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Titlebook: Hidden Markov Models; Estimation and Contr Robert J. Elliott,John B. Moore,Lakhdar Aggoun Book 1995 Springer-Verlag New York 1995 93E11, 93

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Hidden Markov Model Processinglittle less daunting, and yet more mysterious, than the term ., which is a translation familiar to people in systems theory, or its applications areas of estimation and control theory. The term HMM is frequently restricted to models with states and measurements in a discrete set and in discrete time
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Discrete States and Discrete ObservationsThey transit between elements in this set with transition probabilities dependent only on the previous state, and so are .. The . are independent of time, and so the Markov chains are said to be .. The Markov chain is not observed directly; rather there is a discrete-time, finite-state observation p
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Continuous-Range Observationsorrupted by noise. For simplicity, we assume Gaussian noise. The main tool is again a version in discrete time of Girsanov’s theorem. An explicit construction is given of a new measure . under which all components of the observation process are .(0,1) i.i.d. random variables. Working under . we obta
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A General Recursive Filterdynamics are considered. In Section 5.7 the results are extended to a parameter estimation problem. In this case the same noise enters the signal and observations. In Section 5.8, an abstract formulation is given in terms of .. Finally, in Section 5.9 we discuss a correlated noise case, where the no
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Practical Recursive Filterseech processing , and biological signal processing (Rabiner 1989; Chung, Krishnamurthy and Moore 1991). A limitation of the techniques presented in the previous chapters for such applications is the curse of dimensionality which arises because the computational effort, speed, and memory requirements
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