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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 refraction 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 electromagnetic 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 Cramer-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-fromclutter (RFC), spatial and temporal tracking, unscented Kalman filter (UKF).

This paper describes a Markov chain Monte Carlo (MCMC) sampling approach for the estimation of not only the radio refractivity profiles from radar clutter but also the uncertainties in these estimates. This is done by treating the refractivity from clutter (RFC) problem in a Bayesian framework. It uses unbiased MCMC sampling techniques, such as Metropolis and Gibbs sampling algorithms, to gather more accurate information about the uncertainties. Application of these sampling techniques using an electromagnetic split-step fast Fourier transform parabolic equation propagation model within a Bayesian inversion framework can provide accurate posterior probability distributions of the estimated refractivity parameters. Then these distributions can be used to estimate the uncertainties in the parameters of interest. Two different MCMC samplers (Metropolis and Gibbs) are analyzed and the results compared not only with the exhaustive search results but also with the genetic algorithm results and helicopter refractivity profile measurements. Although it is slower than global optimizers, the probability densities obtained by this method are closer to the true distributions. Index Terms--Atmospheric ducts, genetic algorithms, Markov chain Monte Carlo (MCMC) techniques, radar clutter, refractivity estimation.