From f4d3245b7c3b1c2a5deeabac696a4525fbdb5cad Mon Sep 17 00:00:00 2001 From: Refik Hadzialic Date: Tue, 3 Jul 2012 20:12:43 +0200 Subject: Writing --- vorlagen/thesis/maindoc.pdf | Bin 4805182 -> 4959107 bytes vorlagen/thesis/src/.kapitel_A.tex.kate-swp | Bin 66 -> 0 bytes vorlagen/thesis/src/bib/literatur.bib | 11 +- vorlagen/thesis/src/img/2DSearchSpace.pdf | Bin 8502 -> 8487 bytes vorlagen/thesis/src/img/2DSearchSpace.svg | 105 +- vorlagen/thesis/src/img/GPS-Modulation.pdf | Bin 11222 -> 11226 bytes vorlagen/thesis/src/img/GPS-Modulation.svg | 65 +- vorlagen/thesis/src/img/GPSSubframe.pdf | Bin 0 -> 6105 bytes vorlagen/thesis/src/img/GPSSubframe.svg | 135 + .../thesis/src/img/PRN-PhaseShiftAfterDemod.pdf | Bin 41659 -> 41032 bytes .../thesis/src/img/PRN-PhaseShiftAfterDemod.svg | 75 +- vorlagen/thesis/src/img/TaylorSeries.pdf | Bin 8804 -> 9656 bytes vorlagen/thesis/src/img/TaylorSeries.svg | 138 +- .../img/TaylorSeries.svg.2012_07_02_15_01_15.0.svg | 587 + .../img/TaylorSeries.svg.2012_07_02_15_05_15.0.svg | 623 + vorlagen/thesis/src/img/satelliteRanges.pdf | Bin 0 -> 134359 bytes vorlagen/thesis/src/img/satelliteRanges.svg | 31217 +++++++++++++++++++ vorlagen/thesis/src/kapitel_A.tex | 2 +- vorlagen/thesis/src/kapitel_x.tex | 152 +- vorlagen/thesis/src/maindoc.tex | 5 + 20 files changed, 32921 insertions(+), 194 deletions(-) delete mode 100644 vorlagen/thesis/src/.kapitel_A.tex.kate-swp create mode 100644 vorlagen/thesis/src/img/GPSSubframe.pdf create mode 100644 vorlagen/thesis/src/img/GPSSubframe.svg create mode 100644 vorlagen/thesis/src/img/TaylorSeries.svg.2012_07_02_15_01_15.0.svg create mode 100644 vorlagen/thesis/src/img/TaylorSeries.svg.2012_07_02_15_05_15.0.svg create mode 100644 vorlagen/thesis/src/img/satelliteRanges.pdf create mode 100644 vorlagen/thesis/src/img/satelliteRanges.svg (limited to 'vorlagen') diff --git a/vorlagen/thesis/maindoc.pdf b/vorlagen/thesis/maindoc.pdf index b67d7fa..b8e1711 100644 Binary files a/vorlagen/thesis/maindoc.pdf and b/vorlagen/thesis/maindoc.pdf differ diff --git a/vorlagen/thesis/src/.kapitel_A.tex.kate-swp b/vorlagen/thesis/src/.kapitel_A.tex.kate-swp deleted file mode 100644 index 9c5e48b..0000000 Binary files a/vorlagen/thesis/src/.kapitel_A.tex.kate-swp and /dev/null differ diff --git a/vorlagen/thesis/src/bib/literatur.bib b/vorlagen/thesis/src/bib/literatur.bib index c402983..8cfc634 100644 --- a/vorlagen/thesis/src/bib/literatur.bib +++ b/vorlagen/thesis/src/bib/literatur.bib @@ -45,7 +45,7 @@ } @techreport{daishinku, - author = "CORP, DAISHINKU", + author = {{CORP, DAISHINKU}}, institution = "DAISHINKU CORP. 1389 Shinzaike, Hiraoka-cho, Kakogawa, Hyogo 675-0194 Japan", owner = "refikh", timestamp = "18.06.2012", @@ -316,7 +316,7 @@ note = {[Online; accessed 27-June-2012]} author = "Iglesias, Pablo A.", howpublished = "\url{http://www.ece.jhu.edu/~pi/Courses/454/NotesA.pdf}", institution = "Control Systems Design, Department of Electrical and Computer Engineering, Johns Hopkins University", - note = "Control Systems Design, Department of Electrical and Computer Engineering, Johns Hopkins University, [Online; accessed 27-June-2012]", + note = "[Online; accessed 27-June-2012]", title = "{Linearization}" } @@ -328,3 +328,10 @@ note = {[Online; accessed 27-June-2012]} url = "http://scholar.lib.vt.edu/theses/available/etd-112516142975720/" } +@misc{gpsMoney, + author = {{GPS World}}, + howpublished = {\url{http://www.gpsworld.com/gnss-system/news/european-commission-report-galileo-estimates-1-trillion-europe-depends-satnav-10950}}, + note = {[Online; accessed 27-June-2012]}, + title = {{European Commission Report on Galileo Estimates \$ 1 Trillion in Europe Depends on SatNav}} +} + diff --git a/vorlagen/thesis/src/img/2DSearchSpace.pdf b/vorlagen/thesis/src/img/2DSearchSpace.pdf