EKF on lie groups for radar tracking using polar and Doppler measurements

Abstract

This paper presents a parametrization for 2D-radar targets on Lie group to tackle the filtering tracking problem. By assuming concentrated Gaussian distributions on Lie groups rather than the conventional Gaussian distributions in Euclidean space, it is shown that the proposed 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 a generalization of the Extended Kalman Filter in which the system state and measurements evolve on matrix Lie groups. The considered system dynamics is a constant linear speed and constant turn rate model, adapted to a Lie group structure. The performance of the Discrete Lie Group EKF is compared to the conventional EKF in Euclidean space and an improvement in the filtering performance is verified.