Commit 95dfb396 authored by Claudio Mandrioli's avatar Claudio Mandrioli
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camera ready version 4

parent dd9742b6
......@@ -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
......
......@@ -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
......
......@@ -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
......
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