Notations

The following notations are used in all the algorithms:

$a_{t+k|t}=E\left(\alpha_{t+k} | y_0 \cdots y_{t}\right)$ $P_{t+k|t}=var\left(\alpha_{t+k} | y_0 \cdots y_{t}\right)$ $a_{t+1}=a_{t+1|t}, \: P_{t+1}=P_{t+1|t}$