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Inferring electromagnetic propagation characteristics within the marineatmospheric boundary layer (MABL) from data in real time is crucial for modernmaritime navigation and communications. The propagation of electromagneticwaves is well modeled by a partial differential equation (PDE): a Helmholtzequation. A natural way to solve the MABL characterization inverse problem isto minimize what is observed and what is predicted by the PDE. However, thisoptimization is difficult because it has many local minima. We propose analternative solution that relies on the properties of the PDE but does notinvolve solving the full forward model. Ducted environments result in an EMfield which can be decomposed into a few propagating, trapped modes. Thesemodes are a subset of the solutions to a Sturm-Liouville eigenvalue problem. Wedesign a new objective function that measures the distance from theobservations to a subspace spanned by these eigenvectors. The resultingoptimization problem is much easier than the one that arises in the standardapproach, and we show how to solve the associated nonlinear eigenvalue problemefficiently, leading to a real-time method.

A subspace pursuit method to infer refractivity in the marine atmospheric boundary layer