Sensing and Multiscale Structure

TL;DR

This paper presents a novel method for estimating parameters of fractal random scattering media using multiscale properties, with applications to sea ice thickness measurement via sonar.

Contribution

It introduces an exact analytical solution for parameter estimation in fractal scattering media, including Brownian and Ornstein-Uhlenbeck slopes, validated by numerical simulations.

Findings

Derived an expression for slope volatility in fractal media.

Proved invariance of the volatility expression under probability measure changes.

Applied the method to estimate sea ice thickness using sonar data.

Abstract

We introduce a method of estimating parameters associated with a fractal random scattering medium, which utilizes the multiscale properties of the scattered field. The example of ray-density fluctuations beyond a phase screen with fractal slope is considered. An exact solution to the forward problem, in the case of the Brownian fractal, leads to an expression for the volatility of the slope. This expression is invariant under a change of probability measure, a fact which gives rise to the corresponding result for a (stationary) Ornstein-Uhlenbeck slope. We demonstrate that our analytical results are consistent with numerical simulations. Finally, an application to the determination of sea ice thickness via sonar is discussed.