diff --git a/paper/main.tex b/paper/main.tex index a996547e2120d148adb9b00b09c504ff5fd3a149..b24ad4e96ffd1092548c3bfab961d8f651fdf23b 100644 --- a/paper/main.tex +++ b/paper/main.tex @@ -160,7 +160,7 @@ Abstract. \label{sec:fusion} \input{sections/04-fusion} -\section{Control Strategy} +\section{Analysis and Sampling Strategy} \label{sec:control} \input{sections/05-control} diff --git a/paper/sections/04-fusion.tex b/paper/sections/04-fusion.tex index 8b5a9d49ea53afb7518703ab8112d7713b7fb5e8..f1963a208500f7125edf3715187aab784e803d66 100644 --- a/paper/sections/04-fusion.tex +++ b/paper/sections/04-fusion.tex @@ -61,11 +61,11 @@ the angular rates are provided along the three axis, i.e., $s(k) \in \mathbb{R}^3 [m/s^2]$, and $\omega(k)\in \mathbb{R}^3 [rad/s]$. Equation~\eqref{eq:integration} shows the integration of the IMU measurements $s$ and $\omega$ to -obtain $p$, $v$, and $q$. In the equation, $T_s$ represents -\todo{write me}, $R_b^n$ denotes the directional cosine matrix that +obtain $p$, $v$, and $q$. In the equation, $T_s$ represents the IMU +sampling time, $R_b^n$ denotes the directional cosine matrix that rotates a vector from the body coordinate frame $b$ to the body -coordinate frame $n$ and $g$ is the gravitational force, $I_4$ is -\todo{write me}, +coordinate frame $n$ and $g$ is the gravitational force, $I_{4}$ is +the identity matrix of order 4, \begin{equation} \begin{array}{rcl} diff --git a/paper/sections/05-control.tex b/paper/sections/05-control.tex index d5736ad37fa038f00e675434af903900af117c99..a0baa38932e47ec9da21cecbfdb2441fe81eaaf9 100644 --- a/paper/sections/05-control.tex +++ b/paper/sections/05-control.tex @@ -1,13 +1,3 @@ -%\begin{itemize} -%\item Title: Analysis and sampling strategy -%\item what are the limits that the sensor dynamics poses. (i)initial delay, (ii) delay when position is requested unless always on, (iii) periodical drain of battery for updating ephemeris data, (iv) you can se you have lost visibility only if you are turned on ,(v) the best you can do is turn off the antenna (for this reaosn as soon as we get the position we assume you want to turn off the antenna) -%\item what are the phenomena we have to account for in regular ``working'' conditions. cycling on two different periods. plot of how this looks like? -%\item what are the possible disturbances we have to deal with. expiration of ephemeris data and loss of visibility. the latter is not observable when the antenna is turned off. examples? -%\item how do we do this? state machine of the controller`/ref{fig:controller}. three kind of transitions: some are observed events, some are control actions, some are both -%\end{itemize} - -\textcolor{red}{Title: Analysis and sampling strategy} - Given the sensor fusion algorithm and the sensor model we can now describe which dynamical limitations the sensor imposes and therefore how it can be sampled. 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. \subsection{The dynamics} @@ -50,7 +40,7 @@ font=\footnotesize] \draw [arr] (ni) to node [above] {\texttt{turn\_on}} (re); %arrow from 2 \draw [arr] (re) to node [below] {\texttt{get\_ephemeris}} (gp); -\draw [arr, loop below] (re) to node [left ] {\texttt{sensor in position\_available}} (re); +\draw [arr, loop below] (re) to node [right] {\texttt{sensor in position\_available}} (re); %arrows from 3 \draw [arr, bend left] (gp) to node [below] {\texttt{sensor in position\_available -- turn\_off}} (wst); \draw [arr, bend right] (gp) to node [above] {\texttt{ephemeris\_about\_to\_expire V lost\_visibility}} (re);