Skip to content

Commit

Permalink
SRS: Update IMs and matrices (#72)
Browse files Browse the repository at this point in the history 
* Update IMs and matrices

* Fix subscript

* Fix table line
  • Loading branch information
@adrian-soch
adrian-soch authored Apr 3, 2024
1 parent f723c48 commit 33071b0
Show file tree
Hide file tree
Showing 2 changed files with 129 additions and 64 deletions.
Binary file modified docs/SRS/SRS.pdf
View file
Binary file not shown.
193 changes: 129 additions & 64 deletions docs/SRS/SRS.tex
View file
Original file line number Diff line number Diff line change
Expand Up @@ -135,7 +135,7 @@ \section*{Revision History}
\begin{tabularx}{\textwidth}{p{3cm}p{2cm}X} \toprule {\bf Date} & {\bf Version} & {\bf Notes}\\
\midrule
2024/02/02 & 1.0 & Initial Release.\\
2024/04/01 & 2.0 & Addressed reviewer comments.\\
2024/04/03 & 2.0 & Addressed reviewer comments.\\
\bottomrule
\end{tabularx}

Expand Down Expand Up @@ -196,13 +196,13 @@ \subsection{Table of Symbols}
\midrule
% $v$ & \si[per-mode=symbol] {\meter\per\second} & linear velocity\\
$a$ & \si[per-mode=symbol] {\meter\per\second\squared} & linear acceleration\\
$m$ & \si[per-mode=symbol] {\tesla} & magnetic field strength\\
$m$ & \si[per-mode=symbol] {\micro \tesla} & magnetic field strength\\
$\theta$ & \si[per-mode=symbol] {\radian} & angular position \\
$\omega$ & \si[per-mode=symbol] {\radian\per\second} & angular velocity\\
$\Delta t$ & \si[per-mode=symbol] {\milli\second} & sampling time\\
$\mathbf{g}_0$ & \si[per-mode=symbol] {\meter\per\second\squared} & gravitational acceleration
vector\\
${}^E\mathbf{b}$ & \si{\nano\tesla} & local magnetic field vector\\
${}^E\mathbf{b}$ & \si{\micro\tesla} & local magnetic field vector\\
$\gamma$ & - & Complimentary filter parameter\\
${}^S_E\mathbf{q}$ & \si{\radian} & Attitude (orientation) of the sensor-frame relative to the
earth-frame\\
Expand Down Expand Up @@ -1343,6 +1343,64 @@ \subsubsection{Instance Models} \label{sec_instance}
\end{tabular}
\end{minipage}\\

~\newline
%Instance Model 7
\begin{minipage}{\textwidth}
\renewcommand*{\arraystretch}{1.5}
\begin{tabular}{| p{\colAwidth} | p{\colBwidth}|}
\hline
\rowcolor[gray]{0.9}
Number& IM\refstepcounter{instnum}\theinstnum \label{i:acc_to_quat}\\
\hline
Label& \bf Initial orientation from Accelerometer\\
\hline
Input& $\prescript{S}{}{\mathbf{a}}$\\
& The sensor measurements are from the current time step, and the quaternion estimate is from the
previous time step. \\
\hline
Output & $\theta = \arctan(\cfrac{a_y}{a_z})$\\
& $\phi = \arctan\left(\cfrac{-a_x}{\sqrt{a_y^2 + a_z^2}}\right)$ \\
& $\psi = 0$\\
\hline
Description& Using accelerometer data, roll and pitch Euler angles can be computed. Yaw cannot be
computed and is set to 0. \\
\hline
Sources & \url{https://ahrs.readthedocs.io/en/latest/filters/tilt.html} \\
\hline
Ref.\ By & \rref{r:input2}.\\
\hline
\end{tabular}
\end{minipage}\\

