\newcommand{\be} {\begin{eqnarray}}
\newcommand{\ee} {\end{eqnarray}}
\newcommand{\bi} {\begin{itemize}}
\newcommand{\ei} {\end{itemize}}
\newcommand{\ben} {\begin{enumerate}}
\newcommand{\een} {\end{enumerate}}
\newcommand{\bct} {\begin{center}}
\newcommand{\ect} {\end{center}}
\newcommand{\mct} {\multicolumn{2}{l}}
%\newcommand{\ur} {\ \mu\mbox{rad}}
%\newcommand{\urs} {\ur/ \mbox{sec}}
%\newcommand{\ddeg} {^\circ}
%\newcommand{\mg} {\mbox{mg}}
%\newcommand{\ugg} {\mu\mbox{g/g}^2}
%\newcommand{\sms} {\sigma^2}
%
% Math mode command defs:
%
\newcommand{\eqdef} {\stackrel{\triangle}{=}}
\newcommand{\ddeg} {^\circ}
\newcommand{\nvec} { \vec{n}}
\newcommand{\bvec} { \vec{b}}
\newcommand{\fvec} { \vec{f}}
\newcommand{\Fvec} { \vec{F}}
\newcommand{\Rvec} { \vec{R}}
\newcommand{\txvec} { $\vec{x}$}
\newcommand{\xvec} { \vec{x}}
\newcommand{\rvecnb} { \vec{r}^{\, N_{\circ}B_{\circ}}}
\newcommand{\rvecbb} { \vec{r}^{\, B_{\circ}B^{\ast}}}
\newcommand{\rvecbcb}{ \vec{r}^{\, B_{\circ}\,B_{CB}}}
\newcommand{\rvecbpl} { \vec{r}^{\, B_{\circ}P_1}}
\newcommand{\rvecbpu} { \vec{r}^{\, B_{\circ}P_2}}
\newcommand{\rvecbd} { \vec{r}^{\, B_{\circ}D^{\circ}_i}}
\newcommand{\rvecba} { \vec{r}^{\, B_{\circ}ACS^{\circ}_i}}
\newcommand{\rvecbi} { \vec{r}^{\, B_{\circ}IMU^{\circ}}}
\newcommand{\rveciimuo} { \vec{r}^{\, N^{\circ} IMU^{\circ}}}
\newcommand{\rvecioto} { \vec{r}^{\, N^{\circ}T^{\circ}}}
\newcommand{\rvecvoto} { \vec{r}^{\, B ^{\circ}T^{\circ}}}
\newcommand{\rvecbr} { \vec{r}^{\; B_{\circ} R_{\circ}}}
\newcommand{\fa}{ \vec{f}_{ACS_i}}
\newcommand{\fd}{\vec{f}_{D_i}}
\newcommand{\fas}{f_{ACS_i}}
\newcommand{\fds}{f_{D_i}}
\newcommand{\vel}  {\vec{v}}
\newcommand{\ddtn}  {\! \,^N \frac{d}{dt}}
\newcommand{\ddtb}  {\! \,^B \frac{d}{dt}}
\newcommand{\Tvec} {\vec{T}^{\, B/B_{\circ}}}
\newcommand{\quat} { {\bf q} }
\newcommand{\quatba} { {\bf q}_{B/A} }
\newcommand{\quatbe} { {\bf q}_{B/ECI} }
\newcommand{\TrnNB}{T_{N/B}}
%\newcommand{\TrnBA}{T_{B/ACS_i}}
\newcommand{\TrnBA}{T_{B/A}}
\newcommand{\TrnBD}{T_{B/D_i}}
\newcommand{\ur} {\ \mu\mbox{rad}}        %micro-radians
\newcommand{\urs} {\ur/ \mbox{sec}}       %micro-radians per sec
\newcommand{\mg} {\mbox{mg}}              %milli-gees
\newcommand{\ugg} {\mu\mbox{g/g}^2}       %micro-gees per g squared
\newcommand{\sms} {\sigma^2}              %sigma squared
\newcommand{\acc}  {\vec{a}}
%\newcommand{\accvoi}  {\! \,^N \vec{a}^{\, B^\circ}}
\newcommand{\accpbc}{\:^B\vec{a}^{\:P_\circ}_C}       %acceleration
\newcommand{\accimuoiv}{\:^N\vec{a}^{\:IMU^\circ}_B} %accel IMUo wrto I coord in V
\newcommand{\accimuoi}{\:^N\vec{a}^{\:IMU^\circ}}
\newcommand{\accimuov}{\:^B\vec{a}^{\:IMU^\circ}}
\newcommand{\accvoi}{\:^N\vec{a}^{\:B^\circ}}
\newcommand{\acctoi}{\:^N\vec{a}^{\:T^\circ}}
\newcommand{\avec} {\vec{\alpha}}
\newcommand{\alvi}{\:^N\vec{\alpha}^{\:B}}
\newcommand{\wabc} {\:^B\vec{\omega}^{\:A}_C}   %angular vel
\newcommand{\wx} {\omega_x}
\newcommand{\ovec} {\vec{\omega}}
\newcommand{\omvi}{\:^N\vec{\omega}^{\:B}}
\newcommand{\ombeb}{\:^{ECI}\vec{\omega}^{\:B}_{\:B}}
\newcommand{\ombnb}{\:^{N}\vec{\omega}^{\:B}_{\:B}}
\newcommand{\omimui}{\:^N\vec{\omega}^{\:IMU}}
\newcommand{\omimuv}{\:^B\vec{\omega}^{\:IMU}}
\newcommand{\velpbc}{\:^B\vec{v}^{\:P_\circ}_C}       %acceleration
\newcommand{\velvoi}  {\! \,^N \vec{v}^{\, B^\circ}}
\newcommand{\velimuov}{\:^B\vec{v}^{\:IMU^\circ}}
\newcommand{\velimuoi}{\:^N\vec{v}^{\:IMU^\circ}}
\newcommand{\veltoi}{\:^N\vec{v}^{\:T^\circ}}
\newcommand{\rNoBo}{\vec{r}^{\,N_0 B_0}}
%
% The following commands are from the AIAA star tracker paper.
