  The traditional GNSS-aided inertial navigation system (INS) usually exploits
the extended Kalman filter (EKF) for state estimation, and the initial attitude
accuracy is key to the filtering performance. To spare the reliance on the
initial attitude, this work generalizes the previously proposed trident
quaternion within the framework of Clifford algebra to represent the extended
pose, IMU biases and lever arms on the Lie group. Consequently, a
quasi-group-affine system is established for the low-cost INS/GNSS integrated
navigation system, and the right-error Clifford algebra-based EKF
(Clifford-RQEKF) is accordingly developed. The iterated filtering approach is
further applied to significantly improve the performances of the Clifford-RQEKF
and the previously proposed trident quaternion-based EKFs. Numerical
simulations and experiments show that all iterated filtering approaches fulfill
the fast and global convergence without the prior attitude information, whereas
the iterated Clifford-RQEKF performs much better than the others under
especially large IMU biases.
