diff --git a/paper/sections/04-fusion.tex b/paper/sections/04-fusion.tex
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 \end{itemize}
 
 
-It is now discussed an implementation of the presented model. We will use to discuss some of the different types of analysis that can be done with this abstarction an implementation of GPS-IMU sensor fusion. Sensor fusion is the technique of merging the measurements that come from different sensors. If well made, it enhances the advantages of the different sensors while compensating for the disadvantages.
+It is now discussed one possible implementation and use of the presented model. We will use it to discuss some of the different analysis that can be done with this abstarction. The chosen case study is an implementation of \emph{GPS-IMU sensor fusion}. Sensor fusion is a technique for merging the measurements that come from different sensors. It can enhance the advantages of the different sensors while compensating for the disadvantages.
 
-Inertial measurement units (IMUs) are sensors that measure accelerations and angular velocities of the device. Such sensors are usually carachterized by relatively low power consumption \todo{find reference}, providing relative measurements and continuous availability.
+Inertial measurement units (IMUs) are sensors that usually include one accelerometer and a gyroscope. The former measures the accelerations along the three axis while the latter measures the angular velocities. This kind of sensors can be considered in some sense complementary to the GPS. First they provide a relative measurement (while the position estimaiton of the GPS is absolute). Secondly they are characterized by low power consumption (\todo{quantify and reference this}), since they dont have to rely on any external device providing a reference no antenna for communication must be powered. Third, for the same reason, they are continuously available, not having to rely on any external device that provides a reference.
 
+The main drawback of those sensors is that, given the relative nature of the provided measurement, the ouput must be integrated. This exposes the estimation to low frequency errors introduced by the biases. By rule of thumb, those are usually considered to be growing cubically in time. For this reason inertial sensor are considered only reliable on a short time scale. The idea of GPS-IMU sensor fusion is to use the inertial sensor unit to provide continuous and low-power positioning, while the GPS, being sampled at a lower rate can compensate and not affected by biases can compensate for the low frequency erors.
 
+In this framework the presented model can capture the delays in the position measure of the GPS and its power consumption. This allows rigorous study on what is the optimal sampling method for the GPS sensor.