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[1] This paper addresses the problem of estimating the lower atmospheric refractivity ( M profile) under nonstandard propagation conditions frequently encountered in low-altitude maritime radar applications. This is done by statistically estimating the duct strength (range- and height-dependent atmospheric index of refraction) from the sea surface reflected radar clutter. These environmental statistics can then be used to predict the radar performance. In previous work, genetic algorithms (GA) and Markov chain Monte Carlo (MCMC) samplers were used to calculate the atmospheric refractivity from returned radar clutter. Although GA is fast and estimates the maximum a posteriori ( MAP) solution well, it poorly calculates the multidimensional integrals required to obtain the means, variances, and underlying posterior probability distribution functions of the estimated parameters. More accurate distributions and integral calculations can be obtained using MCMC samplers, such as the Metropolis-Hastings and Gibbs sampling (GS) algorithms. Their drawback is that they require a large number of samples relative to the global optimization techniques such as GA and become impractical with an increasing number of unknowns. A hybrid GA-MCMC method based on the nearest neighborhood algorithm is implemented in this paper. It is an improved GA method which improves integral calculation accuracy through hybridization with a MCMC sampler. Since the number of forward models is determined by GA, it requires fewer forward model samples than a MCMC, enabling inversion of atmospheric models with a larger number of unknowns.

In many maritime regions of the world, such as the Mediterranean, Persian Gulf, East China Sea, and the Californian Coast, atmospheric ducts are common occurrences. They result in various anomalies such as significant variations in the maximum operational radar range, creation of regions where the radar is practically blind (radar holes) and increased sea clutter. Therefore, it is important to predict the real-time 3-D environment in which the radar is operating so that the radar operator will at least know the true system limitations and in some cases even compensate for them. This dissertation addresses the estimation and tracking of the lower atmospheric radio refractivity under non-standard propagation conditions frequently encountered in low altitude maritime radar applications. This is done by statistically estimating the duct strength (range and height-dependent atmospheric index of refraction) from the sea-surface reflected radar clutter. Therefore, such methods are called Refractivity From Clutter (RFC) techniques. These environmental statistics can then be used to predict the radar performance. The electromagnetic propagation in these complex environments is simulated using a split-step fast Fourier transform (FFT) based parabolic equation (PE) approximation to the wave equation. The first part of this thesis discusses various algorithms such as genetic algorithms (GA), Markov chain Monte Carlo samplers (MCMC) and the hybrid GA-MCMC samplers that are used to estimate atmospheric radio refractivity for a given azimuth direction and time. The results show that radar clutter can be a rich source of information about the environment and the techniques mentioned above are used successfully as near real-time estimators for the data collected during the Wallops'98 experiment conducted by the Naval Surface Warfare Center. The second part of this dissertation focuses on both spatial and temporal tracking of the 3-D environment. Techniques such as the extended (EKF) and unscented (UKF) Kalman filters, and particle filters (PF) are used for tracking the spatial and temporal evolution of the lower atmosphere. Even though the tracking performance of the Kalman filters was limited for certain duct types such as the surface-based ducts due to the high non-linearity of the split-step FFT PE, they performed well for other environments such as evaporation ducts. On the other hand, particle filters proved to be very promising in tracking a wide variety of scenarios including even abruptly changing environments