Table 8.

Filter applied to Estimation Mode.

Step	Used Equation
Evolution	${\tilde{\mathbf{X}}}_{k+1}=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]·{\mathbf{X}}_k+\left[\begin{array}{cc}\frac{1}{26}& -\frac{1}{26}\\ 0& 0\end{array}\right]·{\mathbf{U}}_k$
	$[{\tilde{\mathbf{P}}}_{\mathbf{k}+\mathbf{1}}]=\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]·[{\widehat{\mathbf{P}}}_k]·\left[\begin{array}{cc}1& 0\\ 0& 1\end{array}\right]+\left[\mathbf{Q}\right]=[{\widehat{\mathbf{P}}}_k]+\left[\mathbf{Q}\right]$
Prediction/measurement	${\tilde{\mathbf{Y}}}_k=\left(\begin{array}{c}{\tilde{a}}_{X,k}\\ {\tilde{a}}_{Z,k}\end{array}\right)=\left(\begin{array}{c}|{\widetilde{grav}}_{XZ,k}|·\sin ({\tilde{\theta }}_k)\\ |{\widetilde{grav}}_{XZ,k}|·\cos ({\tilde{\theta }}_k)\end{array}\right)$
Correction	${\mathbf{E}}_k={\mathbf{Y}}_k-{\tilde{\mathbf{Y}}}_k$
	$\left[{\mathbf{K}}_k\right]=[{\tilde{\mathbf{P}}}_{\mathbf{k}}]{\left[{\mathbf{H}}_{X,k}\right]}^T{(\left[{\mathbf{H}}_{X,k}\right][{\tilde{\mathbf{P}}}_k]{\left[{\mathbf{H}}_{X,k}\right]}^T+\left[\mathbf{R}\right])}^{-1}$
	${\widehat{\mathbf{X}}}_k={\tilde{\mathbf{X}}}_k+\left[{\mathbf{K}}_k\right]{\mathbf{E}}_k$
	$[{\widehat{\mathbf{P}}}_k]=(\mathbf{I}-\left[{\mathbf{K}}_k\right]\left[{\mathbf{H}}_{X,k}\right])[{\tilde{\mathbf{P}}}_k]$