Abstract
Modern signal processing techniques such as in air traffic control can provide both position and range rate measurements. In this paper, the relationship of the fully coupled filter (a six-state filter) and the decoupled filter (three two-state filters) for radar tracking using extended Kalman filter with range rate measurements is presented. The computational requirements of the complex fully coupled filter are inconsistent with the available computational resources and the numbers of targets desired to be tracked. Therefore, a simple decoupled filter is necessary. In order to represent a mathematical model of the target motion, we use the NEU (North-East-Up) coordinates, which are inertial Cartesian coordinates, for they are convenient for target trajectory extrapolation. Target prediction (state estimate extrapolation) is also carried out in the NEU coordinates. Target updating (state estimate update) is carried out in the rotational Cartesian coordinates which are aligned with the predicted target line-of-sight. Approximately, the decoupled filter is equivalent to the fully coupled filter when the rotation of the coordinates can be neglected, the target angular velocity is almost equal to zero and the plant noise covariance matrix is diagonal where all elements on the diagonal are equal. As a result, the decoupled filter nearly equals the fully coupled filter in tracking accuracy when the target velocity is low, the target range is long, or the target flies straight on toward a radar.
