Kalman filter and state-space approach to blind deconvolution

The state-space model has been introduced as approach to blind deconvolution of dynamical systems. An efficient learning algorithm has been developed for training the external parameters (1998) and a Kalman filter has been applied to to compensate for the model bias and reduce the effect of noise (1999) for linear systems. We generalize the Kalman filter to blind deconvolution of semi-nonlinear systems. First, we introduce a general framework of the state space approach for blind deconvolution and review the state of the art of state space approach for blind deconvolution. The adaptive natural gradient learning algorithm for updating external parameters is presented by minimizing a certain cost function, which is derived from mutual information of output signals. In order to compensate for the model bias and reduce the effect of noise, the extended Kalman filter is applied to the blind deconvolution setting. A new concept, called hidden innovation, is introduced so as to numerically implement the Kalman filter. A computer simulation is given to show the validity and effectiveness of the state-space approach.

[1]  O. Jacobs,et al.  Introduction to Control Theory , 1976, IEEE Transactions on Systems, Man, and Cybernetics.

[2]  Thomas Kailath,et al.