From 07b394d4ef957c09b04392193abc268b27797d03 Mon Sep 17 00:00:00 2001 From: Refik Hadzialic Date: Mon, 10 Sep 2012 21:38:35 +0200 Subject: Changes --- vorlagen/thesis/maindoc.pdf | Bin 8564518 -> 8573241 bytes vorlagen/thesis/src/kapitel_A.tex | 75 ++++++++++++++++++++------------------ vorlagen/thesis/src/kapitel_x.tex | 16 ++++---- vorlagen/thesis/src/maindoc.lof | 5 +++ vorlagen/thesis/src/maindoc.lot | 7 ++++ vorlagen/thesis/src/maindoc.pdf | Bin 0 -> 7713615 bytes 6 files changed, 60 insertions(+), 43 deletions(-) create mode 100644 vorlagen/thesis/src/maindoc.pdf diff --git a/vorlagen/thesis/maindoc.pdf b/vorlagen/thesis/maindoc.pdf index 80bae42..b38d2d6 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 1148f79..6ce6cc0 100644 --- a/vorlagen/thesis/src/kapitel_A.tex +++ b/vorlagen/thesis/src/kapitel_A.tex @@ -14,10 +14,11 @@ \end{itemize} \addchap{Appendix} -\numberwithin{equation}{subsection} -\numberwithin{table}{subsection} -\captionsetup[figure]{list=no} -\captionsetup[table]{list=no} +\numberwithin{equation}{section} +\numberwithin{table}{section} +%\captionsetup[figure]{list=no} +%\captionsetup[table]{list=no} +\numberwithin{figure}{section} \section{Installation and configuration guide} \label{sec:instConf} @@ -711,10 +712,10 @@ Idot&Rate of inclination angle (semicircles/second) \clearpage \section{GPS distance and position estimation} \label{sec:distanceAndPosition} -In this section the focus is set on distance and position estimation inside of the GPS receiver. +In this appendix section the focus is set on distance and position estimation inside of the GPS receiver. GPS system, as discussed earlier, takes advantage of the TOA ranging concept -to determine user position. Time is measured how long it takes for a signal to arrive from a -known location. +to determine user's position. It is measured how long it takes for a signal to arrive from a +known location to the current unknown position on Earth. \begin{figure}[ht!] \centering \includegraphics[scale=0.50]{img/Localization.pdf} @@ -725,9 +726,11 @@ In figure \ref{img:SatLocalization}, an example concept can be seen, where $\vec GPS user position vector with respect to Earth-Centered, Earth-Fixed\footnote{ECEF is a Cartesian coordinate system where the point $(0,0,0)$ is defined as the center of mass of the Earth \citep{earthCoordinates}.} (ECEF) coordinate system, $\vec{r}$ is the distance vector from the satellite to the user and $\vec{s}=(x_s,y_s,z_s)$ -represents the GPS satellite position with respect to ECEF at a timepoint. Vector $\vec{s}$ is computed from ephemeris data broadcasted -by the satellite. The distance vector $\vec{r}$, distance between the satellite and user, can be computed using equation \eqref{eq:r} and its magnitude is -given in equation \eqref{eq:rMag}. +represents the GPS satellite position with respect to ECEF at a timepoint $t_1$. +$t_1$ is the timepoint when the time stamp was generated on the GPS satellite. +Vector $\vec{s}$ is computed from ephemeris data broadcasted +by the satellite. The distance vector $\vec{r}$, which is the distance between the satellite and the GPS receiver, can be computed using equation \eqref{eq:r} +and its magnitude is given in equation \eqref{eq:rMag}. \begin{equation} \label{eq:r} \vec{r}=\vec{s}-\vec{u} @@ -736,9 +739,9 @@ given in equation \eqref{eq:rMag}. \label{eq:rMag} r=\Vert s-u\Vert \end{equation} -The geometric distance of $r$ is computed by measuring the signal propagation time, this is illustrated in figure \ref{img:TimingLoc} -and it was discussed in section \ref{sec:CAdemod}. The PRN code generated on the GPS satellite -at time $t_1$ arrives at the time $t_2$, the difference between these two time stamps, $\Delta t$, represents the +The geometric distance of $r$ is computed by measuring the signal propagation time, this is illustrated in figure \ref{img:TimingLoc}. +The PRN code