Centered hat over bold letter with subscript in \newcommand

Question

I'm relatively inexperienced with LaTex and I'm trying to use \newcommand in a larger project. I have several cascaded \newcommands that I can't get to behave the way I want:

\renewcommand{\vec}[1]{\boldsymbol{#1}}
\newcommand{\gyrobias}{\vec{b}_{g}}
\newcommand{\est}[1]{\hat#1}

With this I would like to be able to write $\est{\gyrobias}$ to get a hat over a bold b with a subscript g. This almost works, but the hat is over the whole expression, not just b.

A similar question here covers essentially this with the help of \expandafter. So I tried the following

\newcommand{\est}[1]{\expandafter\hat#1}

But this gives me the following compilation error:

Extra }, or forgotten $ $\est{\gyrobias}

If I add curly braces to \hat{}, which is what I'm used to, the text compiles fine, but the hat is not moved to where I want it.

\newcommand{\est}[1]{\expandafter\hat{#1}}

Removing the curly braces from \hat to match the answer in the linked question and defining \gyrobias without the \vect gives the desired hat placement, but of course, now the b is no longer bold

\newcommand{\gyrobias}{b_{g}}
\newcommand{\est}[1]{\hat#1}

I suspect I need some more \expandafters, but I have no idea where as I don't fully understand what they do.

---

Edit

I got it to work with a slight modification to @steven-b-segletes answer:

\renewcommand{\vec}[1]{\boldsymbol{#1}}
\newcommand{\est}[1]{\expandafter\hat#1}
\newcommand{\gyrobias}{{\vec{b}}_{g}}

I would now like to achieve the same thing with a couple of slightly more complicated symbols:

\newcommand{\rquat}[2]{{\overline{q}}^{#1}_{#2}}
\newcommand{\camrot}{\rquat{O}{C}}

\newcommand{\pos}[4]{_{#4}\vec{#1}_{#2 #3}}
\newcommand{\trans}[3]{\pos{t}{#1}{#2}{#3}} %\trans{from}{to}{in}
\newcommand{\campos}{\trans{O}{C}{O}}

I want \est{\camrot} and \est{\campos} to place the hat only just above the "central letter". Currently it is set over the whole \rquat/\trans. Similarly \dot{\camrot} and \dot{\est{\camrot}} etc should be placed on top of the central letter only, and not the sub/super-scripts

Answer 1

The key was to set your redefinition of \vec in its own group (as denoted with the extra set of braces).

\documentclass{article}
\usepackage{bm}
\renewcommand{\vec}[1]{{\boldsymbol{#1}}}
\newcommand{\gyrobias}{\vec{b}_{g}}
\newcommand{\est}[1]{\hat#1}
\begin{document}
$\est{\gyrobias}$
\end{document}

If this approach does bad things to \vec in some other way, one could always apply the extra group to the definition of \gyrobias, instead:

\documentclass{article}
\usepackage{bm}
\renewcommand{\vec}[1]{\boldsymbol{#1}}
\newcommand{\gyrobias}{{\vec{b}}_{g}}
\newcommand{\est}[1]{\hat#1}
\begin{document}
$\est{\gyrobias}$
\end{document}

FOLLOW UP

With this follow up, I address the issue of getting a \hat or \dot over the intended letter, using the syntax of the OP. However, it does not address the issue of multiple diacritics over the same letter, as in \dot{\est{\camrot}}.

\documentclass{article}
\usepackage{bm}
\renewcommand{\vec}[1]{\boldsymbol{#1}}
\newcommand{\gyrobias}{{\vec{b}}_{g}}
\newcommand{\rquat}[2]{{\overline{q}}^{#1}_{#2}}
\newcommand{\camrot}{\rquat{O}{C}}
\newcommand{\pos}[5][]{{_{#5}}#1{\vec{#2}}_{#3 #4}}
\newcommand{\trans}[4][]{\pos[#1]{t}{#2}{#3}{#4}} %\trans{from}{to}{in}
\newcommand{\campos}[1][]{\trans[#1]{O}{C}{O}}
\newcommand{\est}[1]{\applydiacritic{\hat}{#1}}
\newcommand{\Dot}[1]{\applydiacritic{\dot}{#1}}
\newcommand\applydiacritic[2]{\ifx\campos#2\campos[#1]\else\expandafter#1#2\fi}
\begin{document}
$\est{\gyrobias}$\medskip

$\camrot\quad\est{\camrot}\quad\Dot{\camrot}$\medskip

$\campos\quad\est{\campos}\quad\Dot{\campos}$\medskip
\end{document}

The OP points out that the above code does not work with amsmath. Here is a fix for that, though I note that amsmath package affects the placement of diacritical marks over the letter "t", and I have verified that it is not related to my solution here, which can be seen in the first line of my output (when amsmath is inserted/removed).

\documentclass{article}
\usepackage{bm}
\usepackage{amsmath}% THIS PACKAGE EFFECTS PLACEMENT OF DIACRITICS OVER \boldsymbol{t}
\renewcommand{\vec}[1]{\boldsymbol{#1}}
\newcommand{\gyrobias}[1][]{#1{\vec{b}}_{g}}
\newcommand{\rquat}[3][]{#1{\overline{q}}^{#2}_{#3}}
\newcommand{\camrot}[1][]{\rquat[#1]{O}{C}}
\newcommand{\pos}[5][]{{_{#5}}#1{\vec{#2}}_{#3 #4}}
\newcommand{\trans}[4][]{\pos[#1]{t}{#2}{#3}{#4}} %\trans{from}{to}{in}
\newcommand{\campos}[1][]{\trans[#1]{O}{C}{O}}
\newcommand{\est}[1]{\applydiacritic{\hat}{#1}}
\newcommand{\mydot}[1]{\applydiacritic{\dot}{#1}}
\newcommand\applydiacritic[2]{%
  \ifx\gyrobias#2\gyrobias[#1]\else
  \ifx\campos#2\campos[#1]\else
  \ifx\camrot#2\camrot[#1]\else
  #1#2\fi\fi\fi}
\begin{document}
$\boldsymbol{t}\quad\hat{\boldsymbol t}\quad\dot{\boldsymbol t}$\medskip

$\gyrobias\quad\est{\gyrobias}\quad\mydot{\gyrobias}$\medskip

$\camrot\quad\est{\camrot}\quad\mydot{\camrot}$\medskip

$\campos\quad\est{\campos}\quad\mydot{\campos}$\medskip
\end{document}

Answer 2

I would suggest a different strategy: redefine \vec to have a *-variant for the hat form.

\documentclass{article}
\usepackage{amsmath,bm,xparse}

\RenewDocumentCommand{\vec}{sm}{%
  \IfBooleanTF{#1}
    {\hat{\bm{#2}}}
    {\bm{#2}}% 
}
\NewDocumentCommand{\gyrobias}{s}{%
  \IfBooleanTF{#1}
    {\vec*{b}_{g}}
    {\vec{b}_{g}}%
}

\begin{document}

$\vec{x}_{g}+\vec*{x}_{g}+\gyrobias+\gyrobias*$

\end{document}