~\newline
%Instance Model 6
\begin{minipage}{\textwidth}
\renewcommand*{\arraystretch}{1.5}
\begin{tabular}{| p{\colAwidth} | p{\colBwidth}|}
\hline
\rowcolor[gray]{0.9}
Number& IM\refstepcounter{instnum}\theinstnum \label{i:mag_to_quat}\\
\hline
Label& \bf Initial orientation from Accelerometer, and Magnetometer\\
\hline
Input& $\prescript{S}{}{\mathbf{a}}, \prescript{S}{}{\mathbf{m}}$\\
& Sensor measurements.\\
\hline
Output & $\theta = \arctan(\cfrac{a_y}{a_z})$\\
& $\phi = \arctan\left(\cfrac{-a_x}{\sqrt{a_y^2 + a_z^2}}\right)$ \\
& $\psi = \mathrm{arctan2}\big(m_z\sin\phi - m_y\cos\phi, \; m_x\cos\theta +
\sin\theta(m_y\sin\phi + m_z\cos\phi)\big) $ \\
\hline
Description & Using accelerometer and magnetometer data, an initial orientation in Euler angles
can be computed. \\
\hline
Sources & \url{https://ahrs.readthedocs.io/en/latest/filters/tilt.html} \\
\hline
Ref.\ By & \rref{r:input2}.\\
\hline
\end{tabular}
\end{minipage}\\

% \subsubsection*{Derivation of ...}

\plt{The derivation shows how the IM is derived from the TMs/GDs. In cases where the derivation
Expand Down Expand Up @@ -1378,7 +1436,7 @@ \subsubsection{Input Data Constraints} \label{sec_DataConstraints}
\tesla} & See sensor datasheet. \\
$\omega$ & $-\infty < \omega < \infty$ & $|\mathbf{\omega}| \leq \omega_{\text{max}}$ & 1.0
\si[per-mode=symbol] {\radian\per\second} & See sensor datasheet. \\
$\gamma$ & - & $0.0 \leq \gamma \leq 1.0$ & 0.5 & - \\
$\gamma$ & - & $0.0 \leq \gamma \leq 1.0$ & 0.041 & - \\
\bottomrule
\end{longtable*}
\end{table}
Expand Down Expand Up @@ -1444,29 +1502,29 @@ \subsection{Functional Requirements}
that are supplied by the user. This information has to be explicit.} The user shall provide
system inputs at initialization and every time step as listed below.

\textbf{Initialization}: the sensor sampling time $\Delta t$, the local magnetic field intensity
vector, the gain parameter $\gamma$, the desired output format, and the initial orientation if
magnetometer measurements are not present.
\textbf{Initialization}: None are required. Optional parameters are: the gain parameter
$\gamma$, and the initial orientation.

\textbf{Each time step}: temporally synchronized (accelerometer, magnetometer, gyroscope)
measurements or (accelerometer, gyroscope) measurements.
measurements or (accelerometer, gyroscope) measurements, and the sensor sampling time $\Delta
t$.

Refs \iref{i:o_from_comp_acc_gyro}, \iref{i:o_from_comp_all_3}.

\item[R\refstepcounter{reqnum}\thereqnum \label{r:input2}:] If an initial orientation is not
provided \progname{} shall use the initial magnetometer measurement to produce an initial
orientation. Refs \iref{i:o_from_comp_acc_gyro}, \iref{i:o_from_comp_all_3}.
provided \progname{} shall use the initial sensor measurements to produce an initial
orientation. Refs \iref{i:acc_to_quat}, \iref{i:mag_to_quat}.

\item[R\refstepcounter{reqnum}\thereqnum \label{r:calculate1}:] \progname{} shall calculate the
orientation relative to the Earth frame when provided with accelerometer, gyroscope, and
magnetometer measurements. Refs \iref{i:o_from_comp_all_3}.

\item[R\refstepcounter{reqnum}\thereqnum \label{r:calculate2}:] \progname{} shall calculate the
yaw and pitch components of the orientation relative to the Earth frame when provided with
accelerometer and gyroscope measurements. Refs \iref{i:o_from_comp_acc_gyro}.
the orientation relative to the Earth frame when provided with accelerometer and gyroscope
measurements. Refs \iref{i:o_from_comp_acc_gyro}.

