UKF on Lie Groups for Radar Tracking using Polar and Doppler Measurements

Abstract

This paper proposes a construction of the Unscented Kalman FIlter (UKF) in which the system state propagates on a Lie Group. It is presented a parametrization for 2D-radar targets on Lie group to tackle the ltering tracking problem. By assuming concentrated Gaussian distributions on Lie groups rather than the conventional Gaussian distributions in Euclidean space, it is shown that the presented parametrization is a better approximation to the curved-shape distribution of the position of moving targets with noise in the linear and angular speeds. The parametrization is applied to the proposed UKF on Lie groups and to an Extended Kalman Filter (EKF) on Lie groups found in the literature. The conventional UKF and EKF, in Euclidean space, were also implemented. The considered system dynamics is a constant linear speed and constant turn rate model adapted to a Lie group structure. The Discrete Lie Group UKF presented the best performance among the implemented lters.