A Forward Backward Algorithm for ML State and Sequence Estimation

The classical Viterbi algorithm is used to estimate the maximum likelihood state sequence from a block of observed data. It achieves this by maximising a forward path probability measure. In an analogous manner a backward path probability measure can be generated which leads to the development of a Viterbi forwardbackward algorithm. This algorithm computes an “a posteriori maximum path probability” for each state at a given time. The resulting probability distribution across all possible state at time t can be used as a soft output for further processing. Maximising a posteriori maximum path probability at each time gives the same state sequence as obtained from the classical Viterbi algorithm.