diff --git a/presentations/2023-04-13_group_meeting/2023-04-13_CRHEP.tex b/presentations/2023-04-13_group_meeting/2023-04-13_CRHEP.tex new file mode 100644 index 0000000..7a52bd9 --- /dev/null +++ b/presentations/2023-04-13_group_meeting/2023-04-13_CRHEP.tex @@ -0,0 +1,207 @@ +\documentclass[showdate=false]{beamer} + +\usepackage[british]{babel} +\usepackage{amsmath} +\usepackage{hyperref} +\usepackage[backend=bibtex,style=trad-plain]{biblatex} +\usepackage{graphicx} +\graphicspath{{.}{../../figures/}} +\usepackage{todo} +\usepackage{physics} +\usepackage{cancel} + +\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{Apr 13, 2023} +\author{E.T. de Boone} + + + + +\newcommand{\pTrue}{\phi} +\newcommand{\PTrue}{\Phi} +\newcommand{\pMeas}{\varphi} + +\newcommand{\pTrueEmit}{\pTrue_0} +\newcommand{\pTrueArriv}{\pTrueArriv'} +\newcommand{\pMeasArriv}{\pMeas_0} +\newcommand{\pProp}{\pTrue_d} +\newcommand{\pClock}{\pTrue_c} + + + + + + +\begin{document} +\frame{\titlepage} + +\begin{frame}{Enhancing time accuracy} + \begin{block}{} + Goal: $\sigma_{ij} < 1\mathrm{ns}$ + (enabling Radio Interferometry) + \end{block} + + \begin{block}{Strategy} + \begin{itemize} + \item Simulating beacons (both pulse and sine) + \item Characterising GNSS (GRAND) + \end{itemize} + \end{block} +\end{frame} + +% Antenna Setup +\section{Beacon} +\begin{frame}{Antenna Setup} + \vskip -2em + Local antenna time $t'_i$ due to time delay $t_{\mathrm{d}i}$ and clock skew $\sigma_i$ + \\ + \begin{figure} + \includegraphics[width=0.4\textwidth]{beacon/antenna_setup_two.pdf} + \end{figure} + \vskip -2em + \begin{equation*} + \Delta t'_{12} = t'_1 - t'_2 = \Delta t_{\mathrm{d}12} + \sigma_{12} + (t_{tx} - t_{tx}) + \end{equation*} +\end{frame} + +\begin{frame}{Beacon: Sine: Two traces} + Required signal: sine (beacon) + single pulse + \begin{equation*} + t'_i = (\frac{\varphi'_i}{2\pi} + n_i)T = A_i + B_i + \end{equation*} + \begin{figure} + \includegraphics<1>[width=1\textwidth]{beacon/08_beacon_sync_timing_outline.pdf} + \includegraphics<2>[width=1\textwidth]{beacon/08_beacon_sync_synchronised_outline.pdf} + \end{figure} + \begin{align*} + \Delta t'_{ij} &= (A_j + B_j) - (A_i + B_i) + \Delta t'_\varphi \\ + &= \Delta A_{ij} + \only<1>{\Delta t'_\varphi}\only<2->{\cancel{\Delta 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_synchronised_outline.pdf} + \includegraphics<2->[width=1\textwidth]{beacon/08_beacon_sync_synchronised_period_alignment.pdf} + \end{figure} + \begin{figure} + \includegraphics<-2>[width=1\textwidth]{beacon/08_beacon_sync_coherent_sum.pdf} + \end{figure} + \only<3>{\begin{equation*}\Delta t'_{ij} = \Delta A_{ij} + \cancel{\Delta t'_\varphi} + \cancel{k_{ij}T} \end{equation*}} +\end{frame} + +\section{Simulations} +\begin{frame}{Simulation} + \begin{block}{} + Apply previous steps to an airshower simulation (which provides the pulse): + \begin{itemize} + \item Add (sine) beacon to each antenna + \item Shift clocks + \item Measure phase + \item Repair clocks for small offset $\Delta A_{ij}$ + \item Iteratively find best $k_{ij}$ + \end{itemize} + \end{block} +\end{frame} + +\begin{frame}{Simulation: Antenna Setup} + \begin{figure} + \includegraphics[width=0.5\textwidth]{path_leading_to_array_setup_with_inset_tx_array} + \end{figure} +\end{frame} + +\begin{frame}{Simulation: Local Phase} + \begin{block}{} + @Antenna $i$: measure phase $\varphi_i$ using DTFT, get $\varphi(\sigma_i) = \varphi_i - \varphi(t_0) - \varphi(t_{\mathrm{d}i})$ + \end{block} + \begin{figure} + \includegraphics<1>[width=1\textwidth]{ba_measure_beacon_phase.py.A63.pdf} + \includegraphics<2>[width=1\textwidth]{ba_measure_beacon_phase.py.A63.zoomed.pdf} + \includegraphics<3>[width=1\textwidth]{bb_measure_true_phase.py.F0.05153.pdf} + \end{figure} +\end{frame} + +\begin{frame}{Sine: Signal to Noise} + \begin{figure} + \includegraphics[width=0.8\textwidth]{beacon/time_res_vs_snr.pdf} + \end{figure} + \begin{columns} + \begin{column}{0.3\textwidth} + \end{column} + \begin{column}{0.7\textwidth} + \tiny\begin{equation*} + p_\PTrue(\pTrue; s, \sigma) = + \frac{ e^{-\left(\frac{s^2}{2\sigma^2}\right)} }{ 2 \pi } + + + \sqrt{\frac{1}{2\pi}} + \frac{s}{\sigma} + e^{-\left( \frac{s^2}{2\sigma^2}\sin^2{\pTrue} \right)} + \frac{\left( + 1 + \erf{ \frac{s \cos{\pTrue}}{\sqrt{2} \sigma }} + \right)}{2} + \cos{\pTrue} + \end{equation*} + \end{column} + \end{columns} +\end{frame} + + +\begin{frame}{Simulation: Phase: Baseline} + Previously, matrix minimisation + \begin{block}{} + @Baseline $i,j$: $\Delta \varphi_{ij} = \varphi(\sigma_i) - \varphi(\sigma_j)$ \\ + + Minimise matrix: + $\left(\begin{matrix} + \Delta_{11} & \Delta_{12} & \Delta_{13} & \\ + \Delta_{21} & \Delta_{22} & \Delta_{23} & \\ + \Delta_{31} & \Delta_{32} & \Delta_{33} & \\ + \end{matrix}\right)$ + \end{block} + \begin{figure} + \includegraphics<1>[width=1\textwidth]{bc_baseline_phase_deltas.py.0ns.1.F0.05153.pdf} + \includegraphics<2>[width=1\textwidth]{bc_baseline_phase_deltas.py.5ns_gauss1.F0.05153.pdf} + \end{figure} +\end{frame} + +\begin{frame}{Simulation: Period $k$} + \begin{block}{} + Interferometry while allowing to shift by $T = 1/f_\mathrm{beacon}$ + \end{block} + + \begin{figure} + \includegraphics<1>[width=0.8\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.pdf} + \includegraphics<2>[width=0.8\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.zoomed.peak.pdf} + \includegraphics<3>[width=0.8\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.zoomed.beacon.pdf} + \includegraphics<4>[width=0.8\textwidth]{figs/bc_period_from_shower.py.maxima.run0.0ns.pdf} + \end{figure} +\end{frame} + + + +% +%\begin{frame}{Interferometry} +% \begin{figure} +% \includegraphics<1>[width=1\textwidth]{figs/reconstruct_5ns.pdf} +% \includegraphics<2>[width=1\textwidth]{figs/reconstruct_15ns.pdf} +% \end{figure} +%\end{frame} +\end{document} diff --git a/presentations/2023-04-13_group_meeting/Makefile b/presentations/2023-04-13_group_meeting/Makefile new file mode 100644 index 0000000..449c34a --- /dev/null +++ b/presentations/2023-04-13_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/2023-04-13_group_meeting/README.md b/presentations/2023-04-13_group_meeting/README.md new file mode 100644 index 0000000..1994125 --- /dev/null +++ b/presentations/2023-04-13_group_meeting/README.md @@ -0,0 +1,14 @@ +# Short Presentation on current status (Beacon) + +Mostly to show what I've been doing uptil now. + +Recap Sine Beacon +DTFT +Deviation Minimisation was poorly explained (and doesn't work) + +!! 150MHz in addition to 50MHz simulation + +Maybe Pulsed beacon scheme if time allows + + + diff --git a/presentations/2023-04-13_group_meeting/config.mk b/presentations/2023-04-13_group_meeting/config.mk new file mode 100644 index 0000000..63d2828 --- /dev/null +++ b/presentations/2023-04-13_group_meeting/config.mk @@ -0,0 +1 @@ +MAIN_SRC=2023-04-13_CRHEP.tex