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authorRefik Hadzialic2012-07-06 14:46:07 +0200
committerRefik Hadzialic2012-07-06 14:46:07 +0200
commit66fd6614b3db33bc40578b7dcb9ba0b0de2bda3e (patch)
treee33d39339dd5870b6f1d56bc7cf71503a9463080
parentWriting and correcting! (diff)
downloadmalign-66fd6614b3db33bc40578b7dcb9ba0b0de2bda3e.tar.gz
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Reviewing chapter on gps and a-gps theory!
-rw-r--r--vorlagen/thesis/maindoc.pdfbin5010849 -> 5040577 bytes
-rw-r--r--vorlagen/thesis/src/img/GPS-Modulation.pdfbin11226 -> 28302 bytes
-rw-r--r--vorlagen/thesis/src/img/GPS-Modulation.svg295
-rw-r--r--vorlagen/thesis/src/img/PRN-ChipRate.svg16
-rw-r--r--vorlagen/thesis/src/img/fftSignal.pdfbin0 -> 14236 bytes
-rw-r--r--vorlagen/thesis/src/img/fftSignal.svg366
-rw-r--r--vorlagen/thesis/src/img/frequencySearch.pdfbin0 -> 8530 bytes
-rw-r--r--vorlagen/thesis/src/img/frequencySearch.svg194
-rw-r--r--vorlagen/thesis/src/kapitel_x.tex148
9 files changed, 810 insertions, 209 deletions
diff --git a/vorlagen/thesis/maindoc.pdf b/vorlagen/thesis/maindoc.pdf
index b259365..278d041 100644
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diff --git a/vorlagen/thesis/src/img/frequencySearch.pdf b/vorlagen/thesis/src/img/frequencySearch.pdf
new file mode 100644
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diff --git a/vorlagen/thesis/src/img/frequencySearch.svg b/vorlagen/thesis/src/img/frequencySearch.svg
new file mode 100644
index 0000000..6c15da8
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+ <path
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+ style="fill:none;stroke:#000000;stroke-width:1.77165353;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
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+ <path
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+ style="fill:none;stroke:#000000;stroke-width:1.77165353;stroke-linecap:butt;stroke-linejoin:miter;stroke-miterlimit:4;stroke-opacity:1;stroke-dasharray:none" />
+ </g>
+ <text
+ xml:space="preserve"
+ style="font-size:16px;font-style:normal;font-weight:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans"
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+ sodipodi:linespacing="125%"><tspan
+ sodipodi:role="line"
+ id="tspan4797"
+ x="368.70569"
+ y="400.81378" /></text>
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+ id="g4862"
+ transform="translate(-10,0)">
+ <text
+ sodipodi:linespacing="125%"
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+ y="380.60373"
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+ xml:space="preserve"><tspan
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+ style="font-size:16px;font-style:normal;font-weight:normal;line-height:125%;letter-spacing:0px;word-spacing:0px;fill:#000000;fill-opacity:1;stroke:none;font-family:Sans"
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+ x="-132.52266"
+ sodipodi:role="line"></tspan><tspan
+ id="tspan4860"
+ y="426.22046"
+ x="-132.52266"
+ sodipodi:role="line">Order of searching:</tspan></text>
+ </g>
+ </g>
+</svg>
diff --git a/vorlagen/thesis/src/kapitel_x.tex b/vorlagen/thesis/src/kapitel_x.tex
index 5017aa0..96bdc5c 100644
--- a/vorlagen/thesis/src/kapitel_x.tex
+++ b/vorlagen/thesis/src/kapitel_x.tex
@@ -50,8 +50,9 @@ By intersecting all the three spheres, the position of the user is estimated.
In the next sections this general idea will be developed in more details,
step by step, and the ideas will be verified using the appropriate mathematical
models.
-
+\newpage
\section{GPS data and signal modulation}
+\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 mentioned in the paragraph earlier, to estimate the position of the GPS receiver, it is
@@ -79,7 +80,7 @@ a unique preamble used to synchronize and identify
the subframes \citep{9780817643904}. HOW is the second
word of the subframe and consists of the \textit{GPS system time}
and subframe ID \citep{9780817643904}.
-GPS system time is the time the atomic clocks on the satellite generate
+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}.
The third segment of the subframe, indicated as rest of data in figure
@@ -115,7 +116,8 @@ 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 24 GPS satellites in case the receiver found only one satellite
+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.
@@ -135,8 +137,8 @@ of L1 will be discussed and analysed seperately in section \ref{sec:Carrierdemod
\begin{figure}[ht!]
\centering
\includegraphics[scale=0.50]{img/BPSKModulation.pdf}
- \caption[]{BPSK Modulation - The top signal is the carrier wave,
- and it is multiplied with the signal in the middle, which is
+ \caption[]{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.}
\label{img:bpskmod}
@@ -144,19 +146,29 @@ of L1 will be discussed and analysed seperately in section \ref{sec:Carrierdemod
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}.
-The PRN sequences have similar autocorrelation properties as noise, when it is shifted in
-time domain it has a low correlation whereas when it is matched with exact image of itself
+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.
+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 satellite and for enabling the reception of different data on the same frequency,
+for identifying the satellites and for finding the exact phase shift.
+The second important property of PRN sequences is the property of
+orthogonality. This proberty 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
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) signal. C/A signal is feed into the BPSK modulation
+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 will be given in the
-C/A demodulation section \ref{sec:CAdemod}.
+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.
+$(1500 \, \mathrm{bits per frame}\, \cdot \, 25 \, \mathrm{frames}) / (50 \,\mathrm{bps} \, \cdot \, 60\, \mathrm{s})$.
\begin{figure}[ht!]
\centering
@@ -168,11 +180,11 @@ C/A demodulation section \ref{sec:CAdemod}.
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 $D(t)$
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 $\varphi_{SV}$, $P$ is output power of the transmitter
+is the generated carrier wave with frequency $f_c$ and phase $\varphi_{GPS}$, $P$ is output power of the transmitter
amplifier.
\begin{equation}
\label{eq:GPSSignalReceived1}
-S(t) = PD(t)C(t)cos(2\pi f_{c}+\varphi_{SV})
+S(t) = PD(t)C(t)cos(2\pi f_{c}+\varphi_{GPS})
\end{equation}
The equation \ref{eq:GPSSignalReceived1} will be rewritten as given in \ref{eq:GPSSignalReceived2}. It
represents the same equation but at the GPS receiver after traveling $\approx 20200 \, km$, where $d_{C/A}$
@@ -180,7 +192,7 @@ is the C/A data and $n(t)$ is the random noise at moment $t$ influenced by vario
electromagnetic waves.
\begin{equation}
\label{eq:GPSSignalReceived2}
-S(t) = \sqrt{\frac{P}{2}}d_{C/A}cos(2\pi f_{c}+\varphi_{SV}) + n(t)
+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).
@@ -191,11 +203,11 @@ correct time and position.
-
+\newpage
\section{GPS signal acquisition and demodulation}
\label{sec:SigDemod}
-The GPS satellites\footnote{Satellites are named as space vehicles
-and the abrevation SV is used in the equation notations
+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}.
@@ -227,7 +239,7 @@ 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 subframe 2 and 3
+parameters encapsulated in subframes 2 and 3
\citep{GPS-Interface-Specification}.
\begin{equation}
@@ -235,7 +247,6 @@ parameters encapsulated in subframe 2 and 3
\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} \\
@@ -256,6 +267,9 @@ 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 will be given in sections \ref{sec:CAdemod}
+and \ref{sec:distanceAndPosition}.
More importantly, $t_{exact}$ time will be later used
to synchronize various time dependent systems like the
GSM, LTE, GNSS or other communication and ranging systems.
@@ -322,27 +336,30 @@ In the ideal case the observed phase
on the antenna and the generated phase on the
receiver, denoted as $\varphi_{rec}$, cancel each other
out, that is to say, equation \eqref{eq:phaseIdealCase}
-equals zero. The circuit responsible for generating the same
-carrier wave is the phase locked loop (PLL).
-The PLL modifies the synthesized wave parameters
-such that, $\lim \Delta \varphi \approx 0$.
+equals zero.
\begin{equation}
\label{eq:phaseIdealCase}
\Delta \varphi = \varphi_{o} - \varphi_{rec}
\end{equation}
+The circuit responsible for generating the same
+carrier wave is the phase locked loop (PLL).
+The PLL circuit is a feedback loop that modifies the synthesized wave parameters
+such that $\Delta \varphi \approx 0$, a phase shift is shown in figure \ref{img:phaseShift}.
\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}
\label{img:phaseShift}
\end{figure}
+
\begin{figure}[ht!]
\centering
\includegraphics[scale=0.5]{img/L1-Demodulation.pdf}
\caption[]{Demodulation of the L1 GPS signal}
\label{img:L1Demod}
\end{figure}
- This is straightforward to understand by looking at the
+
+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
@@ -372,12 +389,13 @@ given in equations \eqref{eq:cos1} and \eqref{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 $d_{C/A}\cos(\omega_{1}t)$, where $\omega_{1}=2\pi f_{1}$ is
+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 a frequency $f_{2}$, the equation results the one
+and synthesized wave with frequency $f_{2}$, the equation results the one
given in \eqref{eq:cosResult}
\begin{equation}
\label{eq:cosResult}
@@ -427,22 +445,23 @@ in figure \ref{img:multCAPhase}.
-
\newpage
\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.
+the demodulation of the C/A wave. Demodulating the C/A wave
+with the PRN code will result in the time and navigation data.
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}.
The PRN codes for each GPS satellite is well defined and
known by the GPS receiver. The receiver has to generate the
-same PRN code with matching code chipping rate (phase)
+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 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}.
\begin{figure}[ht!]
\centering
\includegraphics[scale=0.50]{img/PRN-ChipRate.pdf}
@@ -459,50 +478,54 @@ registers (LFSR) that produces an output according to a predefined function $f(\
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}.
+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 LFSR on the system
+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}
+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.
+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. As an illustration of the idea, an example is
+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
$+5=(+1)\cdot(+1)+(-1)\cdot(-1)+(+1)\cdot(+1)+(+1)\cdot(+1)+(-1)\cdot(-1)$.
+
\begin{figure}[ht!]
\centering
\includegraphics[scale=0.50]{img/Correlation.pdf}
\caption[]{Cross-correlation on three different signals}
\label{img:correlatingSignals}
\end{figure}
-The same principle applies to the sent C/A and
-PRN code sequences in the GPS receiver and thus can be modeled using
+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. Gold.} as a
+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}^{1023} G_{i}(t)G_{i}(t+\tau)d\tau
\end{equation}
-Another correlation property of the PRN codes comes in useful,
+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},
@@ -546,16 +569,18 @@ satellite towards (away from) the receiver and $c$ is the speed of light.
\label{eq:dopplerEffectSpeed}
f_{DE} = f_{e}\frac{v_{SV}}{c}
\end{equation}
-Inserting the appropriate values in equation \eqref{eq:dopplerEffectSpeed}
+By inserting the appropriate values in equation \eqref{eq:dopplerEffectSpeed}
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 range of $\approx8.4 \mathrm{kHz}$.
+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 $\approx 1.46 \mathrm{Hz}$.
+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.
+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 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
@@ -579,10 +604,11 @@ therefore there are about 20-50 bins to search ($10000\, \mathrm{Hz}/500\, \math
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.
+a greater correlation peak magnitude loss, i.e. with larger frequency bands
+it gets 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 sinc function given in equation \eqref{eq:mistunigLoss} \citep{implSoftGPSRec},
+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
@@ -625,6 +651,7 @@ in figure \ref{img:SearchSpace2d}.
\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}
@@ -634,35 +661,45 @@ in figure \ref{img:SearchSpace2d}.
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)
+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,
when some information are known and when almost all information are
-known. These three modes are known as cold (as mentioned earlier),
-warm and hot start. They differ from each other by the amount of known
+known. These three modes are known as \textit{cold} (as mentioned 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 type of start is known as a warm start,
+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}.
-In the same way works the hot start, only the ephemeris data and time data are precisely
+Hot start works the same way, only the ephemeris data and time data are precisely
known (time ought to be known in accuracy of submilliseconds).
-
+\newpage
\section{Distance and position estimation}
-In this section the focus will be on the distance and position estimation inside of the GPS receiver.
+\label{sec:distanceAndPosition}
+In this section the focus is set on distance and position estimation inside of the GPS receiver.
GPS system, as mentioned 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.
@@ -672,7 +709,7 @@ known location.
\caption[]{Basic distance estimation principle for one satellite}
\label{img:SatLocalization}
\end{figure}
-In figure \ref{img:SatLocalization}, an example concept can be seen, where $\vec{u}=(x_u,y_u,z_u)$ represents the
+In figure \ref{img:SatLocalization}, an example concept can be seen, where $\vec{u}=(x_u,y_u,z_u)$ represents the unknown
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 $\vec{s}=(x_s,y_s,z_s)$
@@ -941,6 +978,9 @@ Risks exist that the solutions will still be corrupted but there are different e
mechanisms to solve these problems, like minimizing the error contribution using more than four satellite
measurements \citep{pseudorangeError} \citep[Chapter 7]{understandGPS}.
+
+
+\newpage
\section{Assisted GPS in Wireless networks}
\label{sec:agps}
In the following paragraphs Assisted GPS (A-GPS) will be presented and how it works.