For i = 1 to N do

${\delta }_1\left(i\right)=p_i{f}_i\left(O_1\right)$

End For

For t = 2 to T do

For j = 1 to N do

${\delta }_t\left(j\right)={\max }_i\left({\delta }_{t-1}\left(i\right)a_{ij}\right)f_j\left(O_t\right)$

${\psi }_t\left(j\right)=\arg {\max }_i\left({\delta }_{t-1}\left(i\right)a_{ij}\right)f_j\left(O_t\right)$

End For

End For

$P^{*}={\max }_i\left({\delta }_T\left(i\right)\right)$

$Q_T^{\ast }=\arg {\max }_i\left({\delta }_T\left(i\right)\right)$

For t = T − 1 to 1 do

$Q_t^{*}={\psi }_{t+1}\left(Q_{t+1}^{*}\right)$

End For