CRHEP presentation on beacons

presentations/2022-10-06_group_meeting/2022-10-06_CRHEP.tex

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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}

presentations/2022-10-06_group_meeting/Makefile

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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

presentations/2022-10-06_group_meeting/README.md

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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

presentations/2022-10-06_group_meeting/config.mk

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+MAIN_SRC=2022-10-06_CRHEP.tex