The marine atmospheric boundary layer (MABL) is the region of atmosphere that interacts with the ocean surface. The atmospheric variability (i.e. temperature and relative humidity) in this region can result in rapid changes in the refractive index with increasing height from the sea surface. The complex region can result in non-standard propagation of electromagnetic (EM) waves beyond the horizon under atmospheric ducting conditions. However, when ducting layers are not present, EM waves are limited to line-of-sight transmission. Atmospheric ducting research is typically conducted using radio frequencies in the X-band (around 8-12 GHz) due to its impact on performance of marine radars at those frequencies. Studies typically examine levels of received signal power or effects on radar returns in ducting conditions, but often ignore the time-domain effects of ducting which can also affect communications link performance. In collaboration with the Coastal Observing Research and Development Center at Scripps Institution of Oceanography (SIO), the ducting research in this thesis uses a channel sounder that consists of a X-band transmitter which transmits a coded pseudorandom sequence and a software-defined radio (SDR) receiver. Both transmitter and receiver are GPS synchronized so that the time-domain cross-correlation between the TX and RX signals can be found. In theory, if atmospheric ducting is present, there will be multipath propagation, and the TX-RX cross-correlation indicates multiple “peaks”, indicating multiple arrival times. Conversely, if little to no ducting is present, then the cross-correlation indicates a single “peak”. The channel sounding was evaluated over several over-water communications links, involving fixed-path and variable range sea tests with a moving vessel to verify if this hypothesis is true. The expected ducting conditions were determined by in-situ refractive index measurements of the atmosphere. Results from testing showed multiple peaks when strong ducting was expected, but an extensive sea test in strong ducting conditions is needed to distinguish multipath from ducting from that of terrain reflections. Further work is also needed to determine the computational model that accurately models multipath propagation through a duct, which is beyond the scope of this thesis.

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In science and engineering research, filtering or estimation of system’s states is widely used and developed, so the structure of a new nonlinear filter is proposed. This thesis focuses on the procedures of propagation and update step of the new filter. The algorithms used in the filter, including generalized Polynomial Chaos Algorithms, Markov Chain Monte Carlo algorithms, and Gaussian Mixture Model algorithms, are introduced. Then, the propagation and update step of the proposed filter are applied in solving two nonlinear problems: Van der Pol Oscillator and Two Body System. The simulation shows that the results of the propagation and update step are reasonable and their designs are valuable for further tests. The propagation step has the same accuracy level compared with a Quasi Monte Carlo simulation while using a much smaller number of points. The update step can build a useful Gaussian Mixture Model as the posterior distribution.

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