\item[R\refstepcounter{reqnum}\thereqnum \label{r:output}:] \plt{Output related requirements.}
\progname{} shall output the orientation in the user specified format. Refs
\progname{} shall output the orientation in quaternion format. Refs
\iref{i:o_from_comp_acc_gyro}, \iref{i:o_from_comp_all_3}.
\end{itemize}

Expand Down Expand Up @@ -1526,9 +1584,8 @@ \subsection{Rationale}

The scope and assumptions in this document reflect realistic assumptions for a real-world sensors
and systems. For small drones and robotics applications, the accuracy and quality of the sensors are
too low to require accounting for the rotation of the Earth.

Typical values reflect values in recreational and hobby drones and robots.
too low to require accounting for the rotation of the Earth. Typical values reflect values in
recreational and hobby drones and robots.

\plt{Provide a rationale for the decisions made in the documentation. Rationale should be provided
for scope decisions, modelling decisions, assumptions and typical values.}
Expand All @@ -1538,10 +1595,11 @@ \section{Likely Changes} \label{sec:likely_changes}
\begin{itemize}
% \item[LC\refstepcounter{lcnum}\thelcnum\label{lc:list}:] Add functionality to process a list
% of sequential measurements and output a list of orientations instead of one at a time.
\item[LC\refstepcounter{lcnum}\thelcnum\label{lc:gyro}:] Add online gyroscope bias compensation.
This removes \aref{a:gyro}.
\item[LC\refstepcounter{lcnum}\thelcnum\label{lc:mag}:] Add magnetic disturbance compensation.
This removes \aref{a:mag}.
\item[LC\refstepcounter{lcnum}\thelcnum\label{lc:acc}:] Detect significant linear accerleration,
and ignore accelerometer measurements during large accerleration events. This removes
\aref{a:static}.
\item[LC\refstepcounter{lcnum}\thelcnum\label{lc:mag}:] Detect siginifiacnt magnetic disturbance
and ignore magnetmeter measurements. This removes \aref{a:mag}.
\end{itemize}

