“…The other factor of (5) is immediately related to the local probability, which can be factorized into: P(q1L ,q| X) p(q X)p(ql ql, X)L p(qT q>L ,qf q'TX (7) Now each factor of (7) can be simplified by relaxing the conditional constraint; especially, in the following the factors of (7) are assumed to only depend on the previous state and on a signal window with width 2p+l. In fact, the local probability is simplified as p(ql q,L , q-l, x) = p(qlI q -,X+P ) (8) The following dynamic programming recurrence holds: P(qjX1 ) = max[P(qk X1 )p(q, Xn qk)] (9) Where k runs over all possible states before states ql, and P(q, X7n) denotes the cumulated best path probability of reaching state ql with emitting the partial sequence xl .…”