A novel variable residual coefficient-based GNSS/SINS tightly integrated positioning method in lie group framework for rotor unmanned aerial vehicle

Abstract Rotor unmanned aerial vehicles (UAVs) equipped with global navigation satellite systems and strapdown inertial navigation systems (GNSS/SINS) are often operated in complex environments characterized by signal occlusion and nonlinear flight patterns. The conventional extended Kalman filter (EKF), a filter method commonly used in GNSS/SINS integration has issues such as inconsistent state estimation, especially under these challenging conditions. The issues result in limited adaptability and reduced flexibility for the traditional innovation-based robust filters. To address these challenges, the right-invariant EKF (RIEKF) within a lie group (LG) framework has been developed, demonstrating improved covariance consistency compared to the EKF. Building upon this method, this study proposes a novel robust filtering algorithm named variable residual coefficient-based RIEKF (VRC-RIEKF) for UAV robust positioning. Specifically, the proposed VRC-RIEKF utilizes the accurate predicted covariance provided by the RIEKF to establish an effective criterion for identifying abnormal innovation residuals. In addition, the VRC-RIEKF enables real-time control of robustness intensity by introducing a dynamic threshold adjustment scheme, which updates the residual coefficient k at each epoch based on the predicted covariance. The dynamically updated residual coefficient k is subsequently employed to compute adaptive weights for raw GNSS observations, thereby significantly enhancing the robustness of UAV integrated navigation in challenging scenarios. Experimental results demonstrate that the LG-RIEKF outperforms the standard EKF in terms of variance consistency. Furthermore, compared with the RIEKF and its classical robust counterpart, the IGGIII–based RIEKF (IGG-RIEKF), the proposed VRC-RIEKF achieves approximately 49.0% and 31.0% gains in 3D positioning accuracy, respectively.