\section{Unlikely Changes} \label{sec:unlikely_changes}
Expand Down Expand Up @@ -1578,23 +1636,25 @@ \section{Traceability Matrices and Graphs} \label{sec:trace}
&\aref{a:east_mag}&\aref{a:rotation}&\aref{a:nonlinear}&\aref{a:bandwidth}&\aref{a:gsense}&\aref{a:quant}&\aref{a:range}&\aref{a:gyro}&\aref{a:mag}
&\aref{a:rigid}& \aref{a:static} \\
\hline
\tref{TM:SMM} & & & & X& X& & X& X& & & & \\ \hline
\tref{TM:AV} & & & & & & & & & & & X& \\ \hline
\tref{TM:RK} & & & & & & & & & & & X&X \\ \hline
\tref{TM:SMM} & & & &X&X& &X&X& & & & \\ \hline
\tref{TM:AV} & & & & & & & & & & &X& \\ \hline
\tref{TM:RK} & & & & & & & & & & &X&X\\ \hline
\tref{TM:LA} & & & & & & & & & & & & \\ \hline
\tref{TM:CF} & & & & & & & & & & & & \\ \hline
\tref{TM:OFV} & & & & & & & & & & & & \\ \hline
\dref{gd:q} & & & & & & & & & & & X& \\ \hline
\ddref{dd:acc} & & & & X& X& X& X& X& & & & \\ \hline
\ddref{dd:gyro} & & & X& X& X& & X& X& X& & & \\ \hline
\ddref{dd:mag} & & & & X& X& & X& X& & X& & \\ \hline
\iref{i:o_from_gyro} & & & X& X& X& & X& X& X& & X&X \\ \hline
\iref{i:o_from_min_acc} & X& & & X& X& X& X& X& & & &X \\ \hline
\iref{i:o_from_min_acc_mag} & X& X& & X& X& X& X& X& & X& &X \\ \hline
\iref{i:o_from_comp_acc_gyro}&X& & X& X& X& X& X& X& X& & X&X \\ \hline
\iref{i:o_from_comp_all_3} & X& X& X& X& X& X& X& X& X& X& X&X \\ \hline
\lcref{lc:gyro} & & & & & & & & & X& & & \\ \hline
\lcref{lc:mag} & & & & & & & & & & X& & \\ \hline
\dref{gd:q} & & & & & & & & & & &X& \\ \hline
\ddref{dd:acc} & & & &X&X&X&X&X& & & & \\ \hline
\ddref{dd:gyro} & & &X&X&X& &X&X&X& & & \\ \hline
\ddref{dd:mag} & & & &X&X& &X&X& &X& & \\ \hline
\iref{i:o_from_gyro} & & &X&X&X& &X&X&X& &X&X\\ \hline
\iref{i:o_from_min_acc} &X& & &X&X&X&X&X& & & &X\\ \hline
\iref{i:o_from_min_acc_mag} &X&X& &X&X&X&X&X& &X& &X\\ \hline
\iref{i:o_from_comp_acc_gyro}&X& &X&X&X&X&X&X&X& &X&X\\ \hline
\iref{i:o_from_comp_all_3} &X&X&X&X&X&X&X&X&X&X&X&X \\ \hline
\iref{i:acc_to_quat} &X& & & &X&X& &X& & &X&X\\ \hline
\iref{i:mag_to_quat} &X&X& & &X&X& &X& &X&X&X\\ \hline
\lcref{lc:acc} & & & & & & & & & & & &X\\ \hline
\lcref{lc:mag} & & & & & & & & & &X& & \\ \hline
\end{tabular}
\caption{Traceability Matrix Showing the Connections Between Assumptions and Other Items}
\label{Table:A_trace}
Expand All @@ -1605,27 +1665,29 @@ \section{Traceability Matrices and Graphs} \label{sec:trace}
\begin{landscape}
\begin{table}[h!]
\centering
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
& \tref{TM:SMM} &\tref{TM:AV} &\tref{TM:RK} &\tref{TM:LA} &\tref{TM:CF} &\tref{TM:OFV}
&\dref{gd:q} &\ddref{dd:acc}&\ddref{dd:gyro}&\ddref{dd:mag}&\iref{i:o_from_gyro}
&\iref{i:o_from_min_acc} &\iref{i:o_from_min_acc_mag} &\iref{i:o_from_comp_acc_gyro}
&\iref{i:o_from_comp_all_3} \\ \hline
\tref{TM:SMM} & & & & & & & & & & & & & & & \\ \hline
\tref{TM:AV} & & & & & & & & & & & & & & & \\ \hline
\tref{TM:RK} & &X& & & & & & & & & & & & & \\ \hline
\tref{TM:LA} & & & & & & & & & & & & & & & \\ \hline
\tref{TM:CF} & & & & & & & & & & & & & & & \\ \hline
\tref{TM:OFV} & & & & & & & & & & & & & & & \\ \hline
\dref{gd:q} & &X& & & & & & & & & & & & & \\ \hline
\ddref{dd:acc} &X& & &X& & & & & & & & & & & \\ \hline
\ddref{dd:gyro} &X&X& & & & & & & & & & & & & \\ \hline
\ddref{dd:mag} &X& & & & & & & & & & & & & & \\ \hline
\iref{i:o_from_gyro} &X&X&X& & & &X& & & & & & & & \\ \hline
\iref{i:o_from_min_acc} &X& & &X& &X& &X& & & & & & & \\ \hline
\iref{i:o_from_min_acc_mag} &X& & &X& &X& & & &X& & & & & \\ \hline
\iref{i:o_from_comp_acc_gyro} &X&X&X&X&X&X&X&X&X& &X&X& & & \\ \hline
\iref{i:o_from_comp_all_3} &X&X&X&X&X&X&X&X&X&X&X& &X& & \\ \hline
&\iref{i:o_from_comp_all_3} & \iref{i:acc_to_quat} & \iref{i:mag_to_quat}\\ \hline
\tref{TM:SMM} & & & & & & & & & & & & & & & & & \\ \hline
\tref{TM:AV} & & & & & & & & & & & & & & & & & \\ \hline
\tref{TM:RK} & &X& & & & & & & & & & & & & & & \\ \hline
\tref{TM:LA} & & & & & & & & & & & & & & & & & \\ \hline
\tref{TM:CF} & & & & & & & & & & & & & & & & & \\ \hline
\tref{TM:OFV} & & & & & & & & & & & & & & & & & \\ \hline
\dref{gd:q} & &X& & & & & & & & & & & & & & & \\ \hline
\ddref{dd:acc} &X& & &X& & & & & & & & & & & & & \\ \hline
\ddref{dd:gyro} &X&X& & & & & & & & & & & & & & & \\ \hline
\ddref{dd:mag} &X& & & & & & & & & & & & & & & & \\ \hline
\iref{i:o_from_gyro} &X&X&X& & & &X& & & & & & & & & & \\ \hline
\iref{i:o_from_min_acc} &X& & &X& &X& &X& & & & & & & & & \\ \hline
\iref{i:o_from_min_acc_mag} &X& & &X& &X& & & &X& & & & & & & \\ \hline
\iref{i:o_from_comp_acc_gyro} &X&X&X&X&X&X&X&X&X& &X&X& & & & & \\ \hline
\iref{i:o_from_comp_all_3} &X&X&X&X&X&X&X&X&X&X&X& &X& & & & \\ \hline
\iref{i:acc_to_quat} &X& & &X& & & &X& & & & & & & & & \\ \hline
\iref{i:mag_to_quat} &X& & &X& & & &X& &X& & & & & & & \\ \hline
\end{tabular}
\caption{Traceability Matrix Showing the Connections Between Items of Different Sections}
\label{Table:trace}
Expand All @@ -1635,22 +1697,25 @@ \section{Traceability Matrices and Graphs} \label{sec:trace}

