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authorRefik Hadzialic2012-06-05 18:55:12 +0200
committerRefik Hadzialic2012-06-05 18:55:12 +0200
commit1947cdd8ca8b066a87c6c1539ed2b6c2811eecc2 (patch)
tree560e0afab9182c80e4ee408442e6c62297b82088 /vorlagen/thesis/src/kapitel_A.tex
parentModification and writing appendix (diff)
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Writing appendix
Diffstat (limited to 'vorlagen/thesis/src/kapitel_A.tex')
-rw-r--r--vorlagen/thesis/src/kapitel_A.tex111
1 files changed, 102 insertions, 9 deletions
diff --git a/vorlagen/thesis/src/kapitel_A.tex b/vorlagen/thesis/src/kapitel_A.tex
index 30e02da..35a0367 100644
--- a/vorlagen/thesis/src/kapitel_A.tex
+++ b/vorlagen/thesis/src/kapitel_A.tex
@@ -10,8 +10,8 @@ was successfully tested out on the following operating systems:
Ubuntu 10.04 LTS 64 bit and Ubuntu 12.04 LTS 64 bit. A self-bootable test
USB system is supplied with the thesis and it can be evaluated without executing
the given steps. There is a marking difference between text given in light and
-dark grey background color, the first ought to be typed in into or
-is produced by the terminal window whereas the later emphasizes a
+dark grey background color, the first ought to be typed in into the terminal window or
+it may be an output produced by an application, whereas the later emphasizes a
file modification case.
\subsection{Installation of OpenBSC}
In order to compile OpenBSC it is required to install the following precompiled
@@ -216,6 +216,7 @@ cd libconfig-1.4.8/
make
sudo make install
\end{lstlisting}
+
Once the libraries have been successfully installed, the user may proceed
with the configuration and compiling the GNSS assistance software, which is the
key software produced in this thesis. The configuration file can be found in the
@@ -224,9 +225,9 @@ configuration file is already preconfigured for the location of ``Angewandte
Mathematik und Rechenzentrum'' building. Latitude and longitude of the BTS are
expressed in decimal degrees and are bounded by \textpm90\textdegree and
\textpm180\textdegree respectively. Positive latitudes are north of the equator,
-whereas negative are south of the equator. It is alike for longitude, positive
+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 decimal degrees of the BTS are unknown, it is straightforward to derive
+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
minutes and $S$ are seconds\footnote{An online converter of the Federal
Communication Commission can be used as well to convert from degrees, minutes
@@ -268,13 +269,19 @@ settings =
};
\end{lstlisting}
-The uncertainty of the latitude and longitude correctness can be described
+
+\todo{CHECK IF THIS IS CORRECT}
+The target user, one wants to locate, has to be inside of a geometric estimated shape.
+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
$r$ 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 parameter $K$ as the known variable,
+$r$ = 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},
-where we can get $K$ for a chosen $r$.
+where we can get the integer value $K$ for a previously selected $r$.
\begin{equation}
\label{eq:unclatlong}
\centering
@@ -303,7 +310,7 @@ where we can get $K$ for a chosen $r$.
\end{array}
\end{equation}
-Some uncertainties $r$ are given in table \ref{tab:unclatlong} for $K$.
+A set of uncertainties $r$ is given in table \ref{tab:unclatlong} for various integer values of $K$.
\begin{table}[h]
\centering
\begin{tabular}{|c|c|}
@@ -333,10 +340,96 @@ Value of $K$ & Value of uncertainty $r$\\
- & -\\
\hline
\end{tabular}
-\caption{Uncertainties for different values of $K$}
+\caption{Example uncertainties (latitude and longitude) for various integer values of $K$}
\label{tab:unclatlong}
\end{table}
+Altitude uncertainty can be described using the same Binomial expansion method,
+as given in \ref{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}.
+
+\begin{equation}
+\label{eq:uncalt}
+\centering
+\begin{array}{l}
+\displaystyle h=C\cdot((1+x)^{K}-1) \\
+\displaystyle \\
+\displaystyle where \left\{ \begin{array}{rcl}
+ C & = & 45 \\
+ x & = & 0.025 \\
+ K & \in & [0,127] \wedge \|K\|
+\end{array}\right.
+\end{array}
+\end{equation}
+
+\begin{equation}
+\label{eq:uncaltnew}
+\centering
+\begin{array}{l}
+\displaystyle K=\bigg\lceil\frac{ln(\frac{h}{C}+1)}{ln(1+x)}\bigg\rceil \\
+\displaystyle \\
+\displaystyle where \left\{ \begin{array}{rcl}
+ C & = & 45 \\
+ x & = & 0.025 \\
+ h & \in & [0,990.5]\, \mathrm{m}
+\end{array}\right.
+\end{array}
+\end{equation}
+
+A set of uncertainties $h$ is given in table \ref{tab:uncalt} for various integer values of $K$.
+\begin{table}[h]
+\centering
+\begin{tabular}{|c|c|}
+\hline
+Value of $K$ & Value of uncertainty $h$\\
+\hline
+0 & 0 m\\
+\hline
+1 & 1.13 m \\
+\hline
+2 & 2.28 m\\
+\hline
+3 & 3.46 m\\
+\hline
+- & - \\
+\hline
+20 & 28.74 m\\
+\hline
+- & -\\
+\hline
+60 & 152.99 m\\
+\hline
+- & -\\
+\hline
+100 & 486.62 m\\
+\hline
+- & -\\
+\hline
+\end{tabular}
+\caption{Example uncertainties (altitude) for various integer values of $K$}
+\label{tab:uncalt}
+\end{table}
+
+Confidence level is the next parameter in the configuration file that needs to be set.
+It can take any integer value between 0 and 127. The confidence level defines the
+percentage of the confidence that the target entity, the GSM user one wants to locate, is within
+the geometric shape defined earlier. A value of 0 and between 100 and 127, may be
+interpreted as ``no information'' \citep{3gppequations}. The reason why the values are not
+limited to 100 is because of the nature of binary numbers and that $2^6$ bits is not sufficient
+to represent the number 100, but rather requires one bit more.
+
+Confidence level is followed by the ephemeris repair option. Ephemeris repair is a variable
+of the boolean type, it can take two different values \textit{true} or \textit{false}. Ephemeris
+data may contain errors or miss some satellite information \citep{NASA-Ephem-Errors}
+\citep{Stanford-Ephem-Errors} and the ephemeris repair function, if set to true,
+will take data of the previous measurement report. This introduces an error as well.
+
+To increase the speed of measurement report, reference time can be used to provide extra
+information for the A-GPS in the MS of target entity. This field is of boolean
+type, if set to true, reference time is included in the sent packets.
+
\newpage
\section{Sourcecode}