index 2e6ad05..7997e0f 100644 Binary files a/vorlagen/thesis/src/img/2DSearchSpace.pdf and b/vorlagen/thesis/src/img/2DSearchSpace.pdf differ diff --git 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+ + + + + + + + + + + + + + + + + + + + + + + + + + + + + + r1 + + + + + r2 + + r3 + b) + (x1,y1) + (x3,y3) + (x2,y2) + (xu,yu) + + diff --git a/vorlagen/thesis/src/kapitel_A.tex b/vorlagen/thesis/src/kapitel_A.tex index b84ce51..828182e 100644 --- a/vorlagen/thesis/src/kapitel_A.tex +++ b/vorlagen/thesis/src/kapitel_A.tex @@ -465,7 +465,7 @@ int main(void) \end{lstlisting} \section{GPS Constants and equations} - +\label{sec:gpsConsAndEq} \begin{alignat}{4} & A & = & \; (\sqrt{A})^2 \nonumber \\ & n_{0} & = &\; \sqrt{\frac{\mu}{A^3}} \nonumber \\ diff --git a/vorlagen/thesis/src/kapitel_x.tex b/vorlagen/thesis/src/kapitel_x.tex index 39b9cad..0c3b383 100644 --- a/vorlagen/thesis/src/kapitel_x.tex +++ b/vorlagen/thesis/src/kapitel_x.tex @@ -10,16 +10,114 @@ delivering correct GPS assistance data to cell phone subscribers inside the GSM network - test the protocol on 5-10 different smart phones - describe and analyse the background processes taking place inside of the cell phone -\chapter{Assisted GPS} -\section{GPS Principles} +\chapter{GPS \& Assisted-GPS} +In the new global economy age, GPS positioning has become of important value for various services +and businesses. It has been growing at a rate of 30\% in the past few years and the application +market is expected to be worth \euro 240 billion by 2020 only in Europe \citep{gpsMoney}. +The goal of this chapter is to bring more details and insights of how GPS receivers work. +The chapter is divided in few sections that explain how the data are modulated before transmission, +demodulated on the receiver, how the search space works, how the target user position is estimated and +the errors that can influence the overall working of the system. + + \begin{figure}[ht!] \centering - \includegraphics[scale=0.50]{img/GPS-Principle.pdf} - \caption[]{nanoBTS with its plastic cover. Image courtesy of ip.access ltd} -\label{img:gpsprinciple} + \includegraphics[scale=0.38]{img/satelliteRanges.pdf} + \caption[]{GPS Simple working principle, a) example in 3D space with spheres b) example in 2D space with circles.} +\label{img:GPSSimplePrinciple} \end{figure} -\section{GPS signal modulation} + +In this paragraph the general idea will be given how GPS works and how the position is estimated. +Before all the details are revealed in the following sections, +it is important to understand the basic principle of GPS navigation. +GPS positioning works by using the principle of \textit{trilateration}. +Distances from the satellites to the GPS receiver are measured and +from these distances receiver's position is estimated. The distances are estimated +by measuring the signal propagation time between the satellites and the receiver, +this position estimation technique is also known as time-of-arrival (TOA) method. +Once sufficient amount of measurements from different satellites were generated, +the position of the receiver can be approximated. +It is important to understand that the positions from the satellites +need to be known. The general principle of this idea can be seen in figure +\ref{img:GPSSimplePrinciple}, picture \textit{a)} represents the idea +with spheres in 3D space and picture \textit{b)} the same idea but in 2D space. +The blue, yellow and green wireframes below the GPS satellites represent the spheres +for a given range, between the satellite and the GPS user, where the user might be +located. By intersecting all the three spheres, the position of the user is estimated. +In the next sections this general idea will be developed in more details +step