Tracking refractivity from clutter using Kalman and particle lters

Abstract—We address the problem of tracking the spatial and temporal lower atmospheric variations in maritime environments. The evolution of the range and height-dependent index of re-fraction is tracked using the sea clutter return from sea-borne radars operating in the region. A split-step fast Fourier transform based parabolic equation approximation to the wave equation is used to compute the clutter return in complex environments with varying index of refraction. In addition, regional statistics are incorporated as prior densities, resulting in a highly nonlinear and non-Gaussian tracking problem. Tracking algorithms such as the extended Kalman, unscented Kalman and particle filters are used for tracking both evaporative and surface-based electromag-netic ducts frequently encountered in marine environments. The tracking performances and applicability of these techniques to different types of refractivity-from-clutter problems are studied using the posterior Cramér-Rao lower bound. Track divergence statistics are analyzed. The results show that while the tracking performance of the Kalman filters is comparable to the particle filters in evaporative duct tracking, it is limited by the high non-linearity of the parabolic equation for the surface-based duct case. Particle filters, on the other hand, prove to be very promising in tracking a wide range of environments including the abruptly changing ones. Index Terms—Atmospheric ducts, extended Kalman filter (EKF), parabolic equation, particle filter (PF), refractivity-from-clutter (RFC), spatial and temporal tracking, unscented Kalman filter (UKF). I