CRHEP presentation on beacons

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Eric Teunis de Boone 2022-10-05 18:49:14 +02:00
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\documentclass[showdate=false]{beamer}
\usepackage[british]{babel}
\usepackage{amsmath}
\usepackage{hyperref}
\usepackage[backend=bibtex,style=trad-plain]{biblatex}
\usepackage{graphicx}
\graphicspath{{.}{../../figures/}}
\usepackage{todo}
\addbibresource{../../../bibliotheca/bibliography.bib}
% Disable Captions
\setbeamertemplate{caption}{\raggedright\small\insertcaption\par}
% Show Section overview at beginning of section
%\AtBeginSection[]
%{
% \begin{frame}<beamer>{Table of Contents}
% \tableofcontents[currentsection, currentsubsection, sectionstyle=show/shaded, subsectionstyle=hide]
% \end{frame}
%}
% no to navigation, yes to frame numbering
\beamertemplatenavigationsymbolsempty
\setbeamerfont{page number in head/foot}{size=\normalsize}
\setbeamertemplate{footline}[frame number]
\title[Beacon Timing]{Enhancing Timing Accuracy using Beacons}
\date{Oct 06, 2022}
\author{E.T. de Boone}
\begin{document}
\frame{\titlepage}
\begin{frame}{Enhancing time accuracy}
\begin{block}{}
Goal: $\sigma_t < 1\mathrm{ns}$
(enabling Radio Interferometry)
\end{block}
\begin{block}{Strategy}
\begin{itemize}
\item Simulating beacons
\item Characterising GNSS (GRAND)
\end{itemize}
\end{block}
\begin{block}{Current Timing Methods}
\begin{itemize}
\item GNSS (online) (GPS: $\sigma_t \leq 30 \mathrm{ns}$ $@95\%$ of the time)
\item Beacon (online/offline)
\end{itemize}
\end{block}
\end{frame}
% Antenna Setup
\section{Beacon}
\begin{frame}{Antenna Setup}
\begin{block}{}
Local time $i$ due to time delay $t_{\mathrm{d}i}$ and clock skew $\sigma_i$\\
\end{block}
\begin{figure}
\includegraphics<1>[width=0.8\textwidth]{beacon/antenna_setup_three.pdf}
\includegraphics<2->[width=0.8\textwidth]{beacon/antenna_setup_four.pdf}
\vspace{-2cm}
\end{figure}
\begin{equation*}
\Delta t'_{12} = t'_1 - t'_2 = \Delta t_{\mathrm{d}12} + \sigma_{12}
\end{equation*}
\begin{equation*}
\sigma_{12} + \sigma_{23} + \sigma_{31} = 0
\end{equation*}
\end{frame}
\begin{frame}{Beacon properties}
%\Todo{Pulse vs Sine and why choose one over the other}
%Pulse:
% online only
% direct measurement of \sigma_i
%Sine:
% online and offline
% measurement of phase
% removable if f appropriate
%\begin{table}
% \centering
% \begin{tabular}{r|l|l}
% & Pulse & Sine \\
% \hline \\
% on/offline & online & online + offline \\
% measurement & $t'_i (= t_i + \sigma_i)$ & $\varphi'_i (= 2\pi (\frac{t'_i}{T}\mod 1))$ \\
% resolving & requires high sampling rate & tracelength dependent \\
% removable from trace & unsure & if $f$ appropriate \\
% \end{tabular}
%\end{table}
\begin{columns}[t]
\begin{column}{.45\textwidth}
\begin{block}{Pulse}
\begin{itemize}
\item online
\item $t'_i$ {\small $(= t_i + \sigma_i)$}
\item resolving requires high sampling rate
\end{itemize}
\end{block}
\end{column}
\hfill
\begin{column}{.45\textwidth}
\begin{block}{Sine}
\begin{itemize}
\item online + offline
\item $\varphi'_i$ {\small $(= 2\pi (ft'_i\mod 1))$}
\item resolving is tracelength dependent
\item removable from physics if $f$ appropriate
\end{itemize}
\end{block}
\end{column}
