@@ -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

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