Invariant Extended Kalman Filtering Using Two Position Receivers for Extended Pose Estimation

This paper considers the use of two position receivers and an inertial measurement unit (IMU) to estimate the position, velocity, and attitude of a rigid body, collectively called extended pose. The measurement model consisting of the position of one receiver and the relative position between the two receivers is left invariant, enabling the use of the invariant extended Kalman filter (IEKF) framework. The IEKF possesses various advantages over the standard multiplicative extended Kalman filter, such as state-estimate-independent Jacobians. Monte Carlo simulations demonstrate that the two-receiver IEKF approach yields improved estimates over a two-receiver multiplicative extended Kalman filter (MEKF) and a single-receiver IEKF approach. An experiment further validates the proposed approach, confirming that the two-receiver IEKF has improved performance over the other filters considered.