* Predict*:

$\hat{x}_k = a\hat{x}_{k-1}$ $ + b u_k $

\[p_k = ap_{k-1}a \]
$g_k = p_k$ $c$ $/ ($$c$ $p_k$ $c$$~+~r)$

Here is an extension of our airplane demo, showing a longer duration of time and
adding in a control signal representing the pilot
steadily pulling back on the control column to raise the altitude of the plane. Try moving
around the sliders to adjust the values of the different constants.
As in the previous demo, the original signal is shown blue, the observed signal in red,
and the Kalman-filtered signal in green.
$\hat{x}_k \leftarrow \hat{x}_k + g_k(z_k - $$c$ $\hat{x}_k)$

$p_k \leftarrow (1 - g_k $$c$) $p_k$

$a =$ | $r = $ | |

$b =$ | ||

$c =$ |

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