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Efficient blind system identification of non-Gaussian autoregressive models with HMM modeling of the excitation

Li, Chunjian and Andersen, Sören Vang LU (2007) In IEEE Transactions on Signal Processing 55(6). p.2432-2445
Abstract
We have previously proposed a blind system identification method that exploits the underlying dynamics of non-Gaussian signals in [Li and Andersen, "Blind identification of Non-Gaussian Autoregressive Models for Efficient Analysis of Speech Signals," Proceedings of the International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2006, vol. 1, pp. I-1205-1-1208]. The signal model being identified is an autoregressive (AR) model driven by a discrete-state hidden Markov process. An exact expectation-maximization (EM) algorithm was derived for the joint estimation of the AR parameters and the hidden Markov model (HMM) parameters. In this paper, we extend the system model by introducing an additive measurement noise. The... (More)
We have previously proposed a blind system identification method that exploits the underlying dynamics of non-Gaussian signals in [Li and Andersen, "Blind identification of Non-Gaussian Autoregressive Models for Efficient Analysis of Speech Signals," Proceedings of the International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2006, vol. 1, pp. I-1205-1-1208]. The signal model being identified is an autoregressive (AR) model driven by a discrete-state hidden Markov process. An exact expectation-maximization (EM) algorithm was derived for the joint estimation of the AR parameters and the hidden Markov model (HMM) parameters. In this paper, we extend the system model by introducing an additive measurement noise. The identification of the extended system model becomes much more complicated since the system output is now hidden. We propose an exact EM algorithm that incorporates a novel switching Kalman smoother, which obtains nonlinear minimum mean-square error (MMSE) estimates of the system output based on the state information given by the HMM filter. The exact EM algorithms for both models are obtainable only by appropriate constraints in the model design and have better convergence properties than algorithms employing generalized EM algorithm or empirical iterative schemes. The proposed methods also enjoy good data efficiency since only second-order statistics are involved in the computation. The signal models are general and suitable to numerous signals, such as speech and baseband communication signals. This paper describes the two system identification algorithms in an integrated form and provides supplementary results to the noise-free model and new results to the extended model with applications in speech analysis and channel equalization. (Less)
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author
publishing date
type
Contribution to journal
publication status
published
subject
keywords
identification, modeling, nonlinear estimation, signal analysis
in
IEEE Transactions on Signal Processing
volume
55
issue
6
pages
2432 - 2445
publisher
IEEE--Institute of Electrical and Electronics Engineers Inc.
external identifiers
  • wos:000246705100008
  • scopus:34249844301
ISSN
1053-587X
DOI
10.1109/TSP.2007.893935
language
English
LU publication?
no
id
a35dcf48-5d25-412c-980e-d92fcab1d3b3 (old id 4092494)
date added to LUP
2013-10-17 10:56:14
date last changed
2017-09-03 04:30:07
@article{a35dcf48-5d25-412c-980e-d92fcab1d3b3,
  abstract     = {We have previously proposed a blind system identification method that exploits the underlying dynamics of non-Gaussian signals in [Li and Andersen, "Blind identification of Non-Gaussian Autoregressive Models for Efficient Analysis of Speech Signals," Proceedings of the International Conference on Acoustics, Speech and Signal Processing (ICASSP), May 2006, vol. 1, pp. I-1205-1-1208]. The signal model being identified is an autoregressive (AR) model driven by a discrete-state hidden Markov process. An exact expectation-maximization (EM) algorithm was derived for the joint estimation of the AR parameters and the hidden Markov model (HMM) parameters. In this paper, we extend the system model by introducing an additive measurement noise. The identification of the extended system model becomes much more complicated since the system output is now hidden. We propose an exact EM algorithm that incorporates a novel switching Kalman smoother, which obtains nonlinear minimum mean-square error (MMSE) estimates of the system output based on the state information given by the HMM filter. The exact EM algorithms for both models are obtainable only by appropriate constraints in the model design and have better convergence properties than algorithms employing generalized EM algorithm or empirical iterative schemes. The proposed methods also enjoy good data efficiency since only second-order statistics are involved in the computation. The signal models are general and suitable to numerous signals, such as speech and baseband communication signals. This paper describes the two system identification algorithms in an integrated form and provides supplementary results to the noise-free model and new results to the extended model with applications in speech analysis and channel equalization.},
  author       = {Li, Chunjian and Andersen, Sören Vang},
  issn         = {1053-587X},
  keyword      = {identification,modeling,nonlinear estimation,signal analysis},
  language     = {eng},
  number       = {6},
  pages        = {2432--2445},
  publisher    = {IEEE--Institute of Electrical and Electronics Engineers Inc.},
  series       = {IEEE Transactions on Signal Processing},
  title        = {Efficient blind system identification of non-Gaussian autoregressive models with HMM modeling of the excitation},
  url          = {http://dx.doi.org/10.1109/TSP.2007.893935},
  volume       = {55},
  year         = {2007},
}