jfriedt / lora_sync

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File was created 1 \documentclass[a4paper]{article}
2 \usepackage{color,graphicx,fullpage}
3 \begin{document}
4 \noindent
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7 \input{analyse.pspdftex}
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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.
analyse_pspdftex.eps
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analyse_pspdftex.pdf
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