Left/Right Invariant Lie Group Error for SINS/GNSS Tightly Coupled Vehicular Integrated Navigation

Tightly coupled strapdown inertial navigation system (SINS)/global navigation satellite system (GNSS) integrated navigation, which utilizes GNSS pseudo-range and pseudo-range rate measurements for state estimation in vehicular navigation systems, demonstrates enhanced reliability and accuracy in challenging GNSS environments. While the extended Kalman filter (EKF) remains the predominant nonlinear algorithm in SINS/GNSS integration, it suffers from performance degradation due to covariance inconsistency issues. To address this limitation, this paper proposes a novel nonlinear state error-based Lie group extended Kalman filter (LG-EKF) for tightly coupled SINS/GNSS integrated navigation. The study first presents a tutorial example illustrating the necessity of transformed nonlinear state error and then provides detailed derivations of LG-EKF equations using both right invariant error (LG-EKF-R) and left invariant error (LG-EKF-L). Through Monte Carlo simulations and uncrewed aerial vehicle (UAV) field tests, the research demonstrates the performance differences in system dynamics between LG-EKF-R and LG-EKF-L. The results indicate that LG-EKF-R, operating at a lower propagation rate, achieves comparable accuracy to LG-EKF-L with a higher propagation rate, offering a more efficient solution for integrated navigation systems.