Abstract:

In the current design of invariant extended Kalman filter (EKF), biases states are not included in the kinematic equations with geometric properties due to that the kinematic systems of strapdown inertial navigation system (SINS) with biases no longer have group affine properties. This article constructs a group and a group action to satisfy the equivariant property of the kinematic equation containing biases state, which can naturally handle the problem of inertial based integrated navigation systems containing gyro bias and acceleration bias, and the linearization error of navigation state error dynamics can be reduced theoretically. Although the integrated navigation based on invariant EKF has received widespread attention, there has been few research on GNSS/SINS tightly coupled integrated navigation based on equivariant error in the world frame. Therefore, this article proposes a GNSS/SINS tightly coupled integrated navigation system based on equivariant errors in the world frame. Unlike the currently popular invariant EKF, the equivariant error constructed in this paper is based on a symmetry that appropriately includes all states in the group structure. The experimental results show that the filtering algorithm proposed in this paper has better transient response under different large misalignment angles compared to the right invariant EKF. At the same time, the robust model in the tightly coupled integrated navigation in the world frame effectively improves filtering robustness.

Key words: homogeneous manifold, group action, equivariant system, equivariant error, world frame, GNSS/SINS integrated navigation, robust model