A comparison between the Extended Kalman Filter and a Minimum-Energy Filter in the TSE(2) case

Attitude estimation is a core problem in many rigid body systems. The scientific literature proposed a lot of filters and algorithms to estimate pose and velocity of such rigid body systems. In this paper we compare the extended Kalman filter, that represents a generalization of the standard Kalman filter for non-linear systems, and a second-order-optimal minimum-energy filter on the matrix Lie group TSE(2). Optimality refers to a cost function in the unknown model error and measurement error. The measurement system consists of a GPS-like, that provides the position of two antennas on the vehicle, and an INS unit, that provides the linear and angular velocity.