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authorRefik Hadzialic2012-09-10 17:03:38 +0200
committerRefik Hadzialic2012-09-10 17:03:38 +0200
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AGPS chapter modified
-rw-r--r--vorlagen/thesis/maindoc.pdfbin8590727 -> 8564518 bytes
-rw-r--r--vorlagen/thesis/src/bib/literatur.bib49
-rw-r--r--vorlagen/thesis/src/kapitel_A.tex163
-rw-r--r--vorlagen/thesis/src/kapitel_x.tex719
-rw-r--r--vorlagen/thesis/src/maindoc.lof40
-rw-r--r--vorlagen/thesis/src/maindoc.lot6
-rw-r--r--vorlagen/thesis/src/maindoc.tex3
7 files changed, 497 insertions, 483 deletions
diff --git a/vorlagen/thesis/maindoc.pdf b/vorlagen/thesis/maindoc.pdf
index a7a0a3c..80bae42 100644
--- a/vorlagen/thesis/maindoc.pdf
+++ b/vorlagen/thesis/maindoc.pdf
Binary files differ
diff --git a/vorlagen/thesis/src/bib/literatur.bib b/vorlagen/thesis/src/bib/literatur.bib
index 4edb3d5..5790379 100644
--- a/vorlagen/thesis/src/bib/literatur.bib
+++ b/vorlagen/thesis/src/bib/literatur.bib
@@ -7,6 +7,7 @@
author = "3GPP-Coordinates",
booktitle = "{3rd Generation Partnership Project; Technical Specification Group Core Network; Universal Geographical Area Description (GAD) (Release 6) }",
language = "english",
+ note = "[Online; accessed 18-June-2012]",
month = dec,
organization = "3GPP",
title = "{3GPP TS 23.032 V6.0.0 (2004-12), 3rd Generation Partnership Project; Technical Specification Group Core Network; Universal Geographical Area Description (GAD) (Release 6)}",
@@ -48,6 +49,7 @@
author = {{CORP, DAISHINKU}},
institution = "DAISHINKU CORP. 1389 Shinzaike, Hiraoka-cho, Kakogawa, Hyogo 675-0194 Japan",
owner = "refikh",
+ note = "[Online; accessed 18-June-2012]",
timestamp = "18.06.2012",
title = "{Development of Miniature High-Precision SMD TCXO for GPS}",
url = "http://www.kds.info/html/products/new_product/4567115_en.htm",
@@ -58,7 +60,7 @@
author = "PERICOM",
institution = "Pericom Semiconductor Corporation, 3545 North First St., San Jose, CA 95134, USA",
owner = "refikh",
- timestamp = "18.06.2012",
+ note = "[Online; accessed 18-June-2012]",
title = "{Choice of TCXO for GPS Design}",
url = "http://www.pericom.com/pdf/applications/AN335.pdf",
year = "2008"
@@ -85,7 +87,7 @@
@misc{GPS-Pentagon,
author = "Grimes, John G.",
edition = "4th Edition",
- howpublished = "Online",
+ note = "[Online; accessed 01-June-2012]",
institution = "Pentagon",
location = "Washington DC",
month = sep,
@@ -111,6 +113,7 @@
author = "Ma, Changlin and Lachapelle, Gerard and Cannon, M. Elizabeth",
booktitle = "Proceedings of ION GNSS 2004 (Session A3), Long Beach, CA",
month = "sep.",
+ note = "[Online; accessed 08-June-2012]",
title = "{Implementation of a Software GPS Receiver}",
url = "http://plan.geomatics.ucalgary.ca/papers/04gnss_ion_cmaetal.pdf",
year = "2004"
@@ -145,6 +148,7 @@
@booklet{installnanoBTS,
author = "{ip.access ltd}",
title = "{nanoBTS Installation Manual}",
+ note = "[Online; accessed 10-June-2012]",
url = "http://subversion.assembla.com/svn/bxpgfKRFar3O9EeJe5afGb/PP/ipaccess/NGSM_INST_300_nanoBTS_Install_v3_0.pdf",
year = "2009"
}
@@ -152,6 +156,7 @@
@booklet{multipleTRX,
author = "{ip.access ltd}",
title = "{GSM-over-IP picocells for in-building coverage and capacity}",
+ note = "[Online; accessed 10-June-2012]",
url = "http://www.hexazona.com/nexwave/docs/ipaccess/nanoBTS; 1800-1900.pdf",
year = "2005"
}
@@ -204,9 +209,9 @@
@misc{GPS-Interface-Specification,
chapter = "CHAPTER 3: MINIMUM PERFORMANCE CAPABILITIES OF A GPS RECEIVER",
- howpublished = "Online",
+ note = "[Online; accessed 27-June-2012]",
month = jun,
- organization = "Navigation Center, U.S. Department of Homeland Security",
+ author = "Navigation Center, U.S. Department of Homeland Security",
pages = "55",
title = "{Interface Specification IS-GPS-200}",
url = "http://www.losangeles.af.mil/shared/media/document/AFD-100813-045.pdf",
@@ -215,9 +220,9 @@
@misc{GPS-Guide,
chapter = "CHAPTER 3: MINIMUM PERFORMANCE CAPABILITIES OF A GPS RECEIVER",
- howpublished = "Online",
+ note = "[Online; accessed 27-June-2012]",
month = sep,
- organization = "Navigation Center, U.S. Department of Homeland Security",
+ author = "Navigation Center, U.S. Department of Homeland Security",
pages = "55",
title = "{Navstar GPS User Equipment Introduction}",
url = "http://www.navcen.uscg.gov/pubs/gps/gpsuser/gpsuser.pdf",
@@ -291,9 +296,9 @@ ISSN={0018-9162},}
@misc{earthCoordinates,
author = {James R. Clynch},
title = {{Earth Coordinates}},
+note = "[Online; accessed 27-June-2012]",
howpublished = {\url{http://www.gmat.unsw.edu.au/snap/gps/clynch_pdfs/coorddef.pdf}},
-year = {2006},
-note = {[Online; accessed 27-June-2012]}
+year = {2006}
}
@book{nonlinear,
@@ -324,6 +329,7 @@ note = {[Online; accessed 27-June-2012]}
author = "Kline, Paul A.",
institution = "Faculty of the Virginia Polytechnic Institute and State University",
location = "Blacksburg, Virginia",
+ note = "[Online; accessed 05-July-2012]",
title = "{Atomic Clock Augmentation For Receivers Using the Global Positioning System}",
url = "http://scholar.lib.vt.edu/theses/available/etd-112516142975720/"
}
@@ -347,6 +353,7 @@ note = {[Online; accessed 27-June-2012]}
author = {Zeimpekis, Vasileios and Giaglis, George M. and Lekakos, George},
title = {A taxonomy of indoor and outdoor positioning techniques for mobile location services},
journal = {SIGecom Exch.},
+ note = "[Online; accessed 17-July-2012]",
issue_date = {Winter, 2003},
volume = {3},
number = {4},
@@ -458,21 +465,21 @@ note = {[Online; accessed 27-June-2012]}
@misc{GPSiphoneCost,
author = {{Andrew Rassweiler}},
howpublished = {\url{http://www.isuppli.com/Teardowns/News/Pages/iPhone-3G-S-Carries-178-96-BOM-and-Manufacturing-Cost-iSuppli-Teardown-Reveals.aspx}},
- note = {[Online; accessed 14-July-2012]},
+ note = "[Online; accessed 14-July-2012]",
title = {{iPhone 3GS Carries \$178.96 BOM and Manufacturing Cost, iSuppli Teardown Reveals}}
}
@misc{oscilloquartz,
author = {{Dominik Schneuwly}},
howpublished = {\url{http://www.oscilloquartz.com/file/pdf/Ap17UMTS-screen.pdf}},
- note = {[Online; accessed 14-July-2012]},
+ note = "[Online; accessed 14-July-2012]",
title = {{The Synchronization of 3G UMTS Networks}}
}
@misc{3gNetworkSpeed,
author = {{Phil Mann}},
howpublished = {\url{http://www.eetasia.com/ART_8800354031_590626_NT_14db7f7f.HTM}},
- note = {[Online; accessed 14-July-2012]},
+ note = "[Online; accessed 14-July-2012]",
title = {{Timing synchronization for 3G wireless}}
}
@@ -480,6 +487,7 @@ note = {[Online; accessed 27-June-2012]}
author = "ETSI",
title = "{Universal Mobile Telecommunications System (UMTS); Location Measurement Unit (LMU) performance specification}",
type = "TS",
+ note = "[Online; accessed 25-June-2012]",
institution = "{European Telecommunications Standards Institute (ETSI)}",
number = "{125.111}",
days = 11,
@@ -501,6 +509,7 @@ note = {[Online; accessed 27-June-2012]}
author = "Motorola",
title = "{Overview of 2G LCS Technnologies and Standards}",
institution = "{3GPP TSG SA2 LCS Workshop}",
+ note = "[Online; accessed 18-June-2012]",
number = "{LCS-010019}",
days = 11,
month = jan,
@@ -511,7 +520,7 @@ note = {[Online; accessed 27-June-2012]}
@misc{googleLBS,
author = {{Google}},
howpublished = {\url{http://support.google.com/maps/bin/answer.py?hl=en&answer=1725632}},
- note = {[Online; accessed 18-July-2012]},
+ note = "[Online; accessed 18-July-2012]",
title = {{Location-based services}}
}
@@ -519,6 +528,7 @@ note = {[Online; accessed 27-June-2012]}
author = "3GPP",
title = "{Location Services (LCS); Functional description; Stage 2}",
type = "TS",
+ note = "[Online; accessed 05-July-2012]",
institution = "{3rd Generation Partnership Project (3GPP)}",
number = "{03.71 V7.11.0}",
days = 11,
@@ -538,6 +548,7 @@ note = {[Online; accessed 27-June-2012]}
author = "3GPP",
title = "{Location Services (LCS); Mobile Station (MS) - Serving Mobile Location Centre (SMLC) Radio Resource LCS Protocol (RRLP)}",
type = "TS",
+ note = "[Online; accessed 07-July-2012]",
institution = "{3rd Generation Partnership Project (3GPP)}",
number = "{04.31 V8.18.0}",
days = 11,
@@ -568,6 +579,7 @@ note = {[Online; accessed 27-June-2012]}
author = "3GPP",
title = "{Location Services (LCS); Base Station System Application Part LCS Extension (BSSAP-LE) (Release 8)}",
type = "TS",
+ note = "[Online; accessed 09-July-2012]",
