diff --git a/documents/thesis/chapters/grand_characterisation.tex b/documents/thesis/chapters/grand_characterisation.tex index 892ccfd..bb49174 100644 --- a/documents/thesis/chapters/grand_characterisation.tex +++ b/documents/thesis/chapters/grand_characterisation.tex @@ -38,18 +38,16 @@ This chapter starts an investigation into these systematic delays within \gls{GR % ADC At the base of every single antenna, a \gls{DU} is mounted. -%The \gls{DU} (see Figure~\ref{fig:grand_du}), at the base of every single antenna, is the workhorse of \gls{GRAND}.\Todo{rephrase} Its protective encasing has three inputs to which the different polarisations of the antenna are connected. These inputs are connected to their respective filterchains, leaving a fourth filterchain as spare. Each filterchain bandpasses the signal between $30\MHz$ and $200\MHz$. Finally, the signals are digitised by a four channel 14-bit \gls{ADC} sampling at $500\MHz$. %The input voltage ranges from $-900\mV$ to $+900\mV$. -In our setup, the channels are read out after one of two internal ``monitoring'' triggers fire. -%The ten-second trigger (TD) is linked to the \gls{1PPS} of the \gls{GNSS} chip. +In our setup, the channels are read out after one of two internal ``monitoring'' triggers fire with the ten-second trigger (TD) linked to the \gls{1PPS} of the \gls{GNSS} chip and the other (MD) a variable randomising trigger. \\ % timestamp = GPS + local oscillator -%The \gls{DU} timestamps an event using a combination of the 1\gls{PPS} of a Trimble ICM 360 \gls{GNSS} chip\Todo{ref?} and counting the local oscillator running at $500\MHz$. +%The \gls{DU} timestamps an event using a combination of the 1\gls{PPS} of a Trimble ICM 360 \gls{GNSS} chip and counting the local oscillator running at $500\MHz$. %At trigger time, the counter value is stored to obtain a timing accuracy of roughly $2\ns$. %The counter is also used to correct for fluctuating intervals of the 1\gls{PPS} by storing and resetting it at each incoming 1\gls{PPS}. diff --git a/documents/thesis/chapters/single_sine_interferometry.tex b/documents/thesis/chapters/single_sine_interferometry.tex index 30cefc5..35788de 100644 --- a/documents/thesis/chapters/single_sine_interferometry.tex +++ b/documents/thesis/chapters/single_sine_interferometry.tex @@ -77,7 +77,6 @@ Note that the period mismatch term $\Delta k_{ij}$ in \eqref{eq:synchro_mismatch % \includegraphics[width=\textwidth]{beacon/08_beacon_sync_synchronised_period_alignment.pdf} % \caption{ % Lifting period degeneracy ($k=n-m=7$ periods) using the optimal overlap between impulsive signals. -% \protect\Todo{note misaligned overlap due to different locations} % } % \label{fig:beacon_sync:period_alignment} % \end{subfigure} @@ -91,10 +90,6 @@ Note that the period mismatch term $\Delta k_{ij}$ in \eqref{eq:synchro_mismatch % \subref{fig:beacon_sync:period_alignment}: Expecting the impulsive signals to come from the same source, the overlap between the two impulsive signals is used to lift the period degeneracy ($k=n-m$). % } % \label{fig:beacon_sync:sine} -% \protect\Todo{ -% Redo figure without xticks and spines, -% rename $\Delta \tClockPhase$ -% } \end{figure}%>>> % Same transmitter / Static setup @@ -253,7 +248,6 @@ At each location, after removing propagation delays, each waveform and the refer \footnote{%<<< Note that one could use a correlation method instead of a maximum to select the best time delay. However, for simplicity and ease of computation, this has not been implemented. -%\Todo{incomplete p} %As shown in Figure~\ref{fig:single:annotated_full_waveform}, the air shower signal has a length in the order of a few nanoseconds. %Since it is this peak that is of interest, it would have been possible to cut the waveforms such to only correlate the peaks. } %>>> @@ -346,7 +340,7 @@ The restriction of the possible delays is therefore important to limit the numbe \\ % fall in local extremum, maximum -In this analysis, the initial grid is defined as $8^\circ$ wide around the true axis.\Todo{why?} +In this analysis, the initial grid is defined as $8^\circ$ wide around the true axis. As the number of computations scales linearly with the number of grid points ($N = N_x N_y$), it is favourable to minimise the number of grid locations. Unfortunately, the above process has been observed to fall into local maxima when a too coarse initial grid ($N_x < 13$ at $X=400\,\mathrm{g/cm^2}$) was used while restricting the time delays to $\left| k \right| \leq 3$. \\