by step and the ideas will be verified using the appropriate mathematical +models. + +\section{GPS data and signal modulation} +The aim of this section is to give the reader an overview of the transmitted GPS data and +to understand what type of processing takes place on the GPS satellite itself. +As mentioned in the paragraph earlier, to estimate the position of the GPS receiver, it is +important to know the position of the satellite at the moment of signal transmission. Prior to +releasing the data in the athmosphere, they need to be modulated in order for the GPS receiver +to receive and demodulate them. + +Each one of the GPS satellites transmits the same type of information. +The transmitted data are called \textit{frames} \citep{9780817643904}. +One frame of data can be seen in figure \ref{img:gpsframe}. Every of the 25 transmitted frames +can be divided into five subframes of 300 bits length \citep{diggelen2009a-gps}. The data in the +frames are called \textit{navigation data} because using them the GPS receiver can estimate +user's position. +\begin{figure}[ht!] + \centering + \includegraphics[scale=0.60]{img/NAV-Message.pdf} + \caption[]{One frame of 1500 bits on L1 frequency carrier} +\label{img:gpsframe} +\end{figure} +Each subframe can be divided into three fields of data, +as shown in figure \ref{img:gpssubframe}, telemetry (TLM) +as well as handover (HOW) word and rest of data. +TLM is the first word of the subframe and consists of +a unique preamble used to synchronize and identify +the subframes \citep{9780817643904}. HOW is the second +word of the subframe and consists of the \textit{GPS system time} +and subframe ID \citep{9780817643904}. +GPS system time is the time the atomic clocks on the satellite generate +at the moment of subframe broadcast \citep{GPS-Interface-Specification}. +The third segment of the subframe, indicated as rest of data in figure +\ref{img:gpssubframe}, consists of the navigation data. The first subframe +includes data about the satellite accuracy and health as well as parameters +used for the clock corrections on the receiver side. More details on these +parameters will be given in section \ref{sec:SigDemod}. Subframe two and three +are made of \textit{ephemeris data}. Ephemeris +information are precise parameters for predicting the precise orbital +position of the GPS satellite. Using ephemeris data for the specific +system time stamp and the equations given in appendix section \ref{sec:gpsConsAndEq} +the GPS receiver can precisely estimate the position $(x_s,y_s,z_s)$ of +the satellite. The first three subframes are satellite dependent and do not +change in the transmitted 25 frames beside the system time stamp \citep{GPS-Guide}. +\begin{figure}[ht!] + \centering + \includegraphics[scale=0.50]{img/GPSSubframe.pdf} + \caption[]{Subframes always start with telemetry and handover words} +\label{img:gpssubframe} +\end{figure} +Fourth and fifth subframes include \textit{almanac data}, low-precision clock corrections, +ionospheric model and UTC time calculation parameteres. Almanac information are +rough coarse parameters for predicting the orbital position of the GPS satellites. +These low-precision parameters are used by the GPS receiver to estimate the rough +position of the GPS satellites and to reduce the searching space for the GPS satellite +transmission frequencies\footnote{Although all satellites transmit on the same one frequency, +when the signals are received on Earth, they have a different frequency +from the transmitted one. This will be further explained in more details in the following sections \ref{sec:Carrierdemod}, +\ref{sec:CAdemod} and \ref{sec:2dSearch}.