Estimation of optimal state sequence

In the following, the problem considered is that of estimating the optimal state transition sequence for generating the signal sequence.

For such a purpose, Viterbi algorithm is well known. Also we propose the forward algorithm which is shown below. Using the optimal state transition sequence $\mbox{\boldmath$S$}^*=\{s_1^*~,...,~s_T^*\}$ obtained by such algorithms, the segmentation boundaries and the category identification are directly derived.