generated on the GPS satellite +at time $t_1$ arrives at the time $t_2$. The difference between these two time stamps, $\Delta t$, represents the propagation time. By multiplying the propagation time, $\Delta t$, with the speed of light, $c$, the geometric distance $r$ is computed, as given in equation \eqref{eq:rDist}. \begin{figure}[ht!] @@ -751,13 +754,11 @@ geometric distance $r$ is computed, as given in equation \eqref{eq:rDist}. \label{eq:rDist} r=c\Delta t \end{equation} -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 \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\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 +Since the clocks are not synchronized, clock error offsets have to be added to +the geometric distance $r$. This new distance is called \textit{pseudorange}\footnote{pseudo - Not genuine; sham; not perfect.}, $\rho$, because the range is +determined using the difference of two nonsynchronized clocks that generate PRN codes (one on the GPS satellite and +the other one on the receiver). 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{$t_{u}$ or 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}. \begin{equation} @@ -769,14 +770,14 @@ Equation \eqref{eq:rMag} can be rewritten as \eqref{eq:rhoR} with respect to equ \label{eq:rhoR} \rho - c(t_{u}-\delta t) = \Vert s-u\Vert \end{equation} -Offset of the satellite clock from the system time, $\delta t$, is updated from Earth, as discussed in \ref{sec:SigDemod} -and for that reason it can be removed for sake of simplicity, i.e. it is not an unknown term anymore, -then the eqaution \eqref{eq:rhoR} can be rewritten as \eqref{eq:rhoNew}. +Offset of the satellite clock from the system time, $\delta t$, is updated from Earth and it is inside +the GPS transmitted data. For that reason, it can be removed for sake of simplicity, i.e. it is not an unknown term anymore, +then the equation \eqref{eq:rhoR} can be rewritten as \eqref{eq:rhoNew}. \begin{equation} \label{eq:rhoNew} \rho - ct_{u} = \Vert s-u\Vert \end{equation} -In order to estimate the user (GPS receiver) position, +In order to estimate user's (GPS receiver) position, advance of the receiver clock with respect to the system time, $t_u$, has to be found, in other words equation \eqref{eq:rhoSats} has to be solved, where $i$ is the index of visible satellites at the moment of signal reception \citep{understandGPS}. \begin{equation} @@ -786,10 +787,10 @@ has to be solved, where $i$ is the index of visible satellites at the moment of The estimated position of the user, $\vec{u}=(x_u,y_u,z_u)$, is a three dimensional vector and as stated above the clock offset, $t_u$, is unknown as well. This four dimensional space requires to have at least four pseudorange equations \eqref{eq:rhoSats} to find all the four unknown terms. -As a result of this fact, at least four satellites have to be visible at -the same time to estimate the position of the target user. Equation given in \eqref{eq:rhoSats} takes the form in +As a consequence of this fact, at least four satellites have to be visible at +the same time to estimate user's position. Equation given in \eqref{eq:rhoSats} take the form in \eqref{eq:rhoSatsNew} because the coordinate system is Cartesian and $\rho_i$ is nothing else but Euclidean distance -where $i=1,2,...,n$ such that $n\geq4$ and $\vec{s_i}=(x_i,y_i,z_i)$ is the satellite position estimated from the ephemeris data. +where $i=1,2,...,n$ such that $n\geq4$, and $\vec{s_i}=(x_i,y_i,z_i)$ is the satellite position estimated from the ephemeris data. \begin{equation} \label{eq:rhoSatsNew} \rho_i= \sqrt{(x_i-x_u)^2+(y_i-y_u)^2+(z_i-z_u)^2} + ct_u @@ -799,20 +800,22 @@ equation\footnote{Nonlinear equations, also known as polynomial equations, are equations that can not satisfy both of the linearity properties: additivity $f(x+y)=f(x)+f(y)$ and homogeneity $f(\alpha x) = \alpha f(x)$, $\alpha \in \mathbb{R}$ \citep{nonlinear}.