Thesis: Beacon: wrong k in equation

documents/thesis/chapters/beacon_discipline.tex

@@ -369,7 +369,8 @@ changing the synchronisation mismatches in \eqref{eq:synchro_mismatch_clocks} to
 		(\Delta \tClock)_{ij}
 		&\equiv (\tClock)_i - (\tClock)_j \\
 		&= (\Delta \tMeasArriv)_{ij} - (\Delta \tTrueArriv)_{ij} \\
-		&= (\Delta \tMeasArriv)_{ij} - (\Delta \tProp)_{ij}  - \Delta k_{ij} T\\
+		&= (\Delta \tMeasArriv)_{ij} - (\Delta \tProp)_{ij} \\
+		&= \left[ \frac{ (\Delta \pMeasArriv)_{ij}}{2\pi} - \Delta k'_{ij} \right] T - (\Delta \tProp)_{ij} \\
 		&= \left[ \frac{ (\Delta \pMeasArriv)_{ij}}{2\pi} - \frac{(\Delta \pProp)_{ij} }{2\pi} - \Delta k_{ij} \right] T\\
 		&\equiv \left[ \frac{ (\Delta \pClock)_{ij} }{2\pi} - \Delta k_{ij} \right] T
 		.\\
@@ -555,11 +556,11 @@ where $s$ is the amplitude of the beacon, $\sigma$ the noise amplitude and $\erf
 For sake of brevity, it will be referred to as ``Random Phasor Sum''.
 \\
 This Random Phasor Sum distribution collapses to a gaussian distribution when the beacon amplitude is (much) larger than the noise amplitude.
-This can be seen in Figure~\ref{fig:time_res_vs_snr} where both distributions are shown for a range of \glspl{SNR}.
+This can be seen in Figure~\ref{fig:sine:snr_time_resolution} where both distributions are shown for a range of \glspl{SNR}.
 There, the phase residuals of the simulated waveforms closely follow the distribution.
 \\
 
-From Figure~\ref{fig:time_res_vs_snr} we can conclude that depending on the \gls{SNR}, the timing accuracy of the beacon is below $1\ns$ for our beacon at $51.53\MHz$.
+From Figure~\ref{fig:sine:snr_time_resolution} we can conclude that depending on the \gls{SNR}, the timing accuracy of the beacon is below $1\ns$ for our beacon at $51.53\MHz$.
 Since the time accuracy is derived from the phase accuracy, slightly lower frequencies could be used, but they would require a stronger signal to resolve to the same degree.
 Likewise, higher frequencies are an available method of linearly improving the time accuracy.
 \\