Three-Dimensional Tracking of an Aircraft Using Two-Dimensional Radars

Accurate three-dimensional (3-D) position and velocity estimates of an aircraft are important for air traffic control (ATC) systems. An ATC 2-D radar measures the slant range and azimuth of an aircraft. Thus, a single measurement from a 2-D radar is not sufficient to calculate the 3-D position of an aircraft. Previous researchers have used the multiple-model-based height-parametrized (HP) extended Kalman filter with Cartesian state vector (HP-CEKF) with one or two 2-D radars for an aircraft with nearly constant velocity and altitude. However, the filter initialization algorithms contain errors. In this paper, in addition to the HP-CEKF, we present the HP Cartesian unscented Kalman filter (HP-CUKF) and HP Cartesian cubature Kalman filter (HP-CCKF). We also present two new nonlinear filters for the two-radar problem. The first filter uses modified spherical coordinates based HP-UKF (HP-MSCUKF) where the range and azimuth are components of the target state. The second filter uses a cubature Kalman filter with filter initialization by the bias-compensated pseudolinear estimator. We also consider the climbing motion of an aircraft with nearly constant climbing rate, which has not been studied before. All four aforementioned HP filters use the single-point track initiation algorithm. The state estimation accuracy of an aircraft is analyzed as a function of the distance of the aircraft from the radar(s). We compare the performance of the nonlinear filters with the posterior Cramér-Rao lower bound. The normalized computational times of all algorithms in all scenarios are presented. Our results show that accurate 3-D trajectory estimates of an aircraft can be obtained using one or two ATC 2-D radars.