}. -It is not straightforward to find explicit solutions of nonlinear equations, it is more difficult than +It is not straightforward to find explicit solutions of nonlinear equations. It is more difficult to find the solution compared to linear equations. There are different techniques to solve sets of nonlinear equations \citep[Chapter 7]{understandGPS} but in this work the linearization method\footnote{Linear approximation is a technique where a function is approximated using a linear function.} -shall be presented to find the unknown terms $(x_u,y_u,z_u,t_u)$, i.e. out of an approximate position and clock -offset the true user position and the true clock offset shall be calculated. +shall be presented to find the unknown terms $(x_u,y_u,z_u,t_u)$. In other words, out of an approximate position +and clock offset, the true clock offset will be calculated. Out of this calculation will follow the true user position. + +Let the equation \eqref{eq:rhoSatsNew} for pseudoranges, be rewritten as a function $f$ of four +unknown terms $x_u$, $y_u$, $z_u$ and $t_u$, as +given in \eqref{eq:rhoSatsNewFun} \citep[Chapter 2]{understandGPS}. \begin{equation} \label{eq:rhoSatsNewFun} \rho_i= \sqrt{(x_i-x_u)^2+(y_i-y_u)^2+(z_i-z_u)^2} + ct_u = f(x_u,y_u,z_u,t_u) \end{equation} -Let the equation \eqref{eq:rhoSatsNew} for pseudoranges, be rewritten as a function $f$ of four -unknown terms $x_u$, $y_u$, $z_u$ and $t_u$, as -given in \eqref{eq:rhoSatsNewFun} \citep[Chapter 2]{understandGPS}. Suppose that the approximation of the +Suppose that the approximation of the position and the clock offset are known, denoted as $\hat{x_u}$, $\hat{y_u}$, $\hat{z_u}$ and $\hat{t_u}$, then equation \eqref{eq:rhoSatsNewFun} can be rewritten as an approximate pseudorange \eqref{eq:rhoSatsNewFunApprox}. @@ -821,7 +824,7 @@ can be rewritten as an approximate pseudorange \eqref{eq:rhoSatsNewFunApprox}. \hat{\rho_i}= \sqrt{(x_i-\hat{x_u})^2+(y_i-\hat{y_u})^2+(z_i-\hat{z_u})^2} + c\hat{t_u} = f(\hat{x_u},\hat{y_u},\hat{z_u},\hat{t_u}) \end{equation} In other words, the unknown true position terms $x_u$, $y_u$, $z_u$ and the clock offset term $t_u$, of the GPS receiver, -shall be expressed by the approximate values and an incremental component as shown in equation \eqref{eq:userCoordinates} \citep{understandGPS}. +are expressed by the approximate values and an incremental component as shown in equation \eqref{eq:userCoordinates} \citep{understandGPS}. \begin{equation} \label{eq:userCoordinates} \begin{array}{l} @@ -837,10 +840,10 @@ as in \eqref{eq:rhoSatsNewFunwithApprox}. \label{eq:rhoSatsNewFunwithApprox} f(x_u,y_u,z_u,t_u) = f(\hat{x_u}+\Delta x_u, \hat{y_u}+\Delta y_u, \hat{z_u}+\Delta z_,\hat{t_u}+\Delta t_u) \end{equation} -In the next step the pseudorange function shall be approximated using Taylor series\footnote{Taylor +In the next step the pseudorange function shall be approximated using Taylor series (linearization of the nonlinear equation)\footnote{Taylor series ``is a representation of a function as an infinite sum of terms that are calculated from the values of the function's -derivatives at a single point'' \citep[Chapter 11]{taylor}.} (linearization of the nonlinear equation). Taylor +derivatives at a single point'' \citep[Chapter 11]{taylor}.}. Taylor series for a function $f(x)$ is given in equation \eqref{eq:taylor}, where as $a$ approaches $x$ the estimation error shall be smaller and smaller, i.e. $f(x) = f(a)$ when $x=a$. The approximation error depends on Taylor polynomial degree (the amount of terms or taken derivatives of the function) diff --git a/vorlagen/thesis/src/kapitel_x.tex b/vorlagen/thesis/src/kapitel_x.tex index c839f46..0623f5d 100644 --- a/vorlagen/thesis/src/kapitel_x.tex +++ b/vorlagen/thesis/src/kapitel_x.tex @@ -1111,7 +1111,8 @@ to estimate the rough position of the satellites, therefore the Doppler