3-D track initiation in clutter using 2-D radar measurements

We present an algorithm for initiating 3-D tracks using range and azimuth (bearing) measurements from a 2-D radar on a moving platform. The work is motivated by the need to track possibly low-flying targets, e.g., cruise missiles, using reports from an aircraft-based surveillance radar. Previous work on this problem considered simple linear motion in a flat Earth coordinate frame. Our research extends this to a more realistic scenario where the Earth's curvature is also considered. The target is assumed to be moving along a great circle at a constant altitude. After the necessary coordinate transformations, the measurements are nonlinear functions of the target state and the observability of target altitude is severely limited. The observability, quantified by the Cramer-Rao lower bound (CRLB), is very sensitive to the sensor-to-target geometry. The paper presents a Maximum Likelihood (ML) estimator for estimating the target motion parameters in the Earth-centered Earth-fixed (ECEF) coordinate frame from 2-D range and angle measurements. In order to handle the possibility of false measurements and missed detections, which was not considered previously, we use the Probabilistic Data Association (PDA) algorithm to weight the detections in a frame. The PDA-based modified global likelihood is optimized using a numerical search. The accuracies obtained by the resulting ML-PDA estimator are quantified using the CRLB for different sensor-target configurations. It is shown that the proposed estimator is efficient, that is, it meets the CRLB. Of particular interest is the achievable accuracy for estimating the target altitude, which is not observed directly by the 2-D radar, but can be only inferred from the range and bearing observations.