institution = "{3rd Generation Partnership Project (3GPP)}",
number = "{49.031 V8.1.0}",
days = 11,
@@ -580,6 +592,7 @@ note = {[Online; accessed 27-June-2012]}
author = "ETSI",
title = "{Location Services (LCS); Mobile Station (MS) - Serving Mobile Location Centre (SMLC) Radio Resource LCS Protocol (RRLP)}",
type = "TS",
+ note = "[Online; accessed 09-July-2012]",
institution = "{European Telecommunications Standards Institute (ETSI)}",
number = "{144 031V8}",
days = 11,
@@ -601,6 +614,7 @@ note = {[Online; accessed 27-June-2012]}
author = "ITU",
title = "{Information technology – Abstract Syntax Notation One (ASN.1): Specification of basic notation}",
type = "TS",
+ note = "[Online; accessed 10-July-2012]",
institution = "{International Telecommunication Union (ITU)}",
number = "{ITU-T X.680}",
days = 11,
@@ -616,6 +630,7 @@ Specification of Packed Encoding Rules (PER)
author = "ITU",
title = "{Information technology – ASN.1 encoding rules: Specification of Packed Encoding Rules (PER)}",
type = "TS",
+ note = "[Online; accessed 11-July-2012]",
institution = "{International Telecommunication Union (ITU)}",
number = "{ITU-T X.691}",
days = 11,
@@ -674,7 +689,7 @@ ISSN={0018-9251},}
}
@book{0824740408,
- Author = {Li Deng and Douglas O'Shaughnessy},
+ Author = {{Li Deng and Douglas O'Shaughnessy}},
Title = {Speech Processing: A Dynamic and Optimization-Oriented Approach (Signal Processing and Communications)},
Publisher = {CRC Press},
Year = {2003},
@@ -732,7 +747,7 @@ ISSN={0018-9251},}
@misc{predictMovements,
author = {S. MALM and L. OSBORNE},
howpublished = {\url{http://www.dailymail.co.uk/sciencetech/article-2190531/Mobile-phone-companies-predict-future-movements-users-building-profile-lifestyle.html}},
- note = {[Online; accessed 29-August-2012]},
+ note = "[Online; accessed 29-August-2012]",
title = {Mobile phone companies can predict future movements of users by building a profile of their lifestyle}
}
@@ -793,9 +808,9 @@ ISSN={0018-9251},}
}
@misc{silentPolice,
- author = "European Digital Civil Rights",
- howpublished = "\url{http://www.edri.org/edrigram/number10.2/silent-sms-tracking-suspects}",
+ author = {European Digital Civil Rights},
+ howpublished = {\url{http://www.edri.org/edrigram/number10.2/silent-sms-tracking-suspects}},
note = "[Online; accessed 1-September-2012]",
- title = "Police Frequently Uses Silent SMS To Locate Suspects",
+ title = {Police Frequently Uses Silent SMS To Locate Suspects},
year = "2012"
} \ No newline at end of file
diff --git a/vorlagen/thesis/src/kapitel_A.tex b/vorlagen/thesis/src/kapitel_A.tex
index c4aa1f8..1148f79 100644
--- a/vorlagen/thesis/src/kapitel_A.tex
+++ b/vorlagen/thesis/src/kapitel_A.tex
@@ -415,6 +415,169 @@ Operational &Green - Steady & Default condition if none of the above apply&12 (L
\end {table}
\clearpage
+\section{Carrier wave demodulation}
+\label{sec:carWavDemod}
+The reason why the equivalent carrier wave must be generated is straightforward
+to understand by looking at the multiplication of two sine waves.
+The GPS L1 signal demodulator at the receiver was depicted in figure
+\ref{img:L1Demod}, page \pageref{img:L1Demod}. The incoming signal L1 is multiplied with
+the synthesized sine wave\footnote{Multiplication is the function of
+a mixer, denoted as $\otimes$ in figure \ref{img:L1Demod}.}.
+For the purpose of easier analysis and understanding this concept,
+cosine waves shall be used istead of sine waves. The difference between sine
+and cosine waves is in the phase shift, as denoted in equation
+\eqref{eq:sineEqCosine}.
+\begin{equation}
+\label{eq:sineEqCosine}
+\sin(\pm x) = \cos\bigg(\frac{\pi}{2} \pm x\bigg)
+\end{equation}
+Multiplication of two cosine waves, as in equation \eqref{eq:multCosin},
+can be derived by adding $\cos(A+B)$ and $\cos(A-B)$ together, as respectively
+given in equations \eqref{eq:cos1} and \eqref{eq:cos2}.
+\begin{equation}
+\label{eq:multCosin}
+\cos(A)\cdot\cos(B) = \frac{1}{2}\cos(A-B)+\frac{1}{2}\cos(A+B)
+\end{equation}
+\begin{equation}
+\label{eq:cos1}
+\cos(A+B) = \cos(A)\cos(B)-\sin(A)\sin(B)
+\end{equation}
+\begin{equation}
+\label{eq:cos2}
+\cos(A-B) = \cos(A)\cos(B)+\sin(A)\sin(B)
+\end{equation}
+The incoming GPS L1 signal with a frequency $f_{1}$, given in figure \ref{img:L1Demod},
+can be written as $d_{C/A}\cos(\omega_{1}t)$, a similar form is given in equation \eqref{eq:GPSSignalReceived6},
+where $\omega_{1}=2\pi f_{1}$ is
+the angle frequency and
+$d_{C/A}$ is the C/A data (navigation message modulated with the PRN code),
+$d_{C/A}=d_{PRN}\oplus d_{NAV}$.
+\begin{equation}
+\label{eq:GPSSignalReceived6}
+S(t) = \sqrt{\frac{P}{2}}d_{C/A}cos(2\pi f_{c}+\varphi_{GPS}) + n(t)
+\end{equation}
+If equation \eqref{eq:multCosin} is rewritten with the received GPS signal L1
+and synthesized wave with frequency $f_{2}$ substituted, then the equation results the one
+given in \eqref{eq:cosResult}
+\begin{equation}
+\label{eq:cosResult}
+d_{C/A}\cdot\cos(\omega_{1}t)\cos(\omega_{2}t) = \frac{1}{2}d_{C/A}\cdot\cos(\omega_{1}t-\omega_{2}t) + \frac{1}{2}d_{C/A}\cos(\omega_{1}t+\omega_{2}t)
+\end{equation}
+This leaves the resulting signal with two frequency terms, a low frequency
+term $(\omega_{1}t-\omega_{2}t)$
+and a high frequency term $(\omega_{1}t+\omega_{2}t)$,
+the $t$ can be taken in front of the bracket, as it
+is a common multiplier.
+The high frequency term, $(\omega_{1}+\omega_{2})$, can be filtered out using
+a low-pass filter\footnote{A low-pass filter passes
+low frequency signals and attenuates
+high frequency signals. In other words, signals higher than the
+specified cutoff frequency of the low-pass filter, are cut off by reducing their amplitudes.}.
+Ideally, the difference of the angle frequencies is zero,
+as in equation \eqref{eq:delaOmega}, since $\cos(\Delta \omega)=\cos(0)=1$
+and the remaining left signal is only the C/A code multiplied
+with the DC term (zero frequency producing a constant voltage) leaving only $\frac{1}{2}d_{C/A}$.
+\begin{equation}
+\label{eq:delaOmega}
+\Delta \omega = \omega_{1}-\omega_{2} = 0
+\end{equation}
+However, if the frequencies do not match, $f_{1}\neq f_{2}$,
+then the output signal $\frac{1}{2}d_{C/A}$ will be
+modified by the residual frequency $f_{1}-f_{2}$,
+and subsequently this will change the demodulated C/A output (also known as phase shift). Under those circumstances
+the correlator is unable to match the C/A code with the
+correct PRN code. An illustration of this phenomenon is depicted
+in figure \ref{img:multCAPhase}.
+
+\begin{figure}[ht!]
+ \centering
+ \includegraphics[scale=0.5]{img/PRN-PhaseShiftAfterDemod.pdf}
+ \caption{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}.}
+\label{img:multCAPhase}
+\end{figure}
+
+\clearpage
+\section{C/A wave demodulation}
+\label{sec:CAwaveDemodApend}
+The demodulation process, of finding the correct chipping rate,
+will examined in this appendix section.
+The chipping period $T_{c}$ can be derived from equation \eqref{eq:chipPeriod}.
+The amount of time required to find a matching PRN code shift, $\tau$,
+on the receiverr is proportional to the amount of parallely working LFSRs on the system
+\citep[Chapter 3]{bensky2008wireless}. Clearly with more LFSRs
+the required time for finding the matching phase shift increases.
+\begin{equation}
+\label{eq:chipPeriod}
+T_{c} = \frac{1}{f_{PRN}} = \frac{1}{1.023\cdot 10^6 \mathrm{Hz}}
+\end{equation}
+To determine whether the synthesized PRN code,
+matches the incoming C/A code of the received satellite
+signal, known correlation properties of PRN codes are used,
+as described in section \ref{sec:gpsDataAndSignal}.
+Since the PRN code is modeled as a sequence of +1's and
+-1's, the autocorrelation of
+a signal is at its maximum if it is in phase, i.e.
+summing up the sequence products yields the absolute
+maximum value for the case when each bit from one signal matches
+the bit from the other signal. As an illustration of the idea, an example is
+given in figure \ref{img:correlatingSignals}. The cross-correlation
+of the incoming C/A code with the first synthesized PRN code produces a
+result of $-3=(+1)\cdot(-1)+(-1)\cdot(+1)+(+1)\cdot(-1)+(+1)\cdot(+1)+(-1)\cdot(+1)$.
+However, the cross-correlation of the incoming C/A code
+and the second synthesized PRN code yields a result of
+$+5=(+1)\cdot(+1)+(-1)\cdot(-1)+(+1)\cdot(+1)+(+1)\cdot(+1)+(-1)\cdot(-1)$.
+
+\begin{figure}[ht!]
