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\subsubsection{Boolean State-Based Metrics}

The following states all take on Boolean values. They are based on the
direct raw metrics with a threshold applied. They are

\begin{packed_enumerate}
\item {\em on tail}: Ownship is on tail if the tail range is less
  than twice the inter-mark range.
\item {\em aligned}: Ownship is aligned if the alignment is less than
  a configured threshold, by default 30 degrees.

\vspace{0.1in}
\begin{figure}[H]
  \centering
  \includegraphics[width=0.95\textwidth]{figs_bhv_convoy/bhv_convoy_alignment.png}
  \caption{{\bf Alignment}: Alignment is based both on the marker bearing and the
    tail angle. Ownship is aligned if the sum of the two values is less than
    a defined threshold. On the left ownship is aligned even though the marker
    bearing or tail angle is zero. On the right, neither vehicle is aligned. Vehicle
    one, with marker bearing of zero, is mis-aligned due to a high tail angle.
    Vehicle two, with tail angle of zero, is mis-aligned due to a high marker
    bearing.}
  \label{fig_bhv_convoy_alignment}
\end{figure}
\vspace{0.1in}

\item {\em tethered}: Ownship is tethered if it is both aligned and on tail.
  See Figure \ref{fig_bhv_convoy_states}.

\item {\em ideally tethered}: Ownship is ideally tethered if it is tethered and
  the convoy range is in the ideal range between the configuration parameters
  \bvar{faster\_convoy\_range} and \bvar{slower\_convoy\_range}.
  See Figure \ref{fig_bhv_convoy_states}.
  
\end{packed_enumerate}

\vspace{0.1in}
\begin{figure}[H]
  \centering
  \includegraphics[width=0.8\textwidth]{figs_bhv_convoy/bhv_convoy_states.png}
  \caption{{\bf Metric States}: The Convoy behavior maintains three
    state variables for supporting performance metrics. A following
    vehicle is {\em on tail} if it is sufficiently close to the aft
    marker (shown in red). It is {\em aligned} if sufficiently aligned
    with the aft marker and near-aft marker. It is {\em tethered} if
    it is both on tail and aligned. It is {\em ideally tethered} if it
    is both tethered and sufficiently close to the ideal convoy
    range.}
  \label{fig_bhv_convoy_states}
\end{figure}

%-----------------------------------------------------------------------
\subsubsection{Time Series Metrics}

The time series metrics use the Boolean state-based metrics and
measure either (a) the time required to achieve a given state after a
given point in time, or (b) the percentage of time ownship is in a
given state after a given point in time. The given point in time may
be an event such as initial behavior activation, which may coincide
with a command to the group to form a convoy.  It may also be an event
such as a command to re-order the convoy.

\vspace{0.1in}
\noindent
Time Series Metrics:

\begin{packed_enumerate}
\item {\em on tail interval}: Time required to achieve the on tail
  state from a given time of event.
\item {\em aligned interval}: Time required to achieve the aligned
  state from a given time of event, and given alignment threshold.
\item {\em tethered interval}: Time required to achieve the tethered
  state from a given time of event, and given alignment threshold.
\item {\em ideal tethered interval}: Time required to achieve the
  ideal tethered state from a given time of event, and given alignment
  threshold.
\item {\em on tail rate}: Perctage of time the on tail state is
  achieved starting from a given time of event.
\item {\em aligned rate}: Percentage of time time the aligned
  state is achieved starting from a given time of event, and given
  alignment threshold.
\item {\em tethered rate}: Percentage of time the tethered state is
  achieved starting from a given time of event, and given alignment
  threshold.
\item {\em ideal tethered rate}: Percentage of time the ideal tethered
  state is achieved starting from a given time of event, and given
  alignment threshold.
\end{packed_enumerate}

%-----------------------------------------------------------------------
\subsubsection{Odometry Metrics}

The odometry metrics also use the Boolean state-based metrics and
measure the odometry distance required to achieve a given state after
a given event time. The given event time may be the time of initial
behavior activation, which may coincide with a command to the group to
form a convoy.  It may also be an event such as a command to re-order
the convoy.

\vspace{0.1in}
\noindent
Time Series Metrics:

\begin{packed_enumerate}
\item {\em on tail distance}: Odometry distance required to achieve
  the on tail state from a given time of event.
\item {\em aligned distance}: Odometry distance required to achieve
  the aligned state from a given time of event, and given alignment
  threshold.
\item {\em tethered distance}: Odometry distance required to achieve
  the tethered state from a given time of event, and given alignment
  threshold.
\item {\em ideal tethered distance}: Odometry distance required to
  achieve the ideal tethered state from a given time of event, and
  given alignment threshold.
\end{packed_enumerate}



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