} and +obtaining the precise ephemeris data. +Ionospheric model and UTC time calculation parameters are required +by the GPS receiver to refine the calculation of delays through +the ionosphere \citep{9780817643904}. The reason why there are 25 frames is because of the last two +subframes, four and five. +Subframes four and five have data which cycle through the 25 frames, i.e. almanac data +are transmitted for all the GPS satellites in case the receiver found only one satellite +and once it collected all almanac data, it can precisely search for other GPS satellites. +These 25 frames create a masterframe. Once the 25 frames +have been transmitted, the process is repeated from the start. + +The just mentioned data are modulated in real time at the moment of transmission. The transmitted signal after the RF frontend is given in equation \eqref{eq:GPSSignalReceived} \citep{1656803}. \begin{equation} @@ -32,20 +130,16 @@ in equation \eqref{eq:GPSSignalReceived} \citep{1656803}. \label{eq:GPSSignalReceived} S(t) = \sqrt{\frac{P}{2}}d_{C/A}cos(2\pi f_{c}+\varphi_{SV}) + n(t) \end{equation} - \begin{figure}[ht!] \centering - \includegraphics[scale=0.50]{img/GPS-Modulation.pdf} + \includegraphics[scale=0.60]{img/GPS-Modulation.pdf} \caption[]{Modulation of the GPS signal L1} \label{img:gpsmod} \end{figure} -\begin{figure}[ht!] - \centering - \includegraphics[scale=0.50]{img/NAV-Message.pdf} - \caption[]{One frame of 1500 bits on L1 frequency carrier} -\label{img:gpsframe} -\end{figure} + + + @@ -58,13 +152,10 @@ orbiting our planet, at a distance of approximately $20200 \, km$, are equiped with precise atomic clocks \citep[Chapter 2.7]{diggelen2009a-gps}. These atomic clocks are calibrated and maintained on a daily basis by the U.S. Air Force \citep{GPS-Pentagon}. -The time the atomic clock generates is refered as \textit{GPS -system time}, denoted as $t_{SV}$, -and it is generated as a time stamp at the moment -of the frame broadcast \citep{GPS-Interface-Specification}. -Each satellite signs the frame with its exact -broadcast time. The broadcast time is encapsulated in the -subframe 1 of the 1500 bit long frame. In addition to the +The time the atomic clock generate, refered earlier as GPS +system time, denoted as $t_{SV}$, is generated as a time stamp at the moment +of the subframe broadcast \citep{GPS-Interface-Specification}. +In addition to the broadcast time, subframe 1 contains parameters to account for the deterministic clock errors embedded in the broadcasted GPS system time stamp. These errors can be @@ -500,9 +591,7 @@ when some information are known and when almost all information are known. These three modes are known as cold (as mentioned earlier), warm and hot start. They differ from each other by the amount of known information by the GPS receiver. Cold start indicates the GPS receiver -has no almanac\footnote{Almanac information are rough estimation parameters for -predicting the orbital position of the GPS satellites.}, ephemeris\footnote{Ephemeris -information are precise parameters for predicting the orbital position of the GPS satellite.}, +has no almanac, ephemeris, oscillator offset and time data. In order to track the satellites faster next time the GPS receiver is started, it stores the previously mentioned data (last known almanac, ephemeris, oscillator offset, time and position data) in its electrically erasable @@ -561,9 +650,9 @@ r=c\Delta t Since the clocks are not synchronized, as described in sections \ref{sec:SigDemod} and \ref{sec:2dSearch}, clock error offsets have to be added to -the geometric distance $r$. This new distance is called pseudorange, $\rho$, because the range is +the geometric distance $r$. This new distance is called \textit{pseudorange}, $\rho$, because the range is determined using the difference of two nonsynchronized clocks (one on the GPS satellite and -the other one on the receiver) that generate PRN codes. Pseudorange is calculated as given in equation \eqref{eq:rho}, where +the other one on the receiver) that generate PRN codes\footnote{pseudo - Not genuine; sham; not perfect.