+ \centering
+ \includegraphics[scale=0.50]{img/Correlation.pdf}
+ \caption{Cross-correlation on three different signals. Image courtesy of \citep{understandGPS}.}
+\label{img:correlatingSignals}
+\end{figure}
+The same principle applies to the transmitted C/A and
+generated PRN code sequences in the GPS receiver. Thus, this can be modeled using
+the equation given in \eqref{eq:autocorrelationProperty},
+where $G_{i}(t)$ is the C/A code\footnote{PRN generated codes for GPS satellites
+are called Gold code sequences since they were first discovered by Dr. Robert Gold.} as a
+function of time $t$, for the GPS satellite $i$; $T_{C/A}$ is the
+C/A chipping period of $977.5 \,ns$ and $\tau$ is the phase shift
+in the auto-correlation function \citep[Chapter 4]{understandGPS}.
+
+\begin{equation}
+\label{eq:autocorrelationProperty}
+R_{i}(t) = \frac{1}{1023\cdot T_{C/A}} \int_{t=0}^{1022} G_{i}(t)G_{i}(t+\tau)d\tau
+\end{equation}
+Another correlation property of the PRN codes is used,
+the fact that in the ideal case the cross-correlation of two
+different PRN codes yields a result of zero. The ideal case of
+PRN code can be modeled as in equation \eqref{eq:prnIdealCaseZero}.
+\begin{equation}
+\label{eq:prnIdealCaseZero}
+R_{ij}(\tau) = \int_{-\infty}^{+\infty} PRN_{i}(t)PRN_{j}(t+\tau)d\tau = 0
+\end{equation}
+$PRN_{i}$ is the PRN code waveform for GPS satellite $i$ and
+$PRN_{j}$ is the PRN code waveform for every other GPS satellite other
+than $i$, $i\neq j$ \citep[Chapter 4]{understandGPS}. Equation
+\eqref{eq:prnIdealCaseZero} ``states that the PRN waveform of satellite
+$i$ does not correlate with PRN waveform of any other satellite $j$ for
+any phase shift $\tau$'' \citep[Chapter 4]{understandGPS}.
+Without the property given in \eqref{eq:prnIdealCaseZero},
+the GPS receiver would not be able to smoothly
+differentiate between different GPS satellite signals.
+Once the phase shift, $\tau$, has been found, the C/A code is modulated
+(XORed) with it. The resulting binary code are the transmitted subframes containing data
+required to estimate the position.
+%The implementation problem of finding correct C/A and carrier wave demodulation shall be
+%further explained in the following section \ref{sec:2dSearch}.
+
+\clearpage
\section{GPS assistance data descriptions}
Description of assistance data converted and sent inside the RRLP protocol.
\begin {table}[ht!]
diff --git a/vorlagen/thesis/src/kapitel_x.tex b/vorlagen/thesis/src/kapitel_x.tex
index 291592e..c839f46 100644
--- a/vorlagen/thesis/src/kapitel_x.tex
+++ b/vorlagen/thesis/src/kapitel_x.tex
@@ -588,9 +588,9 @@ it delivers the required assistance data for faster acquisition time.
-\setchapterpreamble[u]{%
- \dictum[Stobaeus] {What use is knowledge if there is no understanding?}
-}
+%\setchapterpreamble[u]{%
+% \dictum[Stobaeus] {What use is knowledge if there is no understanding?}
+%}
\chapter{GPS \& Assisted-GPS}
\label{gpsTheoryChatper}
\begin{figure}[ht!]
@@ -603,44 +603,39 @@ In the new global economy age, GPS positioning has become of important value for
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 milliard 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.
-
+The chapter is divided in few sections that explain what type of data are transmitted by the satellites.
+how they are modulated before transmission, demodulated on the receiver and how the search space works to
+track a GPS satellite.% and % how the target user position is estimated.
-
-In this paragraph the general idea shall be given of 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.
+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.
+this position estimation technique belongs to the group of time-of-arrival (TOA) methods.
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 and same location reference system has to be used.
+%It is important to note that the satellite positions
+%need to be known before proceeding with any calculations.
The general principle of this idea can be seen in figure
-\ref{img:GPSSimplePrinciple}, picture (a) represents the idea
-with spheres in 3D space and picture (b) the same idea but in 2D space.
+\ref{img:GPSSimplePrinciple}, figure (a) shows the idea
+with spheres in 3D space and figure (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 estimated position of the GPS user
-for the given satellite.
-By intersecting all the three spheres, the position of the user is estimated.
-In the next sections this general idea shall be developed in more details,
-in an step by step approach, and the ideas shall be verified using the appropriate mathematical
-models.
+for the given range between the satellites and the GPS user. By knowing the positions
+of the reference points, i.e. positions of GPS satellites, user's position can be estimated.
+By intersecting three spheres, the 2D position of the user can be estimated.
+The GPS satellites are positioned in orbits so that at every moment at any spot on Earth, at least four satellites are visible
+(a spot can be considered as a mountain peak since in the cities GPS signals are blocked by buildings).
-\section{GPS data and signal modulation}
+\section{GPS data and signal modulation/demodulation}
\label{sec:gpsDataAndSignal}
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 discussed 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.
+to receive the data.
Each one of the GPS satellites transmits the same type of information.
The transmitted data are called \textit{frames} \citep{9780817643904}.
@@ -656,7 +651,7 @@ user's position.
\end{figure}
Each subframe can be divided into three fields of data,
as shown in figure \ref{img:gpssubframe}, telemetry (TLM),
-handover (HOW) word and rest of the data (navigation data).
+handover word (HOW) and rest of the data (navigation 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
@@ -665,89 +660,120 @@ and subframe ID \citep{9780817643904}.
GPS system time is the time the atomic clock on the satellite generates
at the moment of subframe broadcast
and it acts as a time stamp \citep{GPS-Interface-Specification}.
+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, denoted as $t_{SV}$, is
+generated at the moment of the 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 shall be given in section \ref{sec:SigDemod}. Subframe two and three
-are made of \textit{ephemeris data}. Ephemeris
+includes data about the satellite accuracy and health parameters as well as data
+used for the clock corrections on the GPS receiver. These clock correction parameters
+can be characterized as bias, drift and aging errors \citep{GPS-Interface-Specification}.
+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. The first three subframes are satellite dependent and do not
-change in the transmitted 25 frames aside from the system time stamp \citep{GPS-Guide}.
+position of the GPS satellite. Without the ephemeris data it is not possible for the GPS receiver
+to estimate its position.
\begin{figure}[ht!]
\centering
\includegraphics[scale=0.50]{img/GPSSubframe.pdf}
- \caption{Subframes always start with telemetry and handover words}
+ \caption{Subframes always start with telemetry and handover words, the rest are parameters for removing errors and for estimating
+ satellite's position.}
\label{img:gpssubframe}
\end{figure}
Fourth and fifth subframes include \textit{almanac data}, low-precision clock corrections,
-ionospheric model and UTC time calculation parameters. 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 shall 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.
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 32 GPS satellites\footnote{24 satellites are used in the GPS system,
-the rest is used in case one of the 24 fails.} in case the receiver found only one satellite
-and once it collected all almanac data, it can search for other visible GPS satellites.
-These 25 frames create a masterframe. Once the 25 frames
-have been transmitted, the process is repeated again.
+the ionosphere \citep{9780817643904}. Almanac information is
+rough coarse parameters for predicting the orbital position of the GPS satellites.
+These low-precision parameters (almanac) are used by the receiver to estimate the rough
+position of the satellites which in return reduces the searching space of emitting
+satellite frequencies. Although all satellites transmit on the same frequency,
+when the signals are received on Earth, they have a different frequency
+from the transmitted one because of the Doppler effect
+\footnote{Doppler effect is a
+phenomenon that happens as a result of relative
+motion of the two bodies, transmitter and
+receiver, towards or away from each other and causes
+frequency shift of the electromagnetic wave
+\citep[Chapter 4]{3540727140}.}.
+Once the frequencies are known, the receiver can track the satellites and
+obtain ephemeris parameters which are required to estimate the position.
+The first three subframes are satellite dependent and do not change in the
+transmitted 25 frames aside from the system time stamp \citep{GPS-Guide}.
+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 32 GPS
+satellites\footnote{24 satellites are used in the GPS system, the rest is
+used in case one of the 24 fails.} in case the receiver found only one
+satellite and once it collected all almanac data, it can search for other
+visible GPS satellites. These 25 frames create a masterframe.
+Once the 25 frames have been transmitted, the process is repeated again.
+
+%This shall be further explained in more details in the following sections \ref{sec:Carrierdemod},
+%\ref{sec:CAdemod} and \ref{sec:2dSearch}.
+
The data are modulated using the binary phase shift keying (BPSK) technique. The
-newly modulated signal is the \textit{L1} signal and it is emitted from the satellite
-directed antennas towards Earth \citep{GPS-Guide}. The BPSK technique works by changing
+newly modulated signal, denoted as \textit{L1}, and it is emitted from the satellite's
+directed antennas toward Earth \citep{GPS-Guide}. The BPSK technique works by changing
the phase of the carrier signal for $180^{\circ}$ at the moment of bit toggle (flipping) in the
data \citep{GPS-Guide} \citep{9780817643904}.
Basic principle of this technique can be seen in figure \ref{img:bpskmod}. The carrier wave
for GPS BPSK modulation is centered at a frequency of 1575.42 MHz \citep{9780817643904}.
These signals travel an average distance of $20200 \, km$ from the satellite to the GPS receiver
and are affected by various sources of noise. BPSK modulation is mostly used for satellite links
-because of its simplicity and immunity to noise and signal intereference for the price of
-transfering data at low speed rates \citep[Chapter 1]{9780849316579}. The demodulation process
-of L1 shall be discussed and analysed seperately in section \ref{sec:Carrierdemod}.
+because of its simplicity, immunity to noise and signal intereference for the cost of
+low speed data transfer rates \citep[Chapter 1]{9780849316579}.
\begin{figure}[ht!]
