diff --git a/paper/sections/04-fusion.tex b/paper/sections/04-fusion.tex
index dcb1d2bd279a2356b2a026620ce0414e7ddc2664..4362c77fa6168c25109204b35ec1804d9fc241a4 100644
--- a/paper/sections/04-fusion.tex
+++ b/paper/sections/04-fusion.tex
@@ -159,7 +159,7 @@ therefore need to estimate the following quantities: the position
 error $\delta x(k)$ (used to correct the position estimation) and the
 biases of the sensors $\delta u(k)$ (to compensate the estimate
 obtained using Equation~\eqref{eq:integration} for future
-measurements).
+measurements),
 \begin{equation}
 \delta x(k) = x(k) - \hat{x}(k) = 
 \begin{bmatrix}
diff --git a/paper/sections/05-control.tex b/paper/sections/05-control.tex
index 0316362ffe89f0fc48edd2aa582bd5a2be0a4811..d4a91cbb41289c6ffe449a2e6ef7f3b06795c4ba 100644
--- a/paper/sections/05-control.tex
+++ b/paper/sections/05-control.tex
@@ -1,13 +1,41 @@
-In this section we will discuss the general features that characterize an effective sampling strategy. Complementary in the next section a simulation evaluation of the available trade-offs will be performed.
+This section discusses the general features that characterize an
+effective sampling strategy and describes the one we advocate using.
 
 \subsection{The dynamics}
-The model discussed in section~\ref{sec:gps} points out two dynamics that characterize the sensor: the availability of the ephemeris data and the availability of ranging data. The two are caracterized by very different time scales, both in terms of acquisition time and validity. 
 
-The ephemeris data live in the time scale of minutes requiring betwen 30 to 59 seconds to be aquired and being valid for 30 minutes. This poses two main constraints. First at the startup a delay equivalent to the acquisition time of the ephemeris data will be present -- this is the so called \emph{Time To First Fix} TTFF. Second during regular working conditions every 30 minutes the ephemeris data must be updated, requiring the antenna to be turned on for enough time and affecting the battery drain of the sensor.
-
-The ranging data are instead caracterized by a time scale of the order of milliseconds. They require from  2 to 10 milliseconds to be acquired and they have istantaneous validitiy since they are the ones used to compute the present position. This means that there is a lower bound the sampling period of the sensor under which the sampling will be equivalent to keep the sensor always turned on. Also for some applications with real time constraints the varying delay for the acquisition could be critical.
-
-Another important consequence of the sampling policy is the observability of the event \texttt{lost\_visibility}. This is in fact observable only when the antenna is on and is listening to the visible satellites. When a satellite disappears, if the antenna is turned off the device wont observe this and at the next sampling it will have to acquire new ephemeris data before being available of providing new positioning (assuming that enough satellites are visible).
+The model presented in Section~\ref{sec:gps} highlights two dynamics
+that characterize the sensor. The first one is the availability of the
+ephemeris data and the second one is the availability of ranging
+data. The two occur at very different time scales, both in terms of
+acquisition time and in terms of data validity.
+
+\textbf{Ephemeris data:} The ephemeris data live in the time scale of
+\emph{minutes}, requiring betwen 30 and 59 seconds to be aquired and
+having a validity of 30 minutes from the aquisition. There are two
+implications of these facts. First, this induces a startup delay
+equivalent to the aquisition time of the ephemeris data. This is
+referred to as \emph{Time To First Fix} (TTFF). Second, an effective
+sampling strategy refreshes the ephemeris data at least every 30
+minutes. This requires the antenna to be turned on for enough time to
+capture the data and affects the sensor battery consumption.
+
+\textbf{Ranging data:} The ranging data are caracterized by a time
+scale of the order of milliseconds. They require from 2 to 10
+milliseconds to be acquired. This could be critical for real-time
+applications. The data validitiy is instantaneous, since they are used
+as soon as they are received to compute the current position (and
+moving will invalidate them). The time scale allows us to derive a
+bound in the sensor sampling period. Sampling as frequently as the
+this (lower) bound is equivalent to keeping the sensor always on.
+
+Another important consequence of the sampling policy is the
+observability of the event \texttt{lost\_visibility}. The occurrence
+event is in fact detectable only when the antenna is turned on and the
+sensor is listening to the visible satellites. When a satellite
+disappears, if the antenna is turned off the device wont observe this
+and at the next sampling it will have to acquire new ephemeris data
+before being available of providing new positioning (assuming that
+enough satellites are visible).
 
 \subsection{Sampling Strategy}
 Given these considerations we designed a simple sampling stategy that tries to keep the ephemeris data updated and samples the GPS sensor according to the uncertainty of the state estimation of the Kalman filter. To do this we use the trace of the covariance matrix $P$ which represents the estimation variance of the position. When this quantity overcomes a defined threshold the position is requested to the sensor. This is formally encoded in the state machine represented in figure~\ref{fig:controller}.