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+\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{Dec 15, 2022} +\author{E.T. de Boone} + +\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} + \begin{block}{} + Local time $t_i$ due to time delay $t_{\mathrm{d}i}$ and clock skew $\sigma_i$\\ + \end{block} + \begin{figure} + \includegraphics[width=0.8\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_0 - t_0) + \end{equation*} +\end{frame} + +\begin{frame}{Beacon: Sine: Two traces} + \begin{equation*} + t'_i = (\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} + \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_timing_outline.pdf} + %\includegraphics<2>[width=1\textwidth]{beacon/08_beacon_sync_synchronised_period_alignment.pdf} + \end{figure} + \begin{figure} + \includegraphics[width=1\textwidth]{beacon/08_beacon_sync_coherent_sum.pdf} + \end{figure} +\end{frame} + +\begin{frame}{Simulation} + \begin{block}{} + Apply same steps to an airshower simulation: + \begin{itemize} + \item Add (sine) beacon to each antenna + \item Shift clocks + \item Measure phase + \item Repair clocks for small offset + \item Approximate + \end{itemize} + \end{block} +\end{frame} +\begin{frame}{} + \begin{figure} + \includegraphics<1>[width=1\textwidth]{figs/orig_antenna_geometry.pdf} + \end{figure} +\end{frame} + +\begin{frame}{Simulation: Phase: Local } + \begin{block}{} + @Antenna $i$: measure phase $\varphi_i$ , get $\varphi(\sigma_i) = \varphi_i - \varphi(t_0) - \varphi(t_{\mathrm{d}i})$ + \end{block} + \begin{figure} + \includegraphics<1>[width=1\textwidth]{figs/ba_measure_beacon_phase.py.A63.pdf} + \includegraphics<2>[width=1\textwidth]{figs/ba_measure_beacon_phase.py.A63.zoomed.pdf} + \includegraphics<3>[width=1\textwidth]{figs/bb_measure_true_phase.py.F0.05153.pdf} + \end{figure} +\end{frame} + +\begin{frame}{Simulation: Phase: Baseline} + \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]{figs/bc_baseline_phase_deltas.py.0ns.1.F0.05153.pdf} + \includegraphics<2>[width=1\textwidth]{figs/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=1\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.pdf} + \includegraphics<2>[width=1\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.zoomed.peak.pdf} + \includegraphics<3>[width=1\textwidth]{figs/ca_period_from_shower.py.loc12.0-2894.2-7780.1.i5.run2.zoomed.beacon.pdf} + \includegraphics<4>[width=1\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/2022-12-15_group_meeting/README.md b/presentations/2022-12-15_group_meeting/README.md new file mode 100644 index 0000000..b0147ee --- /dev/null +++ b/presentations/2022-12-15_group_meeting/README.md @@ -0,0 +1,3 @@ +# Short Presentation on current status (Beacon) + +Mostly to show what I've been doing uptil now. diff --git a/presentations/2022-12-15_group_meeting/figs/ba_measure_beacon_phase.py.A63.pdf b/presentations/2022-12-15_group_meeting/figs/ba_measure_beacon_phase.py.A63.pdf new file mode 100644 index 0000000..de0531e Binary files /dev/null and b/presentations/2022-12-15_group_meeting/figs/ba_measure_beacon_phase.py.A63.pdf differ diff --git a/presentations/2022-12-15_group_meeting/figs/ba_measure_beacon_phase.py.A63.zoomed.pdf b/presentations/2022-12-15_group_meeting/figs/ba_measure_beacon_phase.py.A63.zoomed.pdf new file mode 100644 index 0000000..7e53983 Binary files /dev/null and b/presentations/2022-12-15_group_meeting/figs/ba_measure_beacon_phase.py.A63.zoomed.pdf differ diff --git a/presentations/2022-12-15_group_meeting/figs/bb_measure_true_phase.py.F0.05153.pdf b/presentations/2022-12-15_group_meeting/figs/bb_measure_true_phase.py.F0.05153.pdf new file mode 100644 index 0000000..99c45a9 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b/presentations/2023-04-13_group_meeting/2023-04-13_CRHEP.tex @@ -0,0 +1,286 @@ +\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 $\sigma_i$ + \\ + \small\begin{equation*} + t'_i = t_{tx} + t_{\mathrm{d}i} + \sigma_i + \end{equation*} + \begin{figure} + \includegraphics[width=0.6\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*}} + \only<3>\vfill +\end{frame} + +\section{Simulations} +\begin{frame}{Simulation: Sine} + Apply previous steps to an airshower simulation (providing the pulse): + \begin{block}{} + \begin{itemize} + \item Add (sine) beacon to each antenna + \item Shift clocks + \item Measure phase + \item Repair clocks for small offset $\Delta t'_{ij}$ + \item Iteratively find best $k_{ij}$ + \end{itemize} + \end{block} +\end{frame} + +\begin{frame}{Simulation: Antenna Setup} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{figure} + \includegraphics[width=\textwidth]{ZH_simulation/tx_array_geometry.png} + \end{figure} + \end{column} + \hfill + \begin{column}{0.45\textwidth} + \begin{figure} + \includegraphics[width=\textwidth]{ZH_simulation/array_geometry_beacon_amplitude.png} + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Simulation: Measure 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=0.8\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.no_mask.pdf} + \includegraphics<2>[width=0.8\textwidth]{ZH_simulation/ba_measure_beacon_phase.py.A74.masked.pdf} + \end{figure} +\end{frame} + +\begin{frame}{Simulation: Phase measurement} + Beacon frequency: $51.53~\mathrm{MHz}$ + \begin{figure} + \includegraphics<1>[width=0.8\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e1.pdf} + \includegraphics<2>[width=0.45\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e1.pdf} + \hfill + \includegraphics<2>[width=0.45\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e3.pdf} + \\ + \vspace{0.5cm} + \includegraphics<2>[width=0.45\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e4.pdf} + \hfill + \includegraphics<2>[width=0.45\textwidth]{ZH_simulation/bd_antenna_phase_deltas.py.phase.residuals.c5_b_N4096_noise1e5.pdf} + \end{figure} +\end{frame} + +\begin{frame}{Simulation: 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*} + + \tiny{Random Phasor Sum: ``Statistical Optics'', J. Goodman} + \end{column} + \end{columns} +\end{frame} + + +\begin{frame}{Simulation: Phase: Baseline} + \begin{block}{Correction to previous talk: modifies global phase only} + @Baseline $i,j$: $\Delta \varphi_{ij} = \varphi(\sigma_i) - \varphi(\sigma_j)$ \\ + + Minimise matrix: + \tiny$\left(\begin{matrix} + \Delta_{11} & \Delta_{12} & \Delta_{13} & \\ + \Delta_{21} & \Delta_{22} & \Delta_{23} & \\ + \Delta_{31} & \Delta_{32} & \Delta_{33} & \\ + \end{matrix}\right)$ + \end{block} + \begin{figure} + \includegraphics<1>[width=0.8\textwidth]{ZH_simulation/bc_baseline_phase_deltas.py.residuals.c5_b_N4096_noise1e3.pdf} + \end{figure} +\end{frame} + +\begin{frame}{Simulation: Period $k_i$} + \small{ + Interferometry while allowing to shift by $T = 1/f_\mathrm{beacon}$ + \\ + Iterative process: \\ + \; Scan positions finding the best $\{k_i\}$ set, then zoom in on strongest. + } + + \only<1-4>{\begin{figure} + \includegraphics<1>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.run0.i5.loc8.0-2795.4-7816.0.pdf} + \includegraphics<2>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.run0.i99.loc8.0-2795.4-7816.0.pdf} + \includegraphics<3>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run0.pdf} + \includegraphics<4>[width=0.8\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run0.power.pdf} + \end{figure}} + \only<5>{\begin{figure} + \includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run0.pdf} + \hfill + \includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run0.power.pdf} + \vspace{0.5cm} + \includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.maxima.run1.pdf} + \hfill + \includegraphics[width=0.45\textwidth]{ZH_simulation/findks/ca_period_from_shower.py.reconstruction.run1.power.pdf} + \end{figure}} +\end{frame} + +\begin{frame}{Simulation: Effects of Corrections} + Found both phase and period differences + \visible<2->{\begin{figure} + \includegraphics[width=0.45\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_none.scale4d.pdf} + \hfill + \includegraphics[width=0.45\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_phases.scale4d.pdf} + \vspace{0.5cm} + \includegraphics[width=0.45\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_all.scale4d.pdf} + \hfill + \includegraphics[width=0.45\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.no_offset.scale4d.pdf} + \end{figure}} +\end{frame} + +\begin{frame}{Simulation Conclusions} + \begin{columns} + \begin{column}{0.5\textwidth} + \begin{itemize} + \item (Single) Sine beacon:\\ + $\sigma < 1\mathrm{ns}$ from $\mathrm{SNR} > 3$\\ + depends on beacon period. + \vspace{1cm} + \item Pulsed beacon:\\ + (small) ongoing work\\ + while writing thesis. + \end{itemize} + \end{column} + \begin{column}{0.5\textwidth} + \begin{figure} + \includegraphics[width=1.1\textwidth]{beacon/time_res_vs_snr.pdf} + \end{figure} + \end{column} + \end{columns} +\end{frame} + +\begin{frame}{Simulation: Effects of Corrections (fullsize)} + \begin{figure} + \includegraphics<+>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_none.scale4d.pdf} + \includegraphics<+>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_phases.scale4d.pdf} + \includegraphics<+>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.repair_all.scale4d.pdf} + \includegraphics<+>[width=\textwidth]{radio_interferometry/dc_grid_power_time_fixes.py.X400.no_offset.scale4d.pdf} + \end{figure} +\end{frame} + +\begin{frame}{Signal to Noise definition} + \begin{figure} + \includegraphics[width=\textwidth]{ZH_simulation/signal_to_noise_definition.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