for the design and analysis of geometric filters in inertial navigation systems.

Abstract

Geometric filters have recently been introduced to improve the accuracy and consistency of inertial-based integrated navigation systems. Error states were defined through specific group operations, introducing state correlations in error definition, which were lacked in the additive error used by a conventional indirect Kalman filter. The desirable consistent filtering models can be obtained based on specific geometric errors. For zero-velocity measurements expressed in the reference frame, this paper derives left-error process and measurement models from invariant filtering, two-frame-group filtering, and equivariant filtering. Importantly, a new group operation is introduced for the left tangent-group equivariant error. The analysis shows that the two-frame-group invariant extended Kalman filter (TFG-IEKF) and the tangent-group equivariant filter (TG-EqF) do not offer a significant consistency advantage over the invariant extended Kalman filter (IEKF). Experiments with an INS/ZUPT measurement system show that, under small initial attitude errors, the conventional indirect extended Kalman filter (EKF) achieves loop-closure position errors below $0.1\%$ of the traveled distance, while the three geometric filters achieve comparable positioning accuracy.

Problem

• INS/ZUPT
• geometric error
• filtering accuracy
• invariant filtering
• equivariant filtering

Innovation

• Invariant Filtering
• Equivariant Filtering
• Two-Frame-Group
• INS/ZUPT
• Geometric Error