Best choice of coordinate system for tracking coordinated turns

A standard approach to tracking is to use the extended Kalman filter (EKF) applied to a nonlinear state-space model. We compare two conceivable choices of state variables for modeling civil aircrafts. One where Cartesian velocities are used and one where absolute velocity and heading angle are used. In both choices, Cartesian coordinates are used for position and angular velocity for turning. It is shown that the latter state vector always performs better. This is proven by considering the linearization error made in the extended Kalman filter applied either to a time-continuous model or a discretized model. The result is supported by a Monte Carlo simulation study.