Best Choice of State Variables for Tracking Coordinated

Best Choice of State Variables for Tracking Coordinated Turns Fredrik Gustafsson Alf J. Isaksson Abstract A standard approach to tracking is to use the Extended Kalman Filter (EKF) applied to a non-linear state-space model. The main contribution here is a general analysis of the linearization error made in the EKF, and the result is applied to a particular tracking problem. In target tracking of so called coordinated turns, two choices of state variables have appeared in literature: one where Cartesian velocities are used and one where absolute velocity and heading angle, i.e. polar velocity, are used. Common practice appears to be the use of Cartesian velocity. However, the analysis herein shows that polar velocity gives a much smaller upper bound on the linearization error. This result is supported by a simulation study. A second contribution is to compare three di erent implementations of EKF's. The general recommendation to use polar velocity holds for all of them. The choice of EKF, in this simulation study, is of less importance than the choice of state variables.