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

## TL;DR

This paper introduces a real-time subspace pursuit method for inferring refractivity in the marine atmospheric boundary layer by leveraging eigenmodes of the Helmholtz equation, avoiding complex PDE solutions.

## Contribution

It proposes a novel subspace-based optimization approach that simplifies the inverse problem for electromagnetic propagation in the MABL, enabling efficient real-time inference.

## Key findings

- Efficient eigenmode-based objective function for MABL inference
- Reduced computational complexity compared to traditional PDE-based methods
- Successful demonstration of real-time refractivity estimation

## Abstract

Inferring electromagnetic propagation characteristics within the marine atmospheric boundary layer (MABL) from data in real time is crucial for modern maritime navigation and communications. The propagation of electromagnetic waves is well modeled by a partial differential equation (PDE): a Helmholtz equation. A natural way to solve the MABL characterization inverse problem is to minimize what is observed and what is predicted by the PDE. However, this optimization is difficult because it has many local minima. We propose an alternative solution that relies on the properties of the PDE but does not involve solving the full forward model. Ducted environments result in an EM field which can be decomposed into a few propagating, trapped modes. These modes are a subset of the solutions to a Sturm-Liouville eigenvalue problem. We design a new objective function that measures the distance from the observations to a subspace spanned by these eigenvectors. The resulting optimization problem is much easier than the one that arises in the standard approach, and we show how to solve the associated nonlinear eigenvalue problem efficiently, leading to a real-time method.