From 92774383f1294568cb84e47961f9431abdbc2945 Mon Sep 17 00:00:00 2001 From: Refik Hadzialic Date: Fri, 8 Jun 2012 21:09:33 +0200 Subject: GPS --- vorlagen/thesis/maindoc.pdf | Bin 4299752 -> 4303852 bytes vorlagen/thesis/src/kapitel_A.tex | 12 +++++------ vorlagen/thesis/src/kapitel_x.tex | 41 ++++++++++++++++++++++++++++++++------ 3 files changed, 41 insertions(+), 12 deletions(-) (limited to 'vorlagen') diff --git a/vorlagen/thesis/maindoc.pdf b/vorlagen/thesis/maindoc.pdf index f16212b..b981a19 100644 Binary files a/vorlagen/thesis/maindoc.pdf and b/vorlagen/thesis/maindoc.pdf differ diff --git a/vorlagen/thesis/src/kapitel_A.tex b/vorlagen/thesis/src/kapitel_A.tex index bdfd07a..21f20e4 100644 --- a/vorlagen/thesis/src/kapitel_A.tex +++ b/vorlagen/thesis/src/kapitel_A.tex @@ -147,7 +147,7 @@ correct free ARFCN channel,in this case 877. arfcn 877 \end{lstlisting} The ARFCN channel value can be -calculated using the given formula in \ref{eq:arfcn}, where $f_{start}$ +calculated using the given formula in \eqref{eq:arfcn}, where $f_{start}$ is the starting frequency of the uplink bandwitdh for DCS1800, $f_{CB}$ is the channel bandwidth and \textit{Offset} is the offset\footnote{ A table with frequency channels can be found at the following URL: @@ -228,7 +228,7 @@ expressed in decimal degrees and are bounded by \textpm90\textdegree and whereas negative are south of the equator. It is alike for longitude coordinates, positive longitudes are east of Prime Meridian and negative are west of the Prime Meridian. If the position in decimal degrees of the BTS is unknown, it is straightforward to derive -them using the formula given in \ref{eq:dd}, where $D$ are degrees, $M$ are +them using the formula given in \eqref{eq:dd}, where $D$ are degrees, $M$ are minutes and $S$ are seconds\footnote{An online converter of the Federal Communication Commission can be used as well to convert from degrees, minutes and seconds to decimal degrees and vice versa @@ -276,11 +276,11 @@ This shape can be described using an ellipsoid point with altitude and uncertainty ellipsoid. \todo{CHECK IF THIS IS CORRECT} The uncertainty of the latitude and longitude correctness can be described -using equation \ref{eq:unclatlong} \citep{3gppequations}. The uncertainty of +using equation \eqref{eq:unclatlong} \citep{3gppequations}. The uncertainty of $r$ is expressed in meters, it defines how accurate is the specified location of the BTS. In the configuration file, $K$ is set to 7, which corresponds to $r$ = 9.4872 m. Instead of using the integer parameter $K$ as the known variable, -the equation \ref{eq:unclatlong} can be rewritten as in \ref{eq:unclatlongnew}, +the equation \eqref{eq:unclatlong} can be rewritten as in \eqref{eq:unclatlongnew}, where we can get the integer value $K$ for a previously selected $r$. \begin{equation} \label{eq:unclatlong} @@ -345,10 +345,10 @@ Value of $K$ & Value of uncertainty $r$\\ \end{table} Altitude uncertainty can be described using the same Binomial expansion method, -as given in \ref{eq:uncalt}, +as given in \eqref{eq:uncalt}, however with altered constant values \citep{3gppequations}. The altitude uncertainty ranges between 0 m and 990.5 m ($h\in[0,990.5]\, \mathrm{m}$). Although the same constant name $K$ is used, it -describes the altitude uncertainty, \ref{eq:uncaltnew}. +describes the altitude uncertainty, \eqref{eq:uncaltnew}. \begin{equation} \label{eq:uncalt} 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 \\ -- cgit v1.2.3-55-g7522