Inverting for Maritime Environments Using Proper Orthogonal Bases From Sparsely Sampled Electromagnetic Propagation Data

Fountoulakis, Vasileios; Earls, Christopher J.

doi:10.1109/tgrs.2016.2597138

Cited by 14 publications

(18 citation statements)

References 25 publications

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“…If the gradient extends sufficiently high (always within a few tens of meters), an anomalous atmospheric structure forms in which the propagation of electromagnetic waves is similar as when trapped in a waveguide. This kind of structure is known as the evaporation duct, and the relevant anomalous effectknown as ducting-can significantly affect radio systems, especially those working at the microwave band (Brooks 2001;Shi et al 2015a,b;Lentini and Hackett 2015;Zhang et al 2016b;Fountoulakis and Earls 2016;Kang and Wang 2016).…”

Section: Introductionmentioning

confidence: 99%

Statistical Analysis of the Quantified Relationship between Evaporation Duct and Oceanic Evaporation for Unstable Conditions

Zhang

Yang

2017

Journal of Atmospheric and Oceanic Technology

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An analysis is conducted for the first time to statistically quantify the relationship between the evaporation duct and oceanic evaporation. Through sensitivity analysis, under unstable conditions (air–sea temperature difference less than zero), evaporation duct and evaporation are found to maintain a similar trend with variations in air–sea variables, indicating a possible inherent connection. Furthermore, scatterplots of relevant historical data reveal that the evaporation duct generally increases in a power-law manner with evaporation. Therefore, logarithmic transformation is performed on the data, and then linear regression is adopted to derive the analytical expression of the linear trend. Additionally, based on this analytical expression, a three-parameter empirical model is proposed to estimate the temporal clustering, and the estimated result shows good agreement with the real distribution. The spatial variations of the parameters modeled over different focus areas reflect the influence of geophysical parameters.

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Section: Introductionmentioning

confidence: 99%

Statistical Analysis of the Quantified Relationship between Evaporation Duct and Oceanic Evaporation for Unstable Conditions

Zhang

Yang

2017

Journal of Atmospheric and Oceanic Technology

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“…The most important feature of this method is that it is able to overcome the highly multimodal behavior associated with the physics of EM wave propagation. This allows the use a local optimization method instead of a global optimization method which is typically used in the literature (such as genetic algorithms in, for example, [3], [19], [23], [27], [35]). As this method is able to cheaply find an estimate of the refractivity profile using local optimization, it could also be used to warm-start a different method which would typically require a global optimization method.…”

Section: Discussionmentioning

confidence: 99%

A Subspace Pursuit Method to Infer Refractivity in the Marine Atmospheric Boundary Layer

Gilles

Earls

Bindel

2019

IEEE Trans. Geosci. Remote Sensing

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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.

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“…In the presence of evaporation ducts under neutral stability conditions, the modified refractivity profile within the MABL can be modeled as a log‐linear curve using the Paulus‐Jeske model (Karimian et al, 2011):

M false(z false) = M_{0} + c ()(, z - z_{d} \ln ()(, \frac{z + z_{0}}{z_{0}})),

where M 0 is surface refractivity, c =0.13 M ‐units/m is critical potential refractivity gradient for neutral evaporation ducts, z 0 =0.00015 m is aerodynamic surface roughness of the ocean, and z d is the duct height. To be consistent with the South China Sea Monsoon Experiments in 1998 (SCSMEX, 1998), we chose M 0 =428.89 M ‐units and solve the EM wave equation using SSPE for all considered duct heights, z d , at every half meter between 2‐ and 40‐min altitude, which encompasses practical evaporation duct height instances (Fountoulakis & Earls, 2016).…”

Section: Forward Modelmentioning

confidence: 99%

“…Apart from RFC methods, approaches for constructing simplified forward models using observations obtained by sparsely sampling EM power within the MABL have emerged. Fountoulakis and Earls (2016) utilize blurring operators to approximate effects of the MABL, so that “just in time” estimates, for inferring duct parameters, may be obtained by manifold interpolation within a library of sparse proper orthogonal decomposition (POD) modes calculated offline from field observations. These field observations are sparsely sampled along a sinusoidal UAV flight path or a linear rocketsonde flight path.…”

Section: Introductionmentioning

confidence: 99%

Gaussian Process Regression for Estimating EM Ducting Within the Marine Atmospheric Boundary Layer

Sit

Earls

2020

Radio Science

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We show that Gaussian process regression (GPR) can be used to infer the electromagnetic (EM) duct height within the marine atmospheric boundary layer (MABL) from sparsely sampled propagation factors within the context of bistatic radars. We use GPR to calculate the posterior predictive distribution on the labels (i.e., duct height) from both noise-free and noise-contaminated array of propagation factors. For duct height inference from noise-contaminated propagation factors, we compare a naïve approach, utilizing one random sample from the input distribution (i.e., disregarding the input noise), with an inverse-variance weighted approach, utilizing a few random samples to estimate the true predictive distribution. The resulting posterior predictive distributions from these two approaches are compared to a "ground truth" distribution, which is approximated using a large number of Monte-Carlo samples. The ability of GPR to yield accurate and fast duct height predictions using a few training examples indicates the suitability of the proposed method for real-time applications.

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Inverting for Maritime Environments Using Proper Orthogonal Bases From Sparsely Sampled Electromagnetic Propagation Data

Cited by 14 publications

References 25 publications

Statistical Analysis of the Quantified Relationship between Evaporation Duct and Oceanic Evaporation for Unstable Conditions

Statistical Analysis of the Quantified Relationship between Evaporation Duct and Oceanic Evaporation for Unstable Conditions

A Subspace Pursuit Method to Infer Refractivity in the Marine Atmospheric Boundary Layer

Gaussian Process Regression for Estimating EM Ducting Within the Marine Atmospheric Boundary Layer

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