\centering
\includegraphics[scale=0.50]{img/BPSKModulation.pdf}
- \caption{BPSK Modulation - First signal is the carrier wave,
+ \caption{BPSK Modulation - First depicted signal is the carrier wave,
and it is multiplied (mixed) with the second signal, which are
the data to be transmitted. The resulting signal at the output
of the satellite antenna is the third one.}
\label{img:bpskmod}
\end{figure}
-However, before the raw navigation data enter the BPSK modulation process, they are XORed
-with pseudo random noise (PRN) sequences for different satellites (each satellite
-owns a unique PRN sequence) \citep{9780817643904}. PRN sequences are used to identify
-which satellite signal is being decoded, transmission of the data on the same frequency
-as well as to enable the distance measuring mechanism between the satellite and the GPS receiver.
-Equivalent PRN sequence is generated on the
-GPS receiver and it is compared with the received PRN sequence which is delayed (shifted)
-due to the distance. This delay multiplied with the speed of light yields the distance
-between the satellite and the GPS receiver.
+However, before the raw subframes enter the BPSK modulation process, they are XORed
+with Pseudo Random Noise (PRN) sequences for different satellites (each satellite
+owns a unique PRN sequence) \citep{9780817643904}. PRN sequences are used because they allow
+the identification of each satellite's transmitted data on the receiver, same satellite emitting
+frequency as well as to enable the distance measuring mechanism between the satellite and
+the GPS receiver. When the received signals are processed, equivalent PRN sequences are generated
+on the GPS receiver and then they are compared with the received PRN sequences which are delayed (shifted)
+due to the distance between the satellite and the receiver. This delay multiplied with the speed of
+light yields the distance between the satellite and the GPS receiver.
PRN sequences have similar autocorrelation properties as noise, when it is shifted in
time domain it has a low correlation value whereas when it is matched with exact image of itself
it produces a high correlation peak \citep[Chapter 3]{bensky2008wireless}. This property is used
-for identifying the satellites and for finding the exact phase shift.
+for identifying the satellites and for finding the exact phase shift. This phase shift
+is a consequence of the relationship between the instantaneous frequency and instantaneous phase,
+the relationship between frequency and phase can be seen in equations \eqref{eq:freqPhase}
+and \eqref{eq:phaseFreq}. In other words, due to the Doppler effect the phase of the PRN sequence is
+disordered. Without the exact phase shift it is not possible to demodulate the original data (TLM, HOW and
+navigation data) from the received signals.
+\begin{equation}
+\label{eq:freqPhase}
+f(t)=\frac{1}{2\pi}\frac{\partial}{\partial t}\phi(t)
+\end{equation}
+\begin{equation}
+\label{eq:phaseFreq}
+\phi(t) = 2\pi \int_{-\infty}^{t} f(\tau) d\tau
+\end{equation}
The second important property of PRN sequences is the property of
-orthogonality. This proberty enables the reception of different data on the same frequency,
+orthogonality. This property enables the reception of different data on the same frequency,
also known as code division multiple access (CDMA). It is important to note that the PRN sequences
-must have a higher frequency than the data, i.e. the bit duration of a PRN sequence is much shorter
+must have a higher frequency rate than the data, i.e. the bit duration of a PRN sequence is much shorter
than of the data \citep[Chapter 3]{bensky2008wireless}. Single bits in PRN sequences are called \textit{chips}
and the complete sequence as \textit{code} \citep[Chapter 3]{bensky2008wireless}. This newly generated
signal is called direct sequence spread spectrum (DSSS) \citep[Chapter 3]{bensky2008wireless}. In
GPS terminology it is named as Code/Acquisition (C/A) code. C/A code is feed into the BPSK modulation
-process, where it is mixed with the carrier wave and producing the L1 signal. More details shall be given in the
-C/A demodulation section \ref{sec:CAdemod}. Transmission speed of the navigation message is
-50 bps, therefore the reception of a complete masterframe requires around $\approx12.5$ minutes, i.e.
+process, where it is mixed with the carrier wave. The new produced signal is the L1.
+Transmission speed of the navigation message is 50 bps, therefore the reception of a complete
+masterframe requires around $\approx12.5$ minutes, i.e.
$(1500 \, \mathrm{bits per frame}\, \cdot \, 25 \, \mathrm{frames}) / (50 \,\mathrm{bps} \, \cdot \, 60\, \mathrm{s})$.
\begin{figure}[ht!]
@@ -757,8 +783,8 @@ $(1500 \, \mathrm{bits per frame}\, \cdot \, 25 \, \mathrm{frames}) / (50 \,\mat
\label{img:gpsmod}
\end{figure}
-The described GPS navigation data modulation can be seen in figure \ref{img:gpsmod} and it
-can be represented in form of equation \eqref{eq:GPSSignalReceived1} \citep{1656803}, where $D(t)$
+The described GPS navigation data modulation can be seen in figure \ref{img:gpsmod}. The figure
+can be mathematically represented in the form of equation \eqref{eq:GPSSignalReceived1} \citep{1656803}, where $D(t)$
are the navigation data at the moment $t$, $C(t)$ is the PRN chip at the moment $t$, $cos(2\pi f_{c}+\varphi_{SV})$
is the generated carrier wave with frequency $f_c$ and phase $\varphi_{GPS}$, $P$ is output power of the transmitter
amplifier.
@@ -766,97 +792,95 @@ amplifier.
\label{eq:GPSSignalReceived1}
S(t) = PD(t)C(t)cos(2\pi f_{c}+\varphi_{GPS})
\end{equation}
-The equation \ref{eq:GPSSignalReceived1} shall be rewritten as given in \ref{eq:GPSSignalReceived2}. It
-represents the same equation but at the GPS receiver after traveling $\approx 20200 \, km$, where $d_{C/A}$
-is the C/A data and $n(t)$ is the random noise at moment $t$ influenced by various factors that influence
-electromagnetic waves.
+The equation \ref{eq:GPSSignalReceived1} shall be rewritten as shown in \ref{eq:GPSSignalReceived2}. It
+is the equivalent equation but at the GPS receiver, where $d_{C/A}$
+is the C/A data and $n(t)$ is the random noise at moment $t$ generated by various factors that influence
+electromagnetic waves.
+In the next section, more details shall be revealed on the process of demodulating the GPS L1 signal and acquiring the
+correct time and position.
\begin{equation}
\label{eq:GPSSignalReceived2}
S(t) = \sqrt{\frac{P}{2}}d_{C/A}cos(2\pi f_{c}+\varphi_{GPS}) + n(t)
\end{equation}
-The GPS satellites are positioned in orbits so that at every moment at any spot on Earth, at least four satellites are visible
-(a spot can be considered as a mountain peak since in the cities GPS signals are blocked by buildings).
-In the next section, more details shall be revealed on the process of demodulating the GPS L1 signal and acquiring the
-correct time and position.
-\section{GPS signal acquisition and demodulation}
-\label{sec:SigDemod}
-GPS satellites\footnote{Ssatellites are named as space vehicles
-in GPS terminology and the abrevation SV is used in the equation notations
-to denote a parameter related to the satellite itself.}
-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 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
-characterized as bias, drift and aging errors
-\citep{GPS-Interface-Specification}. The correct broadcast
-time, denoted as $t$, can be estimated using the model given in equation
-\eqref{eq:timecorrection1} \citep{GPS-Interface-Specification}.
-In equation \eqref{eq:timecorrection2}, where the GPS
-receiver is required to calculate the satellite clock
-offset, denoted as $\Delta t_{SV}$, a number of unknown terms can be
-seen. These terms are encapsulated inside of the transmitted frames. The polynomial
-coefficients: $a_{f0}$ - \textit{clock offset}, $a_{f1}$ -
-\textit{fractional frequency offset}, $a_{f2}$ - \textit{
-fractional frequency drift}; and
-$t_{0c}$ - \textit{reference epoch} are encapsulated inside
-of subframe 1. The only remaining unknown term left in equation
-\eqref{eq:timecorrection2} is the \textit{relativistic correction
-term}, denoted as $\Delta t_{r}$. $\Delta t_{r}$ can be evaluated
-by applying the equation given 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 encapsulated in subframes 2 and 3
-\citep{GPS-Interface-Specification}.
-
-\begin{equation}
-\label{eq:timecorrection1}
-\centering
-t=t_{SV}-\Delta t_{SV}
-\end{equation}
-\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_{e}}} {c^{2}} = -4.442807633 \cdot 10^{-10} \frac{s}{\sqrt{m}} \label{eq:timecorrection4}
-\end{alignat}
-
-Nevertheless, the broadcast satellite time
-information is not sufficient to estimate the precise
-time at the moment of the signal arrival. Even though the signal
-arrives in approximately\footnote{Propagation time
-depends on user and GPS satellite position.} $77 \, ms$,
-the precision of the atomic clock is in the
-range of 10 ns \citep[Chapter 2]{diggelen2009a-gps}.
-Undoubtedly the signal propagation (travel)
-time, denoted as $t_{prop}$, has to be taken into account.
-In that case, the exact time at the moment of arrival is known,
-denoted as $t_{exact}$ and is given in equation \eqref{eq:exactTime}.
-%The signal propagation time must be known to
-%estimate the distance from the satellite
-%but is not sufficient to estimate the position of the GPS receiver.
-Propagation time is computed by measuring the phase shift of the C/A
-signal, more details shall be given in sections \ref{sec:CAdemod}
-and \ref{sec:distanceAndPosition}.
-More importantly, $t_{exact}$ time shall be later used
-to synchronize various time dependent systems like the
-GSM, LTE, GNSS or other communication and ranging systems.
-\begin{equation}
-\label{eq:exactTime}
-t_{exact} = t_{prop}+t
-\end{equation}
+% \section{GPS signal acquisition and demodulation}
+% \label{sec:SigDemod}
+% GPS satellites\footnote{Ssatellites are named as space vehicles
+% in GPS terminology and the abrevation SV is used in the equation notations
+% to denote a parameter related to the satellite itself.}
+% 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 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
+% characterized as bias, drift and aging errors
+% \citep{GPS-Interface-Specification}. The correct broadcast
+% time, denoted as $t$, can be estimated using the model given in equation
+% \eqref{eq:timecorrection1} \citep{GPS-Interface-Specification}.
