Extended Trident Quaternion Framework for INS/GNSS Integrated Navigation With IMU Biases and Lever Arms

The performance of low-cost INS/GNSS integrated navigation system is significantly affected by the bias estimation accuracy of the inertial measurement unit (IMU). Inspired by the two-frame group that modeled the body-frame vectors on a matrix group, this work proposes an extended trident quaternion (ETQ) representation, allowing for the representation of IMU biases, lever arms, and the extended pose in an algebraic group structure. Importantly, the matrix Lie group isomorphic to the ETQ group is proposed, providing the matrix representation of vectors in two frames. Then, the left and right ETQ error-based indirect Kalman filters (L/R-ETQEKF) are derived for integrating the information from inertial navigation system (INS) and the Global Navigation Satellite System (GNSS). Based on the matrix representation, the covariance switch-based ETQEKF is further proposed to combine the right error-based process model with the left error-based GNSS measurement model, named as the right-to-left ETQEKF (R2L-ETQEKF), showing the potential of simultaneously incorporating the left and right error-based measurement models in a filter. Numerical simulations and experiments show that the proposed L-ETQEKF and R2L-ETQEKF perform identically and can fulfill fast convergence under extremely large prior attitude errors.