Recursive Kalman-type optimal estimation and detection of hidden markov chains

被引：29

作者：

Baccarelli, E ^{[1
]}

Cusani, R ^{[1
]}

机构：

[1] UNIV ROMA LA SAPIENZA, INFOCOM DEPT, I-00184 ROME, ITALY

来源：

SIGNAL PROCESSING | 1996年 / 51卷 / 01期

关键词：

hidden Markov models; innovations approach; multivariate point process; recursive nonlinear finite-dimensional detectors;

D O I：

10.1016/0165-1684(96)00030-8

中图分类号：

TM [电工技术]; TN [电子技术、通信技术];

学科分类号：

0808 ; 0809 ;

摘要：

Efficient algorithms for computing the 'a posteriori' 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.

引用

页码：55 / 64

页数：10

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