+% In equation \eqref{eq:timecorrection2}, where the GPS
+% receiver is required to calculate the satellite clock
+% offset, denoted as $\Delta t_{SV}$, a number of unknown terms can be
+% seen. These terms are encapsulated inside of the transmitted frames. The polynomial
+% coefficients: $a_{f0}$ - \textit{clock offset}, $a_{f1}$ -
+% \textit{fractional frequency offset}, $a_{f2}$ - \textit{
+% fractional frequency drift}; and
+% $t_{0c}$ - \textit{reference epoch} are encapsulated inside
+% of subframe 1. The only remaining unknown term left in equation
+% \eqref{eq:timecorrection2} is the \textit{relativistic correction
+% term}, denoted as $\Delta t_{r}$. $\Delta t_{r}$ can be evaluated
+% by applying the equation given 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 encapsulated in subframes 2 and 3
+% \citep{GPS-Interface-Specification}.
+%
+% \begin{equation}
+% \label{eq:timecorrection1}
+% \centering
+% t=t_{SV}-\Delta t_{SV}
+% \end{equation}
+% \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_{e}}} {c^{2}} = -4.442807633 \cdot 10^{-10} \frac{s}{\sqrt{m}} \label{eq:timecorrection4}
+% \end{alignat}
+%
+% Nevertheless, the broadcast satellite time
+% information is not sufficient to estimate the precise
+% time at the moment of the signal arrival. Even though the signal
+% arrives in approximately\footnote{Propagation time
+% depends on user and GPS satellite position.} $77 \, ms$,
+% the precision of the atomic clock is in the
+% range of 10 ns \citep[Chapter 2]{diggelen2009a-gps}.
+% Undoubtedly the signal propagation (travel)
+% time, denoted as $t_{prop}$, has to be taken into account.
+% In that case, the exact time at the moment of arrival is known,
+% denoted as $t_{exact}$ and is given in equation \eqref{eq:exactTime}.
+% %The signal propagation time must be known to
+% %estimate the distance from the satellite
+% %but is not sufficient to estimate the position of the GPS receiver.
+% Propagation time is computed by measuring the phase shift of the C/A
+% signal, more details shall be given in sections \ref{sec:CAdemod}
+% and \ref{sec:distanceAndPosition}.
+% More importantly, $t_{exact}$ time shall be later used
+% to synchronize various time dependent systems like the
+% GSM, LTE, GNSS or other communication and ranging systems.
+% \begin{equation}
+% \label{eq:exactTime}
+% t_{exact} = t_{prop}+t
+% \end{equation}
\subsection{Carrier wave demodulation}
\label{sec:Carrierdemod}
@@ -868,37 +892,18 @@ of the GPS satellite \citep{4560215}. In other words,
the identical carrier wave replica has to be generated
on the receiver as on the satellite \citep{736341}.
However, the received signal is not the equivalent
-of the transmitted signal. Due to the nature of the
-Doppler effect\footnote{Doppler effect is a
-phenomenon that happens as a result of relative
-motion of the two bodies, transmitter and
-receiver, towards or away from each other and causes
-frequency shift of the electromagnetic wave
-\citep[Chapter 4]{3540727140}.}
-and wave propagation, the transmitted signal arrives
+of the transmitted signal due to the nature of the
+Doppler effect and wave propagation properties. The transmitted signals arrive
phase disordered at the receiver \citep{4560215}.
-This phase disorder is a consequence of the relationship
-between the instantaneous frequency and instantaneous phase
-according to equations \eqref{eq:freqPhase} and \eqref{eq:phaseFreq}.
-\begin{equation}
-\label{eq:freqPhase}
-f(t)=\frac{1}{2\pi}\frac{\partial}{\partial t}\phi(t)
-\end{equation}
-\begin{equation}
-\label{eq:phaseFreq}
-\phi(t) = 2\pi \int_{-\infty}^{t} f(\tau) d\tau
-\end{equation}
-
Considering that the GPS satellites orbit the Earth with
a speed of around $3.9 \, km/s$, the Earth rotates
around its axis and the target user
with the GPS receiver may move as well, the Doppler effect
-is unavoidable.
-The observed phase at the receiver antenna,
+is unavoidable. The observed phase at the receiver antenna,
denoted as $\varphi_{o}$, can be described using
the equation given in \eqref{eq:phaseShift},
-where $\varphi_{GPS}$ represents the known satellite
-carrier wave phase, $\delta \varphi_{SV}$ the clock
+where $\varphi_{GPS}$ is the known satellite
+carrier wave phase (as specified in the standard), $\delta \varphi_{SV}$ the clock
instabilities on the GPS satellite,
$\varphi_{a}$ the phase shift error
caused by propagation delays in the ionosphere
@@ -928,118 +933,37 @@ such that $\Delta \varphi \approx 0$, a phase shift is shown in figure \ref{img:
\begin{figure}[ht!]
\centering
\includegraphics[scale=0.5]{img/Phase-Diff.pdf}
- \caption{Two equivalent carrier waves with the same frequency but different phase shift}
+ \caption{Two carrier waves with the same frequency but different phase shift.}
\label{img:phaseShift}
\end{figure}
\begin{figure}[ht!]
\centering
\includegraphics[scale=0.5]{img/L1-Demodulation.pdf}
- \caption{Demodulation of the L1 GPS signal}
+ \caption{Demodulation of the L1 GPS signal.}
\label{img:L1Demod}
\end{figure}
-The reason for this is straightforward to understand by looking at the
- multiplication of two sine waves. The GPS L1 signal
- demodulator at the receiver is depicted in figure
-\ref{img:L1Demod}, the incoming signal L1 is multiplied with
-the synthesized sine wave (multiplication is the function of
-a mixer, denoted as $\otimes$ in figure \ref{img:L1Demod}).
-For the purpose of easier analysis, cosine waves
-shall be used istead of sine waves, the difference between them
-is only in the phase shift, as denoted in equation
-\eqref{eq:sineEqCosine}.
-\begin{equation}
-\label{eq:sineEqCosine}
-\sin(\pm x) = \cos\bigg(\frac{\pi}{2} \pm x\bigg)
-\end{equation}
-Multiplication of two cosine waves, as in equation \eqref{eq:multCosin},
-can be derived by adding $\cos(A+B)$ and $\cos(A-B)$ together, as respectively
-given in equations \eqref{eq:cos1} and \eqref{eq:cos2}.
-\begin{equation}
-\label{eq:multCosin}
-\cos(A)\cdot\cos(B) = \frac{1}{2}\cos(A-B)+\frac{1}{2}\cos(A+B)
-\end{equation}
-\begin{equation}
-\label{eq:cos1}
-\cos(A+B) = \cos(A)\cos(B)-\sin(A)\sin(B)
-\end{equation}
-\begin{equation}
-\label{eq:cos2}
-\cos(A-B) = \cos(A)\cos(B)+\sin(A)\sin(B)
-\end{equation}
-The incoming GPS L1 signal with a frequency $f_{1}$, given in figure \ref{img:L1Demod},
-can be written as $d_{C/A}\cos(\omega_{1}t)$, a similar form is given in equation \eqref{eq:GPSSignalReceived2},
-where $\omega_{1}=2\pi f_{1}$ is
-the angle frequency and
-$d_{C/A}$ is the C/A data (navigation message modulated with the PRN code),
-$d_{C/A}=d_{PRN}\oplus d_{NAV}$.
-If equation \eqref{eq:multCosin} is rewritten with the received GPS signal L1
-and synthesized wave with frequency $f_{2}$, the equation results the one
-given in \eqref{eq:cosResult}
-\begin{equation}
-\label{eq:cosResult}
-d_{C/A}\cdot\cos(\omega_{1}t)\cos(\omega_{2}t) = \frac{1}{2}d_{C/A}\cdot\cos(\omega_{1}t-\omega_{2}t) + \frac{1}{2}d_{C/A}\cos(\omega_{1}t+\omega_{2}t)
-\end{equation}
-This leaves the resulting signal with two frequency terms, a low frequency
-term $(\omega_{1}t-\omega_{2}t)$
-and a high frequency term $(\omega_{1}t+\omega_{2}t)$,
-the $t$ can be taken in front of the bracket as it
-is a common multiplier.
-The high frequency term, $(\omega_{1}+\omega_{2})$, can be filtered out using
-a low-pass filter\footnote{A low-pass filter passes
-low frequency signals and attenuates
-high frequency signals. In other words, signals higher than the
-specified cutoff frequency of the low-pass filter, are cut off by reducing their amplitudes.}.
-Ideally, the difference of the angle frequencies is zero,
-as in equation \eqref{eq:delaOmega}, since $\cos(\Delta \omega)=\cos(0)=1$
-and the remaining left signal is only the C/A code multiplied
-with the DC term (zero frequency producing a constant voltage) leaving only $\frac{1}{2}d_{C/A}$.
-\begin{equation}
-\label{eq:delaOmega}
-\Delta \omega = \omega_{1}-\omega_{2} = 0
-\end{equation}
-However, if the frequencies do not match, $f_{1}\neq f_{2}$,
-then the output signal $\frac{1}{2}d_{C/A}$ shall be
-modified by the residual frequency $f_{1}-f_{2}$,
-and subsequently this shall change the demodulated C/A output (also known as phase shift). Under those circumstances
-the correlator shall be unable to match the C/A code with the
-correct PRN code. An illustration of this phenomenon is depicted
-in figure \ref{img:multCAPhase}.
-
-\begin{figure}[ht!]
- \centering
- \includegraphics[scale=0.5]{img/PRN-PhaseShiftAfterDemod.pdf}
- \caption{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 $d_{C/A}$
- shall vary as well (third figure). Image courtesy of \citep{diggelen2009a-gps}.}
-\label{img:multCAPhase}
-\end{figure}
-
+The reason why the equivalent carrier wave must be generated is explained in more detail in appendix
+\ref{sec:carWavDemod}. At this point, the C/A data (navigation message modulated with the PRN code)
+have been extracted, it is required to demodulate C/A data as well (remove the PRN code).
\subsection{C/A wave demodulation}
\label{sec:CAdemod}
As a result of the previous step, one can continue with
the demodulation of the C/A wave. Demodulating the C/A wave
-with the PRN code shall result in the time and navigation data.
+with the PRN code will result in the required data for
+estimating the position.
Each tracked GPS satellite signal is demodulated seperately
using the same PRN code, code chipping rate and carrier frequency-phase
-(which was determined above) for the given satellite
-\citep[Chapter 4]{understandGPS}.
