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Make Kalman filter formulas more memorizable

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Martin Thoma 2016-07-13 14:58:49 +02:00
parent d65f5d2933
commit f4674abc32
2 changed files with 2 additions and 2 deletions
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tikz/kalman-filter/kalman-filter.tex
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@ -25,7 +25,7 @@
\node[block, text width=6cm, \node[block, text width=6cm,
label={[above,align=center]{Prediction}}] at (4, 0) (prediction) label={[above,align=center]{Prediction}}] at (4, 0) (prediction)
{\begin{align*} {\begin{align*}
\mathbf{x}_{k+1}^{(P)} &= A x_k + B {\color{orange} a_k}\\ \mathbf{x}_{k+1}^{(P)} &= A \mathbf{x}_k + B {\color{orange} a_k}\\
P_{k+1}^{(P)} &= A P_k A^\tran + C_k^{(r_s)} P_{k+1}^{(P)} &= A P_k A^\tran + C_k^{(r_s)}
\end{align*}}; \end{align*}};
\node [block, right of=prediction, \node [block, right of=prediction,
@ -35,7 +35,7 @@
label={[above,align=center]{Innovation}}] at (4, -4) (innovation) label={[above,align=center]{Innovation}}] at (4, -4) (innovation)
{\begin{align*} {\begin{align*}
K_k &= P_k^{(P)} H^\tran {\left (H P_k^{(P)} H^\tran + C_k^{(r_m)} \right)}^{-1}\\ K_k &= P_k^{(P)} H^\tran {\left (H P_k^{(P)} H^\tran + C_k^{(r_m)} \right)}^{-1}\\
{\color{blue} \mathbf{x}_k} &= \mathbf{x}_k^{(P)} + K_k \left ({\color{orange} z_k} - H \mathbf{x}_k^{(P)} \right )\\ {\color{blue} \mathbf{x}_k} &= (I - K_k H) \mathbf{x}_k^{(P)} + K_k {\color{orange} z_k}\\
{\color{blue} P_k} &= (I - K_k H) P_k^{(P)} {\color{blue} P_k} &= (I - K_k H) P_k^{(P)}
\end{align*}}; \end{align*}};