Spherical-Earth-Based Measurement Modeling for Practical OTHR Target Tracking

In this article, we revisit the problem of modeling of over-The-horizon radar (OTHR) target tracking. The accuracies of target kinematic and measurement models are critical factors affecting tracking performance. In most of the existing literature, a flat Earth OTHR measurement model is used. This has two obvious drawbacks: 1) a state vector with components of ground range, range rate, bearing, and bearing rate cannot be used directly in common kinematic models, such as nearly constant velocity (NCV), nearly constant acceleration (NCA), nearly constant turn (NCT), and a combination of these; and 2) the curvature of earth is ignored, which affects the measurement accuracy of the OTHR. We develop a spherical-earth-based measurement model. First, the target kinematic state is modeled in a 2D tracker coordinate frame, which is suitable for common kinematic models. Second, measurement modeling is completed using the spherical earth model, which fully considers the curvature of earth among the receiver, transmitter, and target. Furthermore, the inverse mapping for track initiation is derived. Finally, the effectiveness of the developed model is demonstrated by a nonmaneuvering target moving with the NCV motion and a maneuvering target moving with a sequence of NCV, NCT, and NCA motions. The interacting multiple model algorithm is used for state estimation of the maneuvering target. The unscented Kalman filter, cubature Kalman filter, and quadrature Kalman filter are compared for state estimation.