+for the given satellite \citep[Chapter 4]{understandGPS}.
+The carrier frequency-phase was determined in the previous step.
The PRN codes for each GPS satellite is well defined and
known by the GPS receiver. The receiver has to generate the
equivalent PRN code with matching code chipping rate (phase)
-of the transmitted C/A code,
-this is depicted in figure \ref{img:prnCodeCompare} \citep[Chapter 5]{understandGPS}.
-This phase shift is again a consequence of the Doppler effect described in
-section \ref{sec:Carrierdemod}.
+of the transmitted C/A code, this is depicted in figure \ref{img:prnCodeCompare} \citep[Chapter 5]{understandGPS}.
+This phase shift is again a consequence of the Doppler effect.
\begin{figure}[ht!]
\centering
\includegraphics[scale=0.50]{img/PRN-ChipRate.pdf}
@@ -1055,94 +979,23 @@ manufacturer but it is usually implemented as a linear feedback shift
registers (LFSR) that produces an output according to a predefined function $f(\tau)$.
This function, $f(\tau)$, generates an PRN code, that is
delayed in phase by $\tau$, where $\tau$ is a multiple of the chipping
-rate period $T_{c}=977.5 \,ns$. The chipping period $T_{c}$
-can be derived from equation \eqref{eq:chipPeriod}.
-The amount of time required to find a matching PRN code shift, $\tau$,
-on the receiverr is proportional to the amount of parallely working LFSRs on the system
-\citep[Chapter 3]{bensky2008wireless}. Clearly with more LFSRs
-the required time for finding the matching phase shift increases.
-\begin{equation}
-\label{eq:chipPeriod}
-T_{c} = \frac{1}{f_{PRN}} = \frac{1}{1.023\cdot 10^6 \mathrm{Hz}}
-\end{equation}
-
-To determine whether the synthesized PRN code,
-matches the incoming C/A code of the received satellite
-signal, known correlation properties of PRN codes are used,
-as described in section \ref{sec:gpsDataAndSignal}.
-Since the PRN code is modeled as a sequence of +1's and
--1's, the autocorrelation of
-a signal is at its maximum if it is in phase, i.e.
-summing up the sequence products yields the absolute
-maximum value for the case where each bit from one signal matches
-the bit from the other signal. As an illustration of the idea, an example is
-given in figure \ref{img:correlatingSignals}. The cross-correlation
-of the incoming C/A code with the first synthesized PRN code produces a
-result of $-3=(+1)\cdot(-1)+(-1)\cdot(+1)+(+1)\cdot(-1)+(+1)\cdot(+1)+(-1)\cdot(+1)$,
-whereas the cross-correlation of the incoming C/A code
-and the second synthesized PRN code yields a result of
-$+5=(+1)\cdot(+1)+(-1)\cdot(-1)+(+1)\cdot(+1)+(+1)\cdot(+1)+(-1)\cdot(-1)$.
+rate period $T_{c}=977.5 \,ns$. This demodulation process, of finding the correct chipping rate,
+is given in appendix \ref{sec:CAwaveDemodApend}. Both carrier wave and C/A wave demodulation
+have to be executed at the same time. This can be represented as a 2D search space problem.
+This problem will be further analyzed in the following section. % and it will provide an answer why
+%it takes so long to estimate a position.
-\begin{figure}[ht!]
- \centering
- \includegraphics[scale=0.50]{img/Correlation.pdf}
- \caption{Cross-correlation on three different signals. Image courtesy of \citep{understandGPS}.}
-\label{img:correlatingSignals}
-\end{figure}
-The same principle applies to the transmitted C/A and
-generated PRN code sequences in the GPS receiver. Thus, this can be modeled using
-the equation given in \eqref{eq:autocorrelationProperty},
-where $G_{i}(t)$ is the C/A code\footnote{PRN generated code for GPS satellites
-is called Gold code sequences
-since they were first discovered by Dr. Robert Gold.} as a
-function of time $t$, for the GPS satellite $i$; $T_{C/A}$ is the
-C/A chipping period of $977.5 \,ns$ and $\tau$ is the phase shift
-in the auto-correlation function \citep[Chapter 4]{understandGPS}.
-
-\begin{equation}
-\label{eq:autocorrelationProperty}
-R_{i}(t) = \frac{1}{1023\cdot T_{C/A}} \int_{t=0}^{1022} G_{i}(t)G_{i}(t+\tau)d\tau
-\end{equation}
-Another correlation property of the PRN codes is used,
-the fact that in the ideal case the cross-correlation of two
-different PRN codes yields a result of zero. The ideal case of
-PRN code can be modeled as in equation \eqref{eq:prnIdealCaseZero},
-\begin{equation}
-\label{eq:prnIdealCaseZero}
-R_{ij}(\tau) = \int_{-\infty}^{+\infty} PRN_{i}(t)PRN_{j}(t+\tau)d\tau = 0
-\end{equation}
-where $PRN_{i}$ is the PRN code waveform for GPS satellite $i$ and
-$PRN_{j}$ is the PRN code waveform for every other GPS satellite other
-than $i$, $i\neq j$ \citep[Chapter 4]{understandGPS}. Equation
-\eqref{eq:prnIdealCaseZero} ``states that the PRN waveform of satellite
-$i$ does not correlate with PRN waveform of any other satellite $j$ for
-any phase shift $\tau$'' \citep[Chapter 4]{understandGPS}.
-Without the property given in \eqref{eq:prnIdealCaseZero},
-the GPS receiver would not be able to smoothly
-differentiate between different GPS satellite signals.
-Once the phase shift, $\tau$, has been found, the C/A code is modulated
-(XORed) with it. The resulting binary code shall be the navigation message.
-The implementation problem of finding correct C/A and carrier wave demodulation shall be
-further explained in the following section \ref{sec:2dSearch}.
-
-\subsection{Implementation of the 2D search space problem}
+\newpage
+\section{Implementation of the 2D search space problem}
\label{sec:2dSearch}
-In the following paragraphs an introduction shall be given on
-the implementation problems of the previously discussed concepts.
-As it can be seen,
-from subsections \ref{sec:Carrierdemod} and
-\ref{sec:CAdemod}, decoding the GPS navigation message is a 2D
-search space problem for each GPS satellite
-signal acquisition. The 2D search space is limited by well known
-physical properties of the GNSS system such as the motion speed of GPS satellites
-(and the receiver) as well as the frequency oscillator on the receiver.
-
-GPS satellites move toward or away
+The 2D search space is limited by well known
+physical properties of the GPS navigation system, such as the motion speed of GPS satellites
+and the receiver as well as the frequency oscillator on the receiver. GPS satellites move toward or away
from the GPS receiver with a speed of $800 \, \mathrm{m/s}$
\citep[Chapter 3]{diggelen2009a-gps}. The Doppler effect on the frequency
of the satellite can be estimated using equation \eqref{eq:dopplerEffectSpeed},
where $f_{e}$ is the emitting frequency (L1), $v_{SV}$ is the speed of the
-satellite towards (away from) the receiver and $c$ is the speed of light.
+satellite towards or away from the receiver and $c$ is the speed of light.
\begin{equation}
\label{eq:dopplerEffectSpeed}
f_{DE} = f_{e}\frac{v_{SV}}{c}
@@ -1152,13 +1005,11 @@ yields a result of $\approx4.2 \, \mathrm{kHz}$, for $800 \, \mathrm{m/s}$ and
$\approx-4.2 \, \mathrm{kHz}$ (if the satellite moves away from the GPS receiver
then the speed is taken as negative). This makes a total range of $\approx8.4 \, \mathrm{kHz}$.
The Doppler effect of the GPS receiver motion can be ignored since for
-each $1 \, \mathrm{km/h}$ of movement, it affects the frequency
-range for $\approx 1.46 \,\mathrm{Hz}$.
-
-On the other hand, the frequency offset induced by the reference
+each $1 \, \mathrm{km/h}$ speed of movement, it affects the frequency
+range for $\approx 1.46 \,\mathrm{Hz}$. On the other hand, the frequency offset induced by the reference
oscillator in the GPS receiver can not be ignored. Function of the reference
oscillator is to give the GPS receiver the clock pulse required for all
-the computations and comparisons.
+the computations and comparisons in the process of signal demodulation.
The frequency search space is ``additionaly affected for $1.575 \, \mathrm{kHz}$
of unknown frequency offset for each $1 \, \mathrm{ppm}$
(\textit{parts per million}) of the unknown receiver
@@ -1175,104 +1026,92 @@ unknown frequency to be in range of $10 \, \mathrm{kHz}-25 \, \mathrm{kHz}$.
\caption{Segment of the frequency/code delay search space for a single GPS satellite. Image courtesy of \citep{diggelen2009a-gps}.}
\label{img:prnSearchSpace3d}
\end{figure}
-
A typical receiver searches in frequency bands (bins) of several hundred Hz \citep{1656803}.
Commonly used frequency bin size is $500 \, \mathrm{Hz}$,
therefore there are about 20-50 bins to search ($10000\, \mathrm{Hz}/500\, \mathrm{Hz} = 20$) \citep[Chapter 3]{diggelen2009a-gps}.
-The frequency search bin (band) size is a function of the desired peak magnitude loss (signal to noise ratio)
-due to the frequency mismatch and integration time period. Larger frequency
-bands mean a smaller number of bins to search but
-a greater correlation peak magnitude loss, i.e. with larger frequency bands
-it becomes harder to identify the correlation peaks described in sections \ref{sec:gpsDataAndSignal} and \ref{sec:CAdemod}.
-The frequency search bin size can be
-estimated using the frequency
-mimsmatch loss \textit{sinc} function given in equation \eqref{eq:mistunigLoss} \citep{implSoftGPSRec},
-\citep[Chapter 6]{diggelen2009a-gps},
-where $\Delta f$ is the frequency mismatch in $\mathrm{Hz}$,
-in other words it represents the difference
-between the received signal frequency and
-the synthesized carrier frequency on the receiver;
-and $T_{ci}$ is the coherent integration time (usually $0.5\, ms$ according to \citep{implSoftGPSRec}
-and \citep[Chapter 3]{diggelen2009a-gps} but depends on the implementation).