}. Pseudorange is calculated as given in equation \eqref{eq:rho}, where $t_{u}$ is the advance of the receiver clock with respect to the system time\footnote{System time is the exact time on Earth and it is the most precise time known!} and $\delta t$ is the offset of the satellite clock from the system time \citep{understandGPS}. @@ -660,7 +749,7 @@ f(x) = \sum_{n=0}^{\infty}\frac{f^{(n)}(a)}{n!}(x-a)^n = f(a) + \frac{f'(a)}{1!} \begin{figure}[ht!] \centering \includegraphics[scale=0.50]{img/TaylorSeries.pdf} - \caption[]{Taylor series approximation for a point $a=0.5$ where $n$ is the Taylor polynomial degree} + \caption[]{Taylor series approximation for a point $a=0.5$ where $n$ is the Taylor polynomial degree.} \label{img:taylorSeries} \end{figure} Due to the four unknown terms, Taylor series for multivariables @@ -780,11 +869,15 @@ in the matrix form as in \eqref{eq:userPositionMatrix}. Finally, by multiplying both left sides\footnote{Matrix multiplication is not communitative, $\mathbf{AB\neq BA}$.} of the equation \eqref{eq:userPositionMatrix} with the inverse term of $\boldsymbol{\alpha}$, it yields the result of the unknown terms, as given in equation \eqref{eq:userPositionMatrixFinal}. \begin{equation} +\label{eq:userPositionMatrixInverseMult} +\boldsymbol{\alpha}^{-1}\Delta\boldsymbol{\rho} = \boldsymbol{\alpha}^{-1}\boldsymbol{\alpha} \Delta \boldsymbol{x} +\end{equation} +\begin{equation} \label{eq:userPositionMatrixFinal} \Delta \boldsymbol{x} = \boldsymbol{\alpha}^{-1} \Delta\boldsymbol{\rho} \end{equation} Linearization is repeated in a loop, where in the next round the approximate positions are set -to the just derived position value, that is, $\hat{x_u}=x_u$, $\hat{y_u}=y_u$, $\hat{z_u}=z_u$ and +to the just derived position values, that is, $\hat{x_u}=x_u$, $\hat{y_u}=y_u$, $\hat{z_u}=z_u$ and $\hat{t_u}=t_u$. This process is repeated until the approximated positions converge to their final values. It is not necessarily required that the initial positions are very accurate and the results are usually obtained by 4-5 itterations \citep{pseudorangeError}. @@ -792,7 +885,6 @@ Risks exist that the solutions will still be corrupted but there are different e mechanisms to solve these problems, like minimizing the error contribution using more than four satellite measurements \citep{pseudorangeError} \citep[Chapter 7]{understandGPS}. - \section{Assisted GPS in Wireless networks} \label{sec:agps} In the following paragraphs Assisted GPS (A-GPS) will be presented and how it works. @@ -806,7 +898,7 @@ with an A-GPS receiver. The basic scenario can be seen in figure \ref{img:agpsPr The BTS station is connected to the global navigation satellite system (GNSS) server, which is directly connected to the GPS reference station. The GPS reference station delivers the GNSS server exact time stamps, -approximate location, satellite clock corrections, ephemeris and navigation data +approximate location, satellite health as well as clock corrections, ionospheric and UTC model, almanac and ephemeris data \citep{springerlink:10.1007/s10291-002-0028-0}. \begin{figure}[ht!] \centering diff --git a/vorlagen/thesis/src/maindoc.tex b/vorlagen/thesis/src/maindoc.tex index 82839e6..72168e0 100644 --- a/vorlagen/thesis/src/maindoc.tex +++ b/vorlagen/thesis/src/maindoc.tex @@ -77,6 +77,11 @@ \usepackage{tikz} \usepackage{pgfplots} +%EUROSYMBOLS +\usepackage{eurosym} + +\usepackage[hyphens]{url} + %ermöglicht verschiedene Stile des Literaturverzeichnises %\usepackage{jurabib} %\usepackage{plain} -- cgit v1.2.3-55-g7522