Algorithm 1 Viterbi Algorithm ($\lambda =(A,B,\pi ),O$)
Inputs: $\lambda =(A,B,\pi ),O$
Output: $Q^{*}=\{q_1^{*},q_2^{*},\cdots ,q_T^{*}\}$
1: for $i=1,\cdots ,N$do	▹ Initialization
2:  ${\delta }_1\left(i\right)={\pi }_i{b}_i\left(O_1\right)$
3:  ${\psi }_1\left(i\right)=0$
4: for $j=1,\cdots ,N$, $t=2,\cdots ,T$ do	▹ Recursion
5:  ${\delta }_t\left(j\right)=\underset{1\le i\le N}{max}\left[{\delta }_{t-1}\left(i\right)a_{ij}\right]·B_j\left(O_t\right)$
6:  ${\psi }_t\left(i\right)=\underset{1\le i\le N}{argmax}\left[{\delta }_{t-1}\left(i\right)a_{ij}\right]$
7: $P^{*}=\underset{1\le i\le N}{max}\left[{\delta }_T\left(i\right)\right]$
8: $q_T^{*}=\underset{1\le i\le N}{argmax}\left[{\delta }_T\left(i\right)\right]$
9: for $t=T-1,T-2,\cdots ,1$ do	▹ Reconstruction of state sequence
10:  $q_t^{*}={\psi }_{t+1}\left(q_{t+1}^{*}\right)$
11: return $Q^{*}$