Efficient algorithms for computing the ‘a posterior? probabilities (APPs) of discrete-index finite-state hidden Markov sequences are proposed. They are obtained by reducing the APPs computation to the optimal nonlinear minimum mean square error (MMSE) estimation of the noisily observed sequences of the indicator functions associated with the chain states. Following an innovations approach, finite-dimensional and recursive Kalman-like ‘filter’ and ‘smoothers’ for the Markov chain state sequence are thus obtained, and exact expressions of their MSE performance are given. The filtered and smoothed state estimates coincide with the corresponding APP sequences. Finite-dimensional MMSE nonlinear filter and smoothers are also given for the so-called ‘number of jumps’ and for the ‘occupation time’ processes associated with the Markov state sequence.

Recursive Kalman-type optimal estimation and detection of Hidden Markov chains / Baccarelli, Enzo; Cusani, Roberto. - In: SIGNAL PROCESSING. - ISSN 0165-1684. - 51:(1996), pp. 55-64.

Recursive Kalman-type optimal estimation and detection of Hidden Markov chains

BACCARELLI, Enzo;CUSANI, Roberto
1996

Abstract

Efficient algorithms for computing the ‘a posterior? probabilities (APPs) of discrete-index finite-state hidden Markov sequences are proposed. They are obtained by reducing the APPs computation to the optimal nonlinear minimum mean square error (MMSE) estimation of the noisily observed sequences of the indicator functions associated with the chain states. Following an innovations approach, finite-dimensional and recursive Kalman-like ‘filter’ and ‘smoothers’ for the Markov chain state sequence are thus obtained, and exact expressions of their MSE performance are given. The filtered and smoothed state estimates coincide with the corresponding APP sequences. Finite-dimensional MMSE nonlinear filter and smoothers are also given for the so-called ‘number of jumps’ and for the ‘occupation time’ processes associated with the Markov state sequence.
1996
Hidden Markov models; Innovations approach; Multivariate point proces; Recursive nonlinear finite-dimensional detectors
01 Pubblicazione su rivista::01a Articolo in rivista
Recursive Kalman-type optimal estimation and detection of Hidden Markov chains / Baccarelli, Enzo; Cusani, Roberto. - In: SIGNAL PROCESSING. - ISSN 0165-1684. - 51:(1996), pp. 55-64.
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/244499
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