Formulae

\begin{bmatrix}
hx&  hy& hz
\end{bmatrix} =
\begin{bmatrix}
Ex&  Ey& Ez
\end{bmatrix} *
\begin{bmatrix}
 0&  -g_{z}& g_{y}\\
g_{z}&  0& -g_{x}\\
 -g_{y}&  g_{x}& 0
\end{bmatrix}
\\
H = \begin{bmatrix}
\frac{h_{x}}{| h\,|}
&\frac{h_{y}}{| h\,|}
& \frac{h_{z}}{| h\,|}
\end{bmatrix}
\\
A = \begin{bmatrix}
\frac{g_{x}}{| g\,|}
&\frac{g_{y}}{| g\,|}
& \frac{g_{z}}{| g\,|}
\end{bmatrix}
\\

\begin{bmatrix}
Mx&  My& Mz
\end{bmatrix} =
\begin{bmatrix}
Ax&  Ay& Az
\end{bmatrix} *
\begin{bmatrix}
 0&  -H_{z}& H_{y}\\
H_{z}&  0& -H_{x}\\
 -H_{y}&  H_{x}& 0
\end{bmatrix}\\
R=
\begin{bmatrix}
 H_{x}&  H_{y}& H_{z}\\
 H_{x}&  H_{y}& H_{z}\\
 H_{x}&  H_{y}& H_{z}\\
\end{bmatrix}\\

rates = Axis_{x}, Axis_{y} and \, Axis_{z}\\

time = dT\\

\omega = \sqrt{Axis^{2}_{x} + Axis^{2}_{y} +  Axis^{2}_{z}}\\

a = \begin{bmatrix}
\frac{Axis_{x}}{| Axis\,|}
&\frac{Axis_{y}}{| Axis\,|}
& \frac{Axis_{z}}{| Axis\,|}
\end{bmatrix}\\

\omega =\frac{d\theta }{dT} \Rightarrow d\theta = \omega dT

deltaRotationVector = \begin{bmatrix}
 a_{x} sin(\frac{d\theta}{2})&  a_{y} sin(\frac{d\theta}{2})& a_{z} sin(\frac{d\theta}{2}) & cos(\frac{d\theta}{2})
\end{bmatrix}\\

rotationMatrix = rotationMatrix * deltaRotationMatrix = \begin{bmatrix}
 R_{1}&  R_{2}& R_{3} \\
 R_{4}&  R_{5}& R_{6} \\
R_{7}&  R_{8}& R_{9}
\end{bmatrix}\\

angles = \begin{bmatrix}
 tan^{-1}(\frac{R_{1}}{R_{4}})& sin^{-1}(R_{7}) &  tan^{-1}(\frac{R_{6}}{R_{8}})
\end{bmatrix}\\

(X, Y) = (D*tan(angle_{x}), D*tan(angle_{y}))\\