\end{columns}
\end{frame}
\subsection{Pulse}
\begin{frame}{Beacon: Pulse (single baseline)}
\begin{figure}
\includegraphics<1>[width=\textwidth]{beacon/field_single_center_time.pdf}
\includegraphics<2>[width=\textwidth]{beacon/field_single_left_time.pdf}
\end{figure}
\end{frame}
\begin{frame}{Beacon: Pulse (3 baselines)}
\begin{figure}
\includegraphics<1>[width=\textwidth]{beacon/field_three_center_time.pdf}
\includegraphics<2>[width=\textwidth]{beacon/field_three_left_time.pdf}
\end{figure}
\end{frame}
\begin{frame}{Beacon: Pulse (multi baseline)}
\begin{figure}
\includegraphics<1>[width=\textwidth]{beacon/field_square_ref0_time.pdf}
\includegraphics<2>[width=\textwidth]{beacon/field_square_all_time.pdf}
\end{figure}
\end{frame}
\subsection{Sine}
\begin{frame}{Beacon: Sine (single baseline)}
\begin{figure}
\includegraphics<1>[width=\textwidth]{beacon/field_single_center_phase.pdf}
\includegraphics<2>[width=\textwidth]{beacon/field_single_left_phase.pdf}
\end{figure}
\end{frame}
\begin{frame}{Beacon: Sine (3 baseline)}
\begin{figure}
\includegraphics<1>[width=\textwidth]{beacon/field_three_center_phase.pdf}
\includegraphics<2>[width=\textwidth]{beacon/field_three_left_phase.pdf}
\end{figure}
\end{frame}
\begin{frame}{Beacon: Sine (multi baseline)}
\begin{figure}
\includegraphics<1>[width=\textwidth]{beacon/field_square_ref0_phase.pdf}
\includegraphics<2>[width=\textwidth]{beacon/field_square_all_phase.pdf}
\end{figure}
\end{frame}
\begin{frame}{Beacon: Sine: Two traces}
\begin{equation*}
t'_i = [t_i + \sigma_i] \mod T + n_i T = (\frac{\varphi'_i}{2\pi} + n_i)T = A_i + B_i
\end{equation*}
\begin{figure}
\includegraphics[width=1\textwidth]{beacon/08_beacon_sync_timing_outline.pdf}
\end{figure}
\begin{align*}
\Delta t_{ij} &= (A_j + B_j) - (A_i + B_i) + \Delta t_\varphi \\
&= \Delta A_{ij} + t_\varphi + k_{ij}T\\
\end{align*}
\end{frame}
\begin{frame}{Beacon: Sine: Two traces: Discrete solutions}
\begin{figure}
\includegraphics<1>[width=1\textwidth]{beacon/08_beacon_sync_timing_outline.pdf}
\includegraphics<2-3>[width=1\textwidth]{beacon/08_beacon_sync_synchronised_period_alignment.pdf}
\end{figure}
\alt<1-2>
{
\begin{figure}
\includegraphics[width=1\textwidth]{beacon/08_beacon_sync_coherent_sum.pdf}
\end{figure}
}{
\begin{block}{Work in Progress}
Simulated airshower + sine beacon and determining the relative offsets between the antennas...
\end{block}
}
\end{frame}
\end{document}

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# vim:ft=make
-include config.mk
.PHONY: all clean dist-clean
### Variables
MAIN_SRC ?= main.tex
TEXENGINE ?= latexmk --pdf
MAIN_TARGET = $(patsubst %.tex,%.pdf,$(MAIN_SRC))
### Targets
all: $(MAIN_TARGET)
dist: all clean
$(MAIN_TARGET): $(MAIN_SRC)
$(TEXENGINE) $^
dist-clean: clean
@rm -vf *.pdf *.eps *.dvi *.ps
clean:
@rm -vf *.dat *.log *.out *.aux *.nav *.snm *.toc *.vrb *~ *.fls *.fdb_latexmk *-blx.bib *.bbl *.blg *.run.xml

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# Short Presentation on current status (Beacon)
Mostly to show what I've been doing uptil now.
### Outline
* Timing Mechanisms (GNSS, Beacon)
* Geometry of testing Tx and Antennas

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MAIN_SRC=2022-10-06_CRHEP.tex