From 95dfb396c235b5f3e0bededf64a84ac6d4e3031e Mon Sep 17 00:00:00 2001
From: Claudio <claudio.mandrioli@control.lth.se>
Date: Mon, 11 Feb 2019 16:40:45 +0100
Subject: [PATCH] camera ready version 4

---
 paper/sections/01-intro.tex   | 12 +++++++---
 paper/sections/03-model.tex   | 44 ++++++++++++++++++++---------------
 paper/sections/06-results.tex |  6 +++--
 3 files changed, 38 insertions(+), 24 deletions(-)

diff --git a/paper/sections/01-intro.tex b/paper/sections/01-intro.tex
index 76a7acb..4792fbe 100644
--- a/paper/sections/01-intro.tex
+++ b/paper/sections/01-intro.tex
@@ -15,7 +15,7 @@ sensor benefits and to limit their drawbacks.
 One alternative is merging data from GPS sensors with data provided by
 inertial measurements sensors~\cite{bib:gps-imu}. While the GPS is
 power-hungry but provides very precise information, inertial
-measurements sensors are less demanding in terms of battery, but also
+measurements sensors are less energy-demanding, but also
 less precise. In the literature, optimizations of this type are
 accompanied by experimental data~\cite{bib:microsoft-leap,
   bib:enloc-smartphones, bib:virtualGPS, bib:accuracy-adaptation,
@@ -49,7 +49,7 @@ basic limitations and characteristics of the technology. In this
 specific context, we highlight how a dynamical model is necessary to
 capture the involved \emph{phenomena}. In fact, GPS sensors that
 receive the same \emph{stimula} can behave differently, depending on
-the sensor's internal state.
+their internal state.
 \item \textbf{Design:} It identifies opportunities for battery
 savings. Specifically, modeling the GPS-related \emph{phenomena}
 allows us to devise a sampling strategy that exploits the technology
@@ -61,7 +61,13 @@ merging algorithms) programmatically and to expose the characteristics
 of each solution.
 \end{itemize}
 
-\textcolor{red}{Even though the notions used to build the presented model are known in the litterature, their systematic study and integration has not been seen elsewhere by the authors. The development of this first-principle and simulable model enables the possiblity of (i) performing at design phase a quantitative evaluaion of the energy cost of different sampling strategies, (ii) comparing different sampling strategies without depending on the specific testing conditions.}
+Even though the notions used to build the presented model are known in
+the litterature, their systematic study and integration has not been 
+seen elsewhere by the authors. The development of this first-principle 
+and simulable model enables the possiblity of (i) performing at design 
+phase a quantitative evaluaion of the energy cost of different sampling 
+strategies, (ii) comparing different sampling strategies without 
+depending on the specific testing conditions.
 
 %
 This paper is organized as follows. As much research has been done on
diff --git a/paper/sections/03-model.tex b/paper/sections/03-model.tex
index 69211ef..3ea4838 100644
--- a/paper/sections/03-model.tex
+++ b/paper/sections/03-model.tex
@@ -51,26 +51,20 @@ called \emph{ephemeris data}. The ephemeris data describe the
 satellites' orbits (see for example the trajectory of satellite $s_3$
 in Figure~\ref{fig:globe}), and therefore allow the GPS receiver to
 accurately determine their position in time. The satellite
-trajectories are not constant in time, due to uncertainties and
+trajectories change over time, due to uncertainties and
 disturbances, like corrections for collision avoidance.
 
