# So given data rk we would like 1 to determine the

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Unformatted text preview: HMM’s: Given an observation r K which is a HMM, we are usually interested in determining 1 the underlying Markov chain S K embedded in this data. In Example 3 above, the 1 HMM represents the digital communication received data, and the Markov chain represents the transmitted symbol information. So, given data rK , we would like 1 to determine the state sequence S K which in some sense best ﬁts this data. 1 The MLSE problem is K {S 1 ,S 2 ,···,S K } max p(rn /S n ) N =1 (14) and the MAP problem is K {S 1 ,S 2 ,···,S K } max p(rn /S n ) P (S n /S n−1 ) · P (S 0 ) . n=1 (15) Note that for this MLSE problem statement S n does not necessarily have to be a Markov chain, but for MAP it does. The negative natural log versions of these problems are K {S 1 ,S 2 ,···,S K } min − N =1 ln{p(r n /S n )} (16) and K {S 1 ,S 2 ,···,S K } min − n=1 (ln{p(r n /S n )} + ln{P (S n /S n−1 )}) − ln{P (S 0 )} . (17) respectively. For the discussion direction below on employing the V...
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## This document was uploaded on 10/12/2009.

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