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\begin{document}

\wikidoc{file=Proj.RayTrace}
\wikidoc{auth=tpaine@mit.edu}

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\section*{Geometric Stochastic Ray Tracing}
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In this (unfunded side) project we developed a new model for acoustic
ray tracing that admits stochastic diffusion as a function of
uncertainty in the sound speed profile.  The approach uses recent
tools for analysis of differential motion on the special Euclidean
group.  One target application that would benefit from this approach
is ranged-based localization of underwater vehicles because the
uncertainty of the ray positions is more accurately represented as a
function of the uncertainty of the sound speed profile.


\begin{figure}[ht]
  \centering 
  \includegraphics[width=0.95\textwidth]{figures/raytrace1.png}
\label{fig_linc}
\caption{Model overview and relation to existing work.}
\end{figure}

\vspace{0.1in}
\noindent
To illustrate the capabilities of this new model, we compute the
stochastic ray traces with an uncertain sound speed profile computed
from data observed in the Beaufort Sea.




\vspace{0.1in}
\begin{figure}[ht]
  \centering 
  \includegraphics[width=0.95\textwidth]{figures/raytrace2.png}
\label{fig_raytrace2}
\end{figure}

\vspace{0.3in}

\begin{figure}[ht]
  \centering 
  \includegraphics[width=0.95\textwidth]{figures/raytrace3.png}
\label{fig_raytrace3}
\caption{Left to right: Uncertain SSP, Nominal ray traces (blue) with
  realizations of stochastic rays (gray), Distribution of errors in
  SSP, Distribution of ray trajectories at approximately 40km for a
  ray (a) in the Beaufort lens and (b) reflected about the surface.}
\end{figure}


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%\section*{Quick Facts}
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\vspace{0.15in}
\footnotesize
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\begin{longtable}{|r|p{0.76\textwidth}|} \hline

  \var{Status}: &amp; Ongoing since December 2023 \\ \hline
  \var{People}: &amp; Tyler Paine, Eeshan Bhatt \\ \hline
%  \var{Photos:} &amp; \urlx{https://oceanai.mit.edu/media/WestPoint2022/album} \\ \hline
\end{longtable}
\normalsize


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\section*{Recent Publications}

\input{citations.tex}
\wikinoref

\newpage
\bibliography{biblio.bib}
\bibliographystyle{plain}

\end{document}





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