Merge branch '2023-04-13_group_meeting' into main

presentations/2022-12-15_group_meeting/2022-12-15_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{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}

presentations/2022-12-15_group_meeting/README.md

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+# Short Presentation on current status (Beacon)
+
+Mostly to show what I've been doing uptil now.

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}<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{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}

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

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
+
+
+

presentations/2023-04-13_group_meeting/config.mk

@@ -0,0 +1 @@
+MAIN_SRC=2023-04-13_CRHEP.tex