\begin{table}[h!]
\centering
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|}
\begin{tabular}{|c|c|c|c|c|c|c|c|c|c|c|c|c|}
\hline
&\iref{i:o_from_gyro} &\iref{i:o_from_min_acc} &\iref{i:o_from_min_acc_mag}
&\iref{i:o_from_comp_acc_gyro} &\iref{i:o_from_comp_all_3} & \rref{r:inputs} & \rref{r:input2} &
\rref{r:calculate1} & \rref{r:calculate2}& \rref{r:output} \\
&\iref{i:o_from_comp_acc_gyro} &\iref{i:o_from_comp_all_3} & \iref{i:acc_to_quat} &
\iref{i:mag_to_quat} & \rref{r:inputs} & \rref{r:input2} & \rref{r:calculate1} &
\rref{r:calculate2}& \rref{r:output} \\
\hline
\iref{i:o_from_gyro} & & & & & & & & & &\\ \hline
\iref{i:o_from_min_acc} & & & & & & & & & &\\ \hline
\iref{i:o_from_min_acc_mag} & & & & & & & & & &\\ \hline
\iref{i:o_from_comp_acc_gyro}& & & & & &X&X& &X&\\ \hline
\iref{i:o_from_comp_all_3} & & & & & &X&X&X& &\\ \hline
\rref{r:inputs} & & & & & & & & & &\\ \hline
\rref{r:input2} & & & & & & & & & &\\ \hline
\rref{r:calculate1} & & & & & & & & & &\\ \hline
\rref{r:calculate2} & & & & & & & & & &\\ \hline
\rref{r:output} & & & & & & & & & &\\ \hline
\iref{i:o_from_gyro} & & & & & & & & & & & &\\ \hline
\iref{i:o_from_min_acc} & & & & & & & & & & & &\\ \hline
\iref{i:o_from_min_acc_mag} & & & & & & & & & & & &X\\ \hline
\iref{i:o_from_comp_acc_gyro}& & & & & & & &X& & &X&X\\ \hline
\iref{i:o_from_comp_all_3} & & & & & & & &X& &X& &\\ \hline
\iref{i:acc_to_quat} & & & & & & & & &X& & &\\ \hline
\iref{i:mag_to_quat} & & & & & & & & &X& & &\\ \hline
\rref{r:inputs} & & & & & & & & & & & &\\ \hline
\rref{r:input2} & & & & & & & & & & & &\\ \hline
\rref{r:calculate1} & & & & & & & & & & & &\\ \hline
\rref{r:calculate2} & & & & & & & & & & & &\\ \hline
\rref{r:output} & & & & & & & & & & & &\\ \hline
\end{tabular}
\caption{Traceability Matrix Showing the Connections Between Requirements and Instance Models}
\label{Table:R_trace}
Expand Down

0 comments on commit 33071b0

Please sign in to comment.