table.margcond.onecolumn.tex

这是移动机器人同时定位与地图创建的第三部分

% table.margcond.tex
%-----------------------------------------------------------------
%    History:
%    Date            Who         What
%    -----------     -------     -----------------------------
%    01-11-2005      rme         Created from icra05 paper.
%    01-11-2005      rme         Added \hfil to achieve centering.
%    08-18-2005      mrw         Modified for single-column documents
%                                and moved p(\alpha,\beta) into table

% TABLE: Marginalization & Conditioning
%------------------------------------------------------
\begin{table}[h]
  \begin{center}
  % increase table row spacing, adjust to taste
  \renewcommand{\arraystretch}{1.75}
  \caption{Summary of Marginalization and Conditioning Operations on a Gaussian
    Distribution Expressed in Covariance and Information Form} \label{tab:margcond}
  %\begin{minipage} {0.5\textwidth}
  %% The array package and the MDW tools package offers better commands
  %% for making tables than plain LaTeX2e's tabular which is used here.
  %\bigskip
    %\mbox{$
    %  \pdf{\bvec{\alpha},\bvec{\beta}}
    %  =\normalcov
    %  { \Bigl[
    %    \begin{smallmatrix} \bvec{\mu}_\alpha \\ \bvec{\mu}_\beta \end{smallmatrix}
    %    \Bigr]
    %  }
    %  { \Bigl[
    %    \begin{smallmatrix}
    %      \mat{\Sigma}_{\alpha\alpha} & \mat{\Sigma}_{\alpha\beta} \\
    %      \mat{\Sigma}_{\beta\alpha} & \mat{\Sigma}_{\beta\beta} 
    %    \end{smallmatrix}
    %    \Bigr]
    %  }
    %  =\normalinfo
    %  { \Bigl[
    %    \begin{smallmatrix} \bvec{\eta}_\alpha \\ \bvec{\eta}_\beta \end{smallmatrix}
    %    \Bigr]
    %  }
    %  { \Bigl[
    %    \begin{smallmatrix}
    %      \mat{\Lambda}_{\alpha\alpha} & \mat{\Lambda}_{\alpha\beta} \\
    %      \mat{\Lambda}_{\beta\alpha} & \mat{\Lambda}_{\beta\beta} 
    %    \end{smallmatrix}
    %    \Bigr]
    %  }
    %$}\\
    \centering
    \begin{tabular}{l|l|l|}
      \multicolumn{3}{c}{$
      \pdf{\bvec{\alpha},\bvec{\beta}}
      =\normalcov
      { \Bigl[
        \begin{smallmatrix} \bvec{\mu}_\alpha \\ \bvec{\mu}_\beta \end{smallmatrix}
        \Bigr]
      }
      { \Bigl[
        \begin{smallmatrix}
          \mat{\Sigma}_{\alpha\alpha} & \mat{\Sigma}_{\alpha\beta} \\
          \mat{\Sigma}_{\beta\alpha} & \mat{\Sigma}_{\beta\beta} 
        \end{smallmatrix}
        \Bigr]
      }
      =\normalinfo
      { \Bigl[
        \begin{smallmatrix} \bvec{\eta}_\alpha \\ \bvec{\eta}_\beta \end{smallmatrix}
        \Bigr]
      }
      { \Bigl[
        \begin{smallmatrix}
          \mat{\Lambda}_{\alpha\alpha} & \mat{\Lambda}_{\alpha\beta} \\
          \mat{\Lambda}_{\beta\alpha} & \mat{\Lambda}_{\beta\beta} 
        \end{smallmatrix}
        \Bigr]
      }
    $} \\

        % row 1
        & 
        \hfil\textsc{Marginalization} & \hfil\textsc{Conditioning} \\
        % row 2
        & 
        \hfil\mbox{$\pdf{\bvec{\alpha}}=\int\pdf{\bvec{\alpha},\bvec{\beta}}d\bvec{\beta}$} &
	\hfil\mbox{$\pdf[\bvec{\alpha}]{\bvec{\beta}}=
	  \pdf{\bvec{\alpha},\bvec{\beta}}/\pdf{\bvec{\beta}}$} \\
        \hline
        % row 3
        \multirow{2}{1.0in}{\textsc{Covariance Form}} & 
        \mbox{$\bvec{\mu}=\bvec{\mu}_\alpha$} &
        \mbox{$\bvec{\mu}'=\bvec{\mu}_\alpha +
          \mat{\Sigma}_{\alpha\beta} \mat{\Sigma}_{\beta\beta}^{-1}
          (\bvec{\beta}-\bvec{\mu}_\beta)$} \\
        % row 4
        & 
        \mbox{$\mat{\Sigma}=\mat{\Sigma}_{\alpha\alpha}$} &
        \mbox{$\mat{\Sigma}'=\mat{\Sigma}_{\alpha\alpha} -
          \mat{\Sigma}_{\alpha\beta} \mat{\Sigma}_{\beta\beta}^{-1}
          \mat{\Sigma}_{\beta\alpha}$} \\
        \hline
        % row 5
        \multirow{2}{1.0in}{\textsc{Information Form}} &
        \mbox{$\bvec{\eta}=\bvec{\eta}_\alpha -
          \mat{\Lambda}_{\alpha\beta} \mat{\Lambda}_{\beta\beta}^{-1}
          \bvec{\eta}_\beta$} &
        \mbox{$\bvec{\eta}'=\bvec{\eta}_\alpha-\mat{\Lambda}_{\alpha\beta}\bvec{\beta}$} \\
        % row 6
        & 
        \mbox{$\mat{\Lambda}=\mat{\Lambda}_{\alpha\alpha} -
          \mat{\Lambda}_{\alpha\beta} \mat{\Lambda}_{\beta\beta}^{-1} 
          \mat{\Lambda}_{\beta\alpha}$} &
        \mbox{$\mat{\Lambda}'=\mat{\Lambda}_{\alpha\alpha}$} \\
        \hline
      \end{tabular}
  %\end{minipage}
\end{center}
\end{table}