\[\begin{align}
\int \delta(\tau) d\tau &= 1 \\
[\tau] &= \mathrm{sec} \\
[\delta(\tau)] &= \frac{1}{\mathrm{sec}} = \mathrm{Hz}
\end{align}\]

\[\begin{align}
\dot{q} &= \omega-b_g+\varepsilon_g \\
\dot{b}_g &= \eta_g\\
[\dot{q}] &= [\omega] - [b_g] + [\varepsilon_g] \\
[\dot{b}_g] &= [\eta_g]
\end{align}\]

\[\begin{align}{}
[\omega] = [b_g] = [\varepsilon_g] &= \frac{\mathrm{rad}}{\mathrm{sec}} \\
[\dot{b}_g] = [\eta_g] &= \frac{\mathrm{rad}}{\mathrm{sec}^2}
\end{align}\]

\[\begin{align}{}
[E[\varepsilon_g(t) \varepsilon_g^\top(t+\tau)]] &= \\
[\sigma_g^2\delta(\tau)] &= \frac{\mathrm{rad}^2}{\mathrm{sec}^2} (=[\varepsilon_g]^2) \\
[\sigma_g^2] &= \frac{\mathrm{rad}^2}{\mathrm{sec}^2}\frac{1}{\mathrm{Hz}} \\
[\sigma_g] &= \frac{\mathrm{rad}}{\mathrm{sec}}\frac{1}{\sqrt{\mathrm{Hz}}} \\
&= \frac{\mathrm{rad}}{\mathrm{sec}}\sqrt{\mathrm{sec}} \\
&= \frac{\mathrm{rad}}{\sqrt{\mathrm{sec}}} \\
&= \mathrm{rad}\sqrt{\mathrm{Hz}} \\
[E[\eta_g(t)\eta_g^\top(t+\tau)]] &= \\
[\sigma_{bg}^2 \delta(\tau)] &= \frac{\mathrm{rad}^2}{\mathrm{sec}^4} (=[\eta_g]^2) \\
[\sigma_{bg}^2] &= \frac{\mathrm{rad}^2}{\mathrm{sec}^3} \\
[\sigma_{bg}] &= \frac{\mathrm{rad}}{\mathrm{sec}}\sqrt{\mathrm{Hz}} \\
&=\frac{\mathrm{rad}}{\mathrm{sec}^2}\frac{1}{\sqrt{\mathrm{Hz}}} \\
[\sigma_a] &= \frac{\mathrm{m}}{\mathrm{sec}^2}\frac{1}{\sqrt{\mathrm{Hz}}} \\
[\sigma_{ba}] &= \frac{\mathrm{m}}{\mathrm{sec}^3}\frac{1}{\sqrt{\mathrm{Hz}}}
\end{align}\]