effects roughly estimated. As a consequence of the known Doppler effect, the frequency bins to search through to obtain the correlation peak are this time limited \citep[Chapter 3]{diggelen2009a-gps}. Hot start works in the same manner as warm start however, the ephemeris data and time data are precisely -known (time is known in accuracy of submilliseconds). +known (time is known in accuracy of submilliseconds). The process of finding user's position is explained +in detail in appendix section \ref{sec:distanceAndPosition}. \section{Assisted GPS in wireless networks} \label{sec:agps} @@ -1140,8 +1141,8 @@ off by several seconds and would require additional equipment for synchronizing \citep{springerlink:10.1007/s10291-002-0028-0}, \citep{901174}. However in CDMA networks the time stamp is accurate to within $100 \, \mu s$ \citep{springerlink:10.1007/s10291-002-0028-0}. Approximate location is typically taken to be the location of the BTS from which the target AGPS receiver -acquires the assistance data. Ephemeris and navigation data obtained by the AGPS receiver in the smart phone -help it to estimate the positions of the GPS satellites. This method can greatly +acquires the assistance data. Ephemeris and navigation data obtained from the GSM network provider +help the smart phone to estimate its position. This method can greatly enhance the sensitivity of the receiver especially in urban environments \citep{springerlink:10.1007/s10291-002-0028-0}. Conventional GPS receivers require at least up to extra $18$ to $30\,s$ to receive and decode the navigation data @@ -1153,8 +1154,8 @@ an antenna with a gain of $3\, \mathrm{dB}$ with respect to an isotropic (omnidi \citep[Chapter 2]{diggelen2009a-gps}.} (located near ground) at worst normal orientation'' \citep{GPS-Interface-Specification}. -A simplified AGPS algorithm given in \citep{springerlink:10.1007/s10291-002-0028-0} shall be presented here. This -algorithm benefits in speed the more assistance data is present. As the first satellites are tracked, +A simplified AGPS algorithm given in \citep{springerlink:10.1007/s10291-002-0028-0} will be presented. This +algorithm benefits the more assistance data are known. As the first satellites are tracked, the AGPS algorithm has an estimation of the feasible region where the target AGPS user might be located. Consequently, this feasible region shall shrink until the location has been fully estimated \citep{springerlink:10.1007/s10291-002-0028-0}. @@ -1168,7 +1169,8 @@ Consequently, this feasible region shall shrink until the location has been full Although the AGPS algorithms can be seen as a set of equations with more unknown terms being known. It is straightforward to solve a set of equations when all the terms are known. However, without assistance information which provide additional information to the GPS receiver, -it takes more time to obtain (decode) assistance data from the satellite message. +it takes more time to obtain (decode) assistance data from the satellite message. The set of equations +to be solved is described in detail in appendix section \ref{sec:distanceAndPosition}. Numerous AGPS algorithms exist, some do not require the exact time component and navigation data to be present in the assistance data \citep{998892}. @@ -1560,7 +1562,7 @@ position and would help weak signals to be detected which in return would minimi As listed above, almanac, ephemeris, UTC model, ionospheric model and reference location are transmitted to the MS. Reference location is the location of the BTS and provides the MS with an proximate location which can be used -for the position determination in equations given in appendix \ref{sec:distanceAndPosition}. +for the position determination in equations given in appendix section \ref{sec:distanceAndPosition}. Furthermore, this limits the search space in time and frequency domain for satellites to lock on. For an illustration, if the AGPS receiver has access to these data it can not expect to see satellites which send signals on the opposite side of the Earth \citep[Chapter 4]{harper2010server-side}. diff --git a/vorlagen/thesis/src/maindoc.lof b/vorlagen/thesis/src/maindoc.lof index a4d1bb7..73e6661 100644 --- a/vorlagen/thesis/src/maindoc.lof +++ b/vorlagen/thesis/src/maindoc.lof @@ -36,3 +36,8 @@ \contentsline {figure}{\numberline {6.1}{\ignorespaces Test rooms as well as the results delivered by the smart phones. Image courtesy of Google Maps.\relax }}{59}{figure.caption.39} \contentsline {figure}{\numberline {6.2}{\ignorespaces Test room 2 with the positions of the smart phones.\relax }}{60}{figure.caption.40} \addvspace {10\p@ } +\contentsline {figure}{\numberline {C.1}{\ignorespaces Effects of the low frequency term on the demodulated output C/A wave on the GPS receiver (the explanations and figures are from top to bottom). If the synthesized frequency is correct, $f_{1}=f_{2}$, the low frequency term becomes a DC term and does not modify the output $d_{C/A}$ wave (first figure). If the frequency matches but the phase not, in this case the phase is shifted for $\pi $, then $d_{C/A}$ is inverted (second figure). If the phase shifts with time, then the amplitude and phase of $d_{C/A}$ will vary as well (third figure). Image courtesy of \citep {diggelen2009a-gps}.\relax }}{86}{figure.caption.48} +\contentsline {figure}{\numberline {D.1}{\ignorespaces Cross-correlation on three different signals. Image courtesy of \citep {understandGPS}.\relax }}{87}{figure.caption.49} +\contentsline {figure}{\numberline {F.1}{\ignorespaces Basic distance estimation principle for one satellite. Image courtesy of \citep {understandGPS}.\relax }}{91}{figure.caption.53} +\contentsline {figure}{\numberline {F.2}{\ignorespaces Estimating the distance by phase shift $\Delta t =t_2 - t_1 =\tau $. Image courtesy of \citep {understandGPS}.\relax }}{92}{figure.caption.54} +\contentsline {figure}{\numberline {F.3}{\ignorespaces Taylor series approximation for a point $a=0.5$ where $n$ is the Taylor polynomial degree.\relax }}{94}{figure.caption.55} diff --git a/vorlagen/thesis/src/maindoc.lot b/vorlagen/thesis/src/maindoc.lot index bea3336..2b2ecac 100644 --- a/vorlagen/thesis/src/maindoc.lot +++ b/vorlagen/thesis/src/maindoc.lot @@ -13,3 +13,10 @@ \contentsline {table}{\numberline {6.1}{\ignorespaces Smart phone models used for testing in the thesis.\relax }}{58}{table.caption.38} \contentsline {table}{\numberline {6.2}{\ignorespaces Smart phone RRLP test results from Test room 2.\relax }}{62}{table.caption.41} \addvspace {10\p@ } +\contentsline {table}{\numberline {A.1}{\ignorespaces Example uncertainties (latitude and longitude) for various integer values of $K$\relax }}{83}{table.caption.45} +\contentsline {table}{\numberline {A.2}{\ignorespaces Example uncertainties (altitude) for various integer values of $K$\relax }}{83}{table.caption.46} +\contentsline {table}{\numberline {B.1}{\ignorespaces Indicator LED status on the nanoBTS. Table courtesy of \citep {installnanoBTS}.\relax }}{84}{table.caption.47} +\contentsline {table}{\numberline {E.1}{\ignorespaces Almanac message. Table courtesy of \citep {harper2010server-side}.\relax }}{89}{table.caption.50} +\contentsline {table}{\numberline {E.2}{\ignorespaces GPS Ionosphere Model.\relax }}{89}{table.caption.51} +\contentsline {table}{\numberline {E.3}{\ignorespaces GPS UTC Model.\relax }}{89}{table.caption.51} +\contentsline {table}{\numberline {E.4}{\ignorespaces Navigation message (ephemeris). Table courtesy of \citep {harper2010server-side}.\relax }}{90}{table.caption.52} diff --git a/vorlagen/thesis/src/maindoc.pdf b/vorlagen/thesis/src/maindoc.pdf new file mode 100644 index 0000000..76697a8 Binary files /dev/null and b/vorlagen/thesis/src/maindoc.pdf differ -- cgit v1.2.3-55-g7522