jfriedt / lora_sync

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Commit f56917e000f631a50d4750526ff76f2a8b21c714

Authored by Jean-Michel Friedt
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  1 +#FIG 3.2 Produced by xfig version 3.2.8
  2 +Landscape
  3 +Center
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  45 +4 0 0 50 -1 0 12 0.0000 6 165 675 7020 4365 gateway\001
  46 +4 0 4 50 -1 0 12 0.0000 6 165 480 5625 4680 $t_1$\001
  47 +4 0 4 50 -1 0 12 0.0000 6 165 480 7380 4995 $t_2$\001
  48 +4 0 4 50 -1 0 12 0.0000 6 165 540 7380 5265 $T_3$\001
  49 +4 0 4 50 -1 0 12 0.0000 6 165 540 7380 5760 $T_4$\001
  50 +4 0 4 50 -1 0 12 0.0000 6 165 540 5175 4860 $T_1$\001
  51 +4 0 4 50 -1 0 12 0.0000 6 165 540 5175 6210 $T_2$\001
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  54 +4 0 1 50 -1 0 12 0.0000 6 180 1320 6615 4680 $t\\rightarrow 0$\001
  1 +\begin{picture}(0,0)%
  2 +\includegraphics{analyse_pspdftex}%
  3 +\end{picture}%
  4 +\setlength{\unitlength}{4144sp}%
  5 +%
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  7 +\gdef\SetFigFont#1#2#3#4#5{%
  8 + \reset@font\fontsize{#1}{#2pt}%
  9 + \fontfamily{#3}\fontseries{#4}\fontshape{#5}%
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  13 +\put(5221,-3526){\makebox(0,0)[lb]{\smash{{\SetFigFont{12}{14.4}{\rmdefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}endpoint}%
  14 +}}}}
  15 +\put(7021,-3526){\makebox(0,0)[lb]{\smash{{\SetFigFont{12}{14.4}{\rmdefault}{\mddefault}{\updefault}{\color[rgb]{0,0,0}gateway}%
  16 +}}}}
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  1 +\documentclass[a4paper]{article}
  2 +\usepackage{color,graphicx,fullpage}
  3 +\begin{document}
  4 +\noindent
  5 +\begin{minipage}[t]{\linewidth}
  6 +\begin{minipage}{.37\linewidth}
  7 +\input{analyse.pspdftex}
  8 +\end{minipage}
  9 +\begin{minipage}{.63\linewidth}
  10 +En rouge les grandeurs mesur\'ees, en bleu les grandeurs inconnues~:
  11 +\begin{itemize}
  12 +\item $T_{1,2}$ sont les dates des messages \'emis et re\c cus par endpoint par rapport \`a son 1-PPS~: $T_2-T_1$
  13 +est ind\'ependant de la position du 1-PPS
  14 +\item $T_{3,4}$ sont les dates des messages re\c cus et \'emis par gateway par rapport \`a son 1-PPS~: $T_4-T_3$
  15 +est ind\'ependant de la position du 1-PPS
  16 +\item $t$ est l'\'ecart entre les 1-PPS de endpoint et gateway
  17 +\item on a $T_2-T_1=T_4-T_3+2\delta t\Leftrightarrow \delta t=\frac{1}{2}(T_4-T_3-(T_2-T_1))$ avec les
  18 +$T_{i,\forall i}$ connus donc on d\'eduit $\delta t$
  19 +\item on a $t+t_2=t_1+\delta t$ et on cherche \`a annuler $t$ donc on corrige $t_1$ tel que
  20 +$t_1+\delta t-t_2=T_1+\delta t-T_3$ s'annule
  21 +\end{itemize}
  22 +\end{minipage}
  23 +\end{minipage}\\
  24 +
  25 +LoRa a une port\'ee de 15~km ou 50~$\mu$s de temps de vol. Avec 125~kHz de bande passante on peut esp\'erer
  26 +avoir le temps de vol \`a la microseconde en sur-\'echantillonnant le pic de corr\'elation donc compenser
  27 +le temps de vol au-del\`a de 300~m de distance.
  28 +\end{document}
analyse_pspdftex.eps
Diff comments   View file @ f56917e
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analyse_pspdftex.pdf
Diff comments   View file @ f56917e
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