\newcommand{\sme}{  S_M  } 
\newcommand{\ssme}{  SubS_M  } 
\newcommand{\sfe}{S_F}
\newcommand{\sfem}{S_{\mbox{min}}}
\newcommand{\nfe}{N_F}
\newcommand{\scat}{S_W}
\newcommand{\sscat}{SubS_W}
\newcommand{\ncat}{N_W}
\newcommand{\anglem}{\alpha^{ij}_M}
\newcommand{\anglemb}{\{\alpha^{ij}_M\}}
\newcommand{\angleml}{\alpha^{kl}_M}
\newcommand{\anglemlb}{\{\alpha^{kl}_M\}}
\newcommand{\anglec}{\alpha^{ij}_W}
\newcommand{\anglecb}{\{\alpha^{ij}_W\}}
\newcommand{\nmat}{N_{Ma}}
\newcommand{\ndes}{N_D}
\newcommand{\seci}{\vec{s}_{ECI}}
\newcommand{\sst}{\vec{s}_{ST}}
\newcommand{\ssf}{\vec{s}_{SF}}
\newcommand{\sbb}{\vec{s}_{B}}
\newcommand{\xst}{x_{ST}}
\newcommand{\yst}{y_{ST}}
\newcommand{\zst}{z_{ST}}
\newcommand{\tstsc}{T_{ST/SC}}
\newcommand{\tsceci}{T_{SC/ECI}}
\newcommand{\ppq}{\frac{\partial}{\partial \overline{q}}}
\newcommand{\pxq}[1]{\frac{\partial \xst}{\partial q_{#1}}}
\newcommand{\pyq}[1]{\frac{\partial \yst}{\partial q_{#1}}}
\newcommand{\pzq}[1]{\frac{\partial \zst}{\partial q_{#1}}}
\newcommand{\papq}[2]{\frac{\partial {#1}}{\partial q_{#2}}}
\newcommand{\omhsc}[1]{\hat{\omega}^{SC}_{#1}}
\newcommand{\omvsc}[1]{\vec{\omega}^{SC}_{#1}}
\newcommand{\omvw}[1]{\vec{\omega}^{W}_{#1}}
\newcommand{\ovl}{\overline}
%
\newcommand{\tlvsf}{T_{LV/SF}}
\newcommand{\tsfi}{T_{SF/I}}
\newcommand{\tib}{T_{I/B}}
\newcommand{\slv}{\vec{s}_{LV}}
%
% Commands particular to testsym.m
%
\newcommand{\Cf}{C_f}
\newcommand{\Yuv}{Y_{uv}}
\newcommand{\Yur}{Y_{ur}}
\newcommand{\Nuv}{N_{uv}}
\newcommand{\Nur}{N_{ur}}
\newcommand{\Iyy}{I_{yy}}
\newcommand{\xR}{x_R}
\newcommand{\zB}{z_B}
\newcommand{\zG}{z_G}
\newcommand{\Tp}{T_p}
\newcommand{\Zwdot}{Z_{\dot{w}}}
\newcommand{\Mqdot}{M_{\dot{q}}}
%
% Commands for the UUST paper
%
\newcommand{\velrnb}{\:^N\vec{v}^{\:R_\circ}_B}
%\newcommand{\velrnr}{\:^N\vec{v}^{\:R_\circ}_R}
\newcommand{\velrnr}{\vec{v}^{\:R_\circ}_R}
\newcommand{\velbnb}{\:^N\vec{v}^{\:B_\circ}_B}
\newcommand{\velb}{\vec{v}^{\:B_\circ}}
\newcommand{\velr}{\vec{v}^{\:R_\circ}}
\newcommand{\omb}{\vec{\omega}^{\:B}}
\newcommand{\de}{\delta_E}
\newcommand{\dr}{\delta_R}
\newcommand{\cde}{\cos{\delta_E}}
\newcommand{\cdr}{\cos{\delta_R}}
\newcommand{\sde}{\sin{\delta_E}}
\newcommand{\sdr}{\sin{\delta_R}}
\newcommand{\der}{\begin{rm} d \end{rm}}   %Knut's
%
%\input margins
%\parskip .075in
%\textwidth 5.5in
%\topmargin -.25in
%\textheight 8.5in
%\oddsidemargin -.5in
%\evensidemargin -.5in
%\newcommand{\veldvl}{\:^N\vec{v}^{\:DVL^\circ}}
%
% Commands for the Oceans 2003 paper:
%
\newcommand{\veldvl}{\:^N\vec{v}^{\:DVL}}
\newcommand{\velwi}{\:^I\vec{v}^{\:W}}
\newcommand{\velbi}{\:^I\vec{v}^{\:B}}
\newcommand{\velbw}{\:^W\vec{v}^{\:B}}
\newcommand{\velbii}{\:^I\vec{v}^{\:B}_I}
\newcommand{\velbwi}{\:^W\vec{v}^{\:B}_I}
\newcommand{\velwii}{\:^I\vec{v}^{\:W}_I}
\newcommand{\velbidvl}{\:^I\vec{v}^{\:B}_{DVL}}
\newcommand{\tbi}{T_{B/I}}
\newcommand{\tdvlb}{T_{DVL/B}}