From 6a2513f3135f4f089013a21995ea2d9ee1deb29e Mon Sep 17 00:00:00 2001 From: Eric Teunis de Boone Date: Wed, 5 Oct 2022 18:49:14 +0200 Subject: [PATCH] CRHEP presentation on beacons --- .../2022-10-06_CRHEP.tex | 195 ++++++++++++++++++ .../2022-10-06_group_meeting/Makefile | 24 +++ .../2022-10-06_group_meeting/README.md | 8 + .../2022-10-06_group_meeting/config.mk | 1 + 4 files changed, 228 insertions(+) create mode 100644 presentations/2022-10-06_group_meeting/2022-10-06_CRHEP.tex create mode 100644 presentations/2022-10-06_group_meeting/Makefile create mode 100644 presentations/2022-10-06_group_meeting/README.md create mode 100644 presentations/2022-10-06_group_meeting/config.mk diff --git a/presentations/2022-10-06_group_meeting/2022-10-06_CRHEP.tex b/presentations/2022-10-06_group_meeting/2022-10-06_CRHEP.tex new file mode 100644 index 0000000..8145292 --- /dev/null +++ b/presentations/2022-10-06_group_meeting/2022-10-06_CRHEP.tex @@ -0,0 +1,195 @@ +\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}{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} diff --git a/presentations/2022-10-06_group_meeting/Makefile b/presentations/2022-10-06_group_meeting/Makefile new file mode 100644 index 0000000..449c34a --- /dev/null +++ b/presentations/2022-10-06_group_meeting/Makefile @@ -0,0 +1,24 @@ +# 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 diff --git a/presentations/2022-10-06_group_meeting/README.md b/presentations/2022-10-06_group_meeting/README.md new file mode 100644 index 0000000..1651da3 --- /dev/null +++ b/presentations/2022-10-06_group_meeting/README.md @@ -0,0 +1,8 @@ +# 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 diff --git a/presentations/2022-10-06_group_meeting/config.mk b/presentations/2022-10-06_group_meeting/config.mk new file mode 100644 index 0000000..53e4f12 --- /dev/null +++ b/presentations/2022-10-06_group_meeting/config.mk @@ -0,0 +1 @@ +MAIN_SRC=2022-10-06_CRHEP.tex