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authorRefik Hadzialic2012-06-08 21:09:33 +0200
committerRefik Hadzialic2012-06-08 21:09:33 +0200
commit92774383f1294568cb84e47961f9431abdbc2945 (patch)
treebee8e240eb31a719382823cba741f1c9149f0f19 /vorlagen/thesis/src/kapitel_x.tex
parentGPS description (diff)
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GPS
Diffstat (limited to 'vorlagen/thesis/src/kapitel_x.tex')
-rw-r--r--vorlagen/thesis/src/kapitel_x.tex41
1 files changed, 35 insertions, 6 deletions
diff --git a/vorlagen/thesis/src/kapitel_x.tex b/vorlagen/thesis/src/kapitel_x.tex
index 859dbd4..c81182c 100644
--- a/vorlagen/thesis/src/kapitel_x.tex
+++ b/vorlagen/thesis/src/kapitel_x.tex
@@ -40,18 +40,23 @@ broadcast GPS system time stamp. These errors can be
characterized as bias, drift and aging errors
\citep{GPS-Interface-Specification}. The correct broadcast
time can be estimated using the model equation given in
-\ref{eq:timecorrection1} \citep{GPS-Interface-Specification}.
+\eqref{eq:timecorrection1} \citep{GPS-Interface-Specification}.
$t$ is the correctly estimated GPS system time at broadcast
-moment. In equation \ref{eq:timecorrection2}, where the GPS
+moment. In equation \eqref{eq:timecorrection2}, where the GPS
receiver is required to calculate the satellite clock
offset, $\Delta t_{SV}$, a number of unknown terms can be
seen. These terms are contained in the subframe 1 or
can be estimated using predefined equations. The polynomial
-coefficients, a
+coefficients: $a_{f0}$ - clock offset, $a_{f1}$ - fractional
+frequency offset, $a_{f0}$ - fractional frequency drift; and
+$t_{0c}$ - reference epoch are contained in the subframe 1.
Finally, the only unknown term left in equation
-\ref{eq:timecorrection2} is $t_{r}$, the relativistic correction
+\eqref{eq:timecorrection2} is $t_{r}$, the relativistic correction
term. $t_{r}$ can be evaluated by applying the
-equation in \ref{eq:timecorrection3}.
+equation in \eqref{eq:timecorrection3}. $F$ is a constant
+calculated from the given parameters in \eqref{eq:paramconst1}
+and \eqref{eq:paramconst2}, whereas $e$, $\sqrt{A}$ and $E_{k}$
+are orbit parameters contained in subframe 2 and 3 \citep{GPS-Interface-Specification}.
\begin{equation}
\label{eq:timecorrection1}
@@ -62,9 +67,33 @@ t=t_{SV}-\Delta t_{SV}
\begin{alignat}{4}
& \Delta t_{SV} &= \;& a_{f0} + a_{f1}(t_{SV}-t_{oc}) + a_{f2}(t_{SV}-t_{oc})^{2} + \Delta t_{r} \label{eq:timecorrection2} \\
& \Delta t_{r} &= \; & Fe\sqrt{A}\sin{E_{k}} \label{eq:timecorrection3} \\
- & F &= \;& \frac{-2\sqrt{\mu}} {c^{2}} = -4.442807633 \cdot 10^{-10} \label{eq:timecorrection4}
+ & F &= \;& \frac{-2\sqrt{\mu}} {c^{2}} = -4.442807633 \cdot 10^{-10} \frac{s}{\sqrt{m}} \label{eq:timecorrection4}
\end{alignat}
+\begin{equation}
+\label{eq:paramconst1}
+ \begin{split}
+ \mu = 3.986005\cdot 10^{14} \frac{m^3}{s^2}
+ \end{split}
+\quad\Longleftarrow\quad
+ \begin{split}
+ \mbox{value of Earth's universal gravitational parameters}
+ \end{split}
+\end{equation}
+
+\begin{equation}
+\label{eq:paramconst2}
+ \begin{split}
+ c= 2.99792458\cdot 10^{8} \frac{m}{s}
+ \end{split}
+\quad\Longleftarrow\quad
+ \begin{split}
+ \mbox{speed of light}
+ \end{split}
+\end{equation}
+
+
+
\begin{alignat}{4}
& A & = & \; (\sqrt{A})^2 \nonumber \\