-\begin{equation}
-\label{eq:mistunigLoss}
-D_{F} = \left\vert \frac{\sin(\pi \Delta fT_{ci})}{\pi \Delta fT_{ci}} \right\vert
-\end{equation}
-The frequency mimsmatch loss sinc function, $D_{F}$, is evaluated in dB,
-therefore for a loss of $\approx 0.98 \,\mathrm{dB}$, the frequency mismatch ought to be
-$\Delta f = 250\, \mathrm{Hz}$,
-due to the fact that the maximum loss shall occur when the frequency is differing
-by 1/2 of the bin spacing. That is to say, for a bin space of 500 Hz, it is 250 Hz.
+The frequency search bin size is a function of the desired peak magnitude loss (signal to noise ratio)
+due to the frequency mismatch and integration time period. This means with larger frequency bands,
+it becomes harder to identify the correlation peaks required to obtain the GPS data, described in section \ref{sec:CAdemod}.
+% The frequency search bin size can be estimated using the frequency
+% mimsmatch loss \textit{sinc} function given in equation \eqref{eq:mistunigLoss} \citep{implSoftGPSRec},
+% \citep[Chapter 6]{diggelen2009a-gps},
+% where $\Delta f$ is the frequency mismatch in $\mathrm{Hz}$,
+% in other words it represents the difference
+% between the received signal frequency and
+% the synthesized carrier frequency on the receiver;
+% and $T_{ci}$ is the coherent integration time (usually $0.5\, ms$ according to \citep{implSoftGPSRec}
+% and \citep[Chapter 3]{diggelen2009a-gps} but depends on the implementation).
+% \begin{equation}
+% \label{eq:mistunigLoss}
+% D_{F} = \left\vert \frac{\sin(\pi \Delta fT_{ci})}{\pi \Delta fT_{ci}} \right\vert
+% \end{equation}
+% The frequency mimsmatch loss sinc function, $D_{F}$, is evaluated in dB,
+% therefore for a loss of $\approx 0.98 \,\mathrm{dB}$, the frequency mismatch ought to be
+% $\Delta f = 250\, \mathrm{Hz}$,
+% due to the fact that the maximum loss shall occur when the frequency is differing
+% by 1/2 of the bin spacing. That is to say, for a bin space of 500 Hz, it is 250 Hz.
``The total range of possible GPS code delays is $1\, ms$. This is because the GPS C/A
PRN code is $1 \,ms$ long, and then it repeats. The PRN code chipping rate is $1.023
\,\mathrm{MHz}$, and there are 1023 chips in the complete $1\, ms$ epoch'' \citep[Chapter 3]{diggelen2009a-gps}.
-
%Size of the frequency
%bin is inversely proportional to the ratio between the amplitude of the detected
%peak and other non-peak values,
%the smaller the bins are the higher the peak will be.
-
For the purpose of better understanding, a segment of the
frequency/code delay search space is shown in figure \ref{img:prnSearchSpace3d}.
-The peak implies the correct frequency and code delay have been found. In figure
+The peak implies the correct Doppler frequency and code delay have been found. In figure
\ref{img:prnSearchSpace3d} smaller frequency bins have been used so that the concept
-becomes understandable to the reader.
-
-The speed of searching the 2D search space (finding the peak)
-depends on the complexity and strategy of the
-implemented algorithm \citep[Chapter 6]{9780817643904}. In the worst case,
+becomes understandable to the reader. The speed of searching the 2D search space (finding the peak)
+depends on the complexity and strategy of the implemented algorithm \citep[Chapter 6]{9780817643904}. In the worst case,
there are in total 102300 conbinations in the search space,
-this can be derived from equation \eqref{eq:totalSearch}, visually shown
-in figure \ref{img:SearchSpace2d}.
+this can be derived from equation \eqref{eq:totalSearch}.
\begin{equation}
\label{eq:totalSearch}
\mathrm{Search \, Space} = 50 \,\mathrm{(bins)} \cdot 1023\, \mathrm{(C/A \,codes)} \cdot 2\, \mathrm{(Phases\, per\, C/A\, chip)}
\end{equation}
-
-\begin{figure}[ht!]
- \centering
- \includegraphics[scale=0.50]{img/2DSearchSpace.pdf}
- \caption{The total search space.}
-\label{img:SearchSpace2d}
-\end{figure}
-
-The common strategy is to start searching from the middle frequency bins and to jump
-up and down until the entire search space has been exhausted (first 500 Hz,
-second -500 Hz, then in the 1000 Hz bin and then in the -1000 Hz bin),
-as shown in figure \ref{img:freqSearch}
-\citep[Chapter 3]{diggelen2009a-gps}.
-This procedure is performed when no extra information are known by the receiver (almanac data
-are missing), i.e.
-first time the GPS receiver is turned on. It is known under the name of cold start.
-
-\begin{figure}[ht!]
- \centering
- \includegraphics[scale=0.50]{img/frequencySearch.pdf}
- \caption{Idea of the frequency searching algorithm.}
-\label{img:freqSearch}
-\end{figure}
-
-There are three different working modes when it comes to searching
-for the GPS satellites. If no information are known,
+% \begin{figure}[ht!]
+% \centering
+% \includegraphics[scale=0.50]{img/2DSearchSpace.pdf}
+% \caption{The total search space.}
+% \label{img:SearchSpace2d}
+% \end{figure}
+% The common strategy is to start searching from the middle frequency bins and to jump
+% up and down until the entire search space has been exhausted (first 500 Hz,
+% second -500 Hz, then in the 1000 Hz bin and then in the -1000 Hz bin),
+% as shown in figure \ref{img:freqSearch}
+% \citep[Chapter 3]{diggelen2009a-gps}.
+% This procedure is performed when no extra information are known by the receiver (almanac data
+% are missing), i.e.
+% first time the GPS receiver is turned on. It is known under the name of cold start.
+%
+% \begin{figure}[ht!]
+% \centering
+% \includegraphics[scale=0.50]{img/frequencySearch.pdf}
+% \caption{Idea of the frequency searching algorithm.}
+% \label{img:freqSearch}
+% \end{figure}
+
+There are three different working modes when it comes to finding a solution
+to the 2D search space problem. If no information are known,
when some information are known and when almost all information are
-known. These three modes are known as \textit{cold} (as discussed earlier),
-\textit{warm} and \textit{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, 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
-programmable read only memory (EEPROM). This new type of start,
-is known as a warm start,
-provided that the data in the receivers' EEPROM are not older than 180 days and
-its real time clock counter was constantly updated.
-In this case, the receiver uses the previously saved information
-to estimate the position of the satellites, therefore the Doppler effects can be roughly estimated.
-As a consequence of the known Doppler effect, the frequency bin where to start
-the search first is known this time \citep[Chapter 3]{diggelen2009a-gps}.
-Hot start works in the same manner, only the ephemeris data and time data are precisely
-known (time ought to be known in accuracy of submilliseconds).
+known. These three modes are known as \textit{cold},
+\textit{warm} and \textit{hot} start. Cold start indicates the GPS receiver
+has no almanac, ephemeris, oscillator offset and time data. In this case it is
+the cold start and the GPS receiver needs to obtain all these information manually using
+the described steps in this chapter. Once the receiver obtains all these information,
+it stores them in its Electrically Erasable Programmable Read Only Memory (EEPROM).
+In order for the GPS receiver to track the satellites faster next time it is started,
+it uses the previously stored information (last known almanac,
+oscillator offset, time and position data). This new type of start,
+is known as a warm start, provided that the data in the receiver's EEPROM are not older
+than 180 days and its real time clock counter was constantly updated\footnote{The almanac data
+are valid for 180 days.}. This way the GPS receiver can use the previously saved information
+to estimate the rough position of the satellites, therefore the Doppler effects can be
+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).
\section{Assisted GPS in wireless networks}
\label{sec:agps}
@@ -1280,14 +1119,14 @@ In the following paragraphs Assisted GPS (AGPS) shall be presented and how it wo
AGPS receivers work on the equivalent idea as warm/hot start on GPS receivers.
Instead of loading the recently saved data from the EEPROM, an external
information transfer medium is used to deliver the equivalent type of information that are known
-at a warm/hot start \citep{755159}, \citep{901174}, \citep{springerlink:10.1007/s10291-002-0028-0}.
+at the warm/hot start \citep{755159}, \citep{901174}, \citep{springerlink:10.1007/s10291-002-0028-0}.
In this work, the external transfer medium is air and the information are transferred using electromagnetic
waves. The existing GSM interface was utilised for the purpose of delivering the data to the smart phone
-with an AGPS receiver. The basic scenario can be seen in figure \ref{img:agpsPrinciple}.
-
-The BTS station is connected to the global navigation satellite system (GNSS) server, which is directly
+with an AGPS receiver. The basic scenario can be seen in figure \ref{img:agpsPrinciple}. 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 health as well as clock corrections, ionospheric and UTC model, almanac and ephemeris data
+approximate location, satellite health as well as clock corrections, ionospheric and UTC model, almanac and ephemeris data (data transmitted
+by the GPS satellite)
\citep{springerlink:10.1007/s10291-002-0028-0}.
\begin{figure}[ht!]
\centering
@@ -1395,7 +1234,7 @@ In RRLP the PDU's sent from the SMLC are not allowed be greater than 244 bytes\f
Although the standard defines that larger packets ought to be split into smaller pieces in lower layers, in this work the
rule of 244 bytes has been obeyed due to crashing of the GSM operating software (OpenBSC), thus each PDU packet was not greater
than 211 bytes. In the RRLP standard terms, the messages are entitled
-as \textit{components} and fields in the messages (components) are labelled as \textit{information elements} (IE) \citep{04.31V8.18.0}.
+as \textit{components} and fields in the messages (components) are labeled as \textit{information elements} (IE) \citep{04.31V8.18.0}.
The SMLC may send only the request for the position of the MS or it may assist the MS with assistance data
required to estimate its position. In case of an AGPS request, assistance data may be ephemeris, almanac,
accurate timing data or other assistance data that may help the receiver to estimate its position in a shorter period of time.
diff --git a/vorlagen/thesis/src/maindoc.lof b/vorlagen/thesis/src/maindoc.lof
index 252a80b..a4d1bb7 100644
--- a/vorlagen/thesis/src/maindoc.lof
+++ b/vorlagen/thesis/src/maindoc.lof
@@ -14,29 +14,25 @@
\addvspace {10\p@ }
\contentsline {figure}{\numberline {3.1}{\ignorespaces GPS Simple working principle, a) example in 3D space with spheres b) example in 2D space with circles.\relax }}{19}{figure.caption.19}
\contentsline {figure}{\numberline {3.2}{\ignorespaces One frame of 1500 bits on L1 frequency carrier. Image courtesy of \citep {harper2010server-side}.\relax }}{21}{figure.caption.20}
-\contentsline {figure}{\numberline {3.3}{\ignorespaces Subframes always start with telemetry and handover words\relax }}{21}{figure.caption.21}
-\contentsline {figure}{\numberline {3.4}{\ignorespaces BPSK Modulation - First signal is the carrier wave, and it is multiplied (mixed) with the second signal, which are the data to be transmitted. The resulting signal at the output of the satellite antenna is the third one.\relax }}{22}{figure.caption.22}
-\contentsline {figure}{\numberline {3.5}{\ignorespaces Modulation of the GPS signal L1. Image courtesy of \citep {harper2010server-side}.\relax }}{23}{figure.caption.23}
-\contentsline {figure}{\numberline {3.6}{\ignorespaces Two equivalent carrier waves with the same frequency but different phase shift\relax }}{26}{figure.caption.24}
-\contentsline {figure}{\numberline {3.7}{\ignorespaces Demodulation of the L1 GPS signal\relax }}{27}{figure.caption.25}
-\contentsline {figure}{\numberline {3.8}{\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 $d_{C/A}$ shall vary as well (third figure). Image courtesy of \citep {diggelen2009a-gps}.\relax }}{28}{figure.caption.26}
-\contentsline {figure}{\numberline {3.9}{\ignorespaces Comparison between the original C/A code generated on the GPS satellite with two synthesized PRN codes with a different phase shift on the receiver. Image courtesy of \citep {understandGPS}.\relax }}{29}{figure.caption.27}
-\contentsline {figure}{\numberline {3.10}{\ignorespaces Cross-correlation on three different signals. Image courtesy of \citep {understandGPS}.\relax }}{30}{figure.caption.28}
-\contentsline {figure}{\numberline {3.11}{\ignorespaces Segment of the frequency/code delay search space for a single GPS satellite. Image courtesy of \citep {diggelen2009a-gps}.\relax }}{32}{figure.caption.29}
-\contentsline {figure}{\numberline {3.12}{\ignorespaces The total search space.\relax }}{33}{figure.caption.30}
-\contentsline {figure}{\numberline {3.13}{\ignorespaces Idea of the frequency searching algorithm.\relax }}{33}{figure.caption.31}
-\contentsline {figure}{\numberline {3.14}{\ignorespaces Basic AGPS principle\relax }}{35}{figure.caption.32}
+\contentsline {figure}{\numberline {3.3}{\ignorespaces Subframes always start with telemetry and handover words, the rest are parameters for removing errors and for estimating satellite's position.\relax }}{21}{figure.caption.21}
+\contentsline {figure}{\numberline {3.4}{\ignorespaces BPSK Modulation - First depicted signal is the carrier wave, and it is multiplied (mixed) with the second signal, which are the data to be transmitted. The resulting signal at the output of the satellite antenna is the third one.\relax }}{22}{figure.caption.22}
+\contentsline {figure}{\numberline {3.5}{\ignorespaces Modulation of the GPS signal L1. Image courtesy of \citep {harper2010server-side}.\relax }}{24}{figure.caption.23}
+\contentsline {figure}{\numberline {3.6}{\ignorespaces Two carrier waves with the same frequency but different phase shift.\relax }}{25}{figure.caption.24}
+\contentsline {figure}{\numberline {3.7}{\ignorespaces Demodulation of the L1 GPS signal.\relax }}{25}{figure.caption.25}
+\contentsline {figure}{\numberline {3.8}{\ignorespaces Comparison between the original C/A code generated on the GPS satellite with two synthesized PRN codes with a different phase shift on the receiver. Image courtesy of \citep {understandGPS}.\relax }}{26}{figure.caption.26}
+\contentsline {figure}{\numberline {3.9}{\ignorespaces Segment of the frequency/code delay search space for a single GPS satellite. Image courtesy of \citep {diggelen2009a-gps}.\relax }}{28}{figure.caption.27}
+\contentsline {figure}{\numberline {3.10}{\ignorespaces Basic AGPS principle\relax }}{29}{figure.caption.28}
\addvspace {10\p@ }
-\contentsline {figure}{\numberline {4.1}{\ignorespaces RRLP Request protocol. Assistance data can be sent before the request is made. If the assistance data are sent, their reception acknowledgement is sent as a response from the MS. Image courtesy of \citep {harper2010server-side} and \citep {04.31V8.18.0}.\relax }}{38}{figure.caption.33}
-\contentsline {figure}{\numberline {4.2}{\ignorespaces An example of constructing an RRLP request. Image courtesy of \citep {harper2010server-side}.\relax }}{43}{figure.caption.34}
-\contentsline {figure}{\numberline {4.3}{\ignorespaces Reference location is a 14 octet stream built according to the given rule as specified in the standard \citep {3gppequations} under section \textit {7.3.6}. Image courtesy of \citep {3gppequations}.\relax }}{47}{figure.caption.35}
-\contentsline {figure}{\numberline {4.4}{\ignorespaces World Geodetic System 1984. Image courtesy of \citep {harper2010server-side}.\relax }}{48}{figure.caption.36}
-\contentsline {figure}{\numberline {4.5}{\ignorespaces Requested AGPS assistance data to be delivered. Image courtesy of \citep {49.031V8.1.0}.\relax }}{50}{figure.caption.37}
+\contentsline {figure}{\numberline {4.1}{\ignorespaces RRLP Request protocol. Assistance data can be sent before the request is made. If the assistance data are sent, their reception acknowledgement is sent as a response from the MS. Image courtesy of \citep {harper2010server-side} and \citep {04.31V8.18.0}.\relax }}{32}{figure.caption.29}
+\contentsline {figure}{\numberline {4.2}{\ignorespaces An example of constructing an RRLP request. Image courtesy of \citep {harper2010server-side}.\relax }}{37}{figure.caption.30}
+\contentsline {figure}{\numberline {4.3}{\ignorespaces Reference location is a 14 octet stream built according to the given rule as specified in the standard \citep {3gppequations} under section \textit {7.3.6}. Image courtesy of \citep {3gppequations}.\relax }}{41}{figure.caption.31}
+\contentsline {figure}{\numberline {4.4}{\ignorespaces World Geodetic System 1984. Image courtesy of \citep {harper2010server-side}.\relax }}{42}{figure.caption.32}
+\contentsline {figure}{\numberline {4.5}{\ignorespaces Requested AGPS assistance data to be delivered. Image courtesy of \citep {49.031V8.1.0}.\relax }}{44}{figure.caption.33}
\addvspace {10\p@ }
-\contentsline {figure}{\numberline {5.1}{\ignorespaces nanoBTS with two external antennas and five connection ports\relax }}{54}{figure.caption.39}
-\contentsline {figure}{\numberline {5.2}{\ignorespaces Cable configuration diagram.\relax }}{55}{figure.caption.40}
-\contentsline {figure}{\numberline {5.3}{\ignorespaces Flowchart for the RRLP assistance data generator.\relax }}{60}{figure.caption.41}
+\contentsline {figure}{\numberline {5.1}{\ignorespaces nanoBTS with two external antennas and five connection ports\relax }}{48}{figure.caption.35}
+\contentsline {figure}{\numberline {5.2}{\ignorespaces Cable configuration diagram.\relax }}{49}{figure.caption.36}
+\contentsline {figure}{\numberline {5.3}{\ignorespaces Flowchart for the RRLP assistance data generator.\relax }}{54}{figure.caption.37}
\addvspace {10\p@ }
-\contentsline {figure}{\numberline {6.1}{\ignorespaces Test rooms as well as the results delivered by the smart phones. Image courtesy of Google Maps.\relax }}{65}{figure.caption.43}
-\contentsline {figure}{\numberline {6.2}{\ignorespaces Test room 2 with the positions of the smart phones.\relax }}{66}{figure.caption.44}
+\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@ }
diff --git a/vorlagen/thesis/src/maindoc.lot b/vorlagen/thesis/src/maindoc.lot
index e37ce92..bea3336 100644
--- a/vorlagen/thesis/src/maindoc.lot
+++ b/vorlagen/thesis/src/maindoc.lot
@@ -7,9 +7,9 @@
\contentsline {table}{\numberline {2.4}{\ignorespaces Overview of the localization techniques.\relax }}{18}{table.caption.18}
\addvspace {10\p@ }
\addvspace {10\p@ }
-\contentsline {table}{\numberline {4.1}{\ignorespaces Requested AGPS assistance data bit meaning. Table courtesy of \citep {49.031V8.1.0}.\relax }}{52}{table.caption.38}
+\contentsline {table}{\numberline {4.1}{\ignorespaces Requested AGPS assistance data bit meaning. Table courtesy of \citep {49.031V8.1.0}.\relax }}{46}{table.caption.34}
\addvspace {10\p@ }
\addvspace {10\p@ }
-\contentsline {table}{\numberline {6.1}{\ignorespaces Smart phone models used for testing in the thesis.\relax }}{64}{table.caption.42}
-\contentsline {table}{\numberline {6.2}{\ignorespaces Smart phone RRLP test results from Test room 2.\relax }}{68}{table.caption.45}
+\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@ }
diff --git a/vorlagen/thesis/src/maindoc.tex b/vorlagen/thesis/src/maindoc.tex
index ada5478..d988631 100644
--- a/vorlagen/thesis/src/maindoc.tex
+++ b/vorlagen/thesis/src/maindoc.tex
@@ -232,7 +232,8 @@ stepnumber=1, numbersep=5pt, numbers = none}
%%% Hauptteil %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%
\include{kapitel_x}
-\bibliographystyle{abbrvnat}
+%\bibliographystyle{abbrvnat}
+\bibliographystyle{acm}
\bibliography{bib/literatur}
%%% Anhang %%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%