-The hypothesis that the clocks of the receiver and the satellites are
-synchronized is not valid, so one extra satellite must be tracked and
-used for the trilateration procedure. The fourth satellite allows the
-receiver to compensate its time reference offset.
-
-The ephemeris data expire after 30 minutes, i.e., after 30 minutes
-they are not considered valid anymore. To correctly estimate the
-current position, the receiver should ensure that the ephemeris data
-are frequently updated. The transmission of the ephemeris data has a
-duration of 30 seconds, and the satellites continuously broadcast new
-data. In order to ensure the correct acquisition of one data point,
-the receiver then has to fetch and decode the signal for a time that
-is in the interval $[30,60)$ seconds (in the worst case, the receiver
-starts reading the message right after the start of a new message
-transmission).
-
-All the satellites transmit on the same frequency and then the
+The ephemeris data are considered valid for a time span of 30 
+minutes. To correctly estimate the current position, the receiver 
+should ensure that the ephemeris data are up to date. The 
+transmission of the ephemeris data has a duration of 30 seconds, 
+and the satellites continuously broadcast new data. In order to ensure 
+the correct acquisition of one data point, the receiver then has to 
+fetch and decode the signal for a time that is in the interval 
+$[30,60)$ seconds (in the worst case, the receiver starts reading the 
+message right after the start of a new message transmission).
+
+All the satellites transmit on the same frequency and the
 different signals are multiplexed using the Code Division Multiple
 Access (CDMA) technique. Using CDMA, the signal has three components:
 (i) the carrier wave, (ii) the data waveform, and (iii) a spreading
@@ -95,6 +89,11 @@ can be written as $d_{x} = \Delta_{x} \cdot C$. The set of the
 distances the receiver measures from the visible satellites is called
 \emph{ranging data}.
 
+The hypothesis that the clocks of the receiver and the satellites are
+synchronized is not valid, so one extra satellite must be tracked and
+used for the trilateration procedure. The fourth satellite allows the
+receiver to compensate its time reference offset.
+
 Due to the satellites' and the receiver's movements, the doppler
 effect will distort the signal reception. The effect is a shift in the
 frequency spectrum of the signal. To fetch the signal, the receiver
@@ -205,7 +204,14 @@ font=\footnotesize]
 The GPS receiver provides a position estimate when it has collected
 both the ephemeris and the ranging data for at least 4 satellites.
 Detecting data from more than 4 satellites can improve the positioning
-accuracy. \textcolor{red}{This depents on many factors which are hard to model, like the relative position of the stellites in sapce and the geography of the environment around the sensor. Therefore, for the sake of keeping the model at a reasonable complexity, it is only required to set a minimum number of satellites to be tracked, depending on the specific application. This number has to be equal to or greater than 4 and it being higher represents the the constraint of higher accuracy in the given application.} As for power consumption, the receiver always consumes a
+accuracy. This depents on many factors which are hard to model, like the 
+relative position of the stellites in sapce and the geography of the 
+environment around the sensor. Therefore, for the sake of keeping the 
+model at a reasonable complexity, it is only required to set a minimum 
+number of satellites to be tracked, depending on the specific application. 
+This number has to be equal to or greater than 4 and it being higher 
+represents the the constraint of higher accuracy in the given application. 
+As for power consumption, the receiver always consumes a
 (negligible) idle power. On top of that, the sensor consumes
 additional power when its radio is turned on, which is precisely the
 cause of battery draining. This power has been experimentally shown to
diff --git a/paper/sections/06-results.tex b/paper/sections/06-results.tex
index 1b07cff..b1d8574 100644
--- a/paper/sections/06-results.tex
+++ b/paper/sections/06-results.tex
@@ -35,7 +35,7 @@ implementations\footnote{The code for both the implementation will be
   released in case the paper is accepted.}. The first one is written
 in Modelica\footnote{http://www.modelica.org}, while the second one is
 written in
-Matlab\footnote{http://www.mathworks.com/products/matlab.html}.
+Matlab\footnote{http://www.mathworks.com/products/matlab.html}\footnote{The code and the data used for the simulations are available at: https://gitlab.control.lth.se/mmaggio/gps-modeling/}.
 
 The purpose of the Modelica code is to obtain a powerful simulation
 tool. The nature of Modelica -- in terms of composability and
@@ -368,7 +368,9 @@ show what the tracking would have been when the sensor fusion
 algorithm was live, compared to the continuous sampling of the GPS. We
 then use simulations to further analyze the trade-off between power
 (and therefore battery) consumption and performance (positioning
-accuracy). \textcolor{red}{The sampling rate of the used traces is $1Hz$ but the localization information is of course made available only when the model is in the correct state.}
+accuracy). The sampling rate of the used traces is $1Hz$ but the 
+localization information is of course made available only when the 
+model is in the correct state.
 
 Figures~\ref{fig:cycling-trace} and~\ref{fig:car-trace} respectively
 show traces for the tracking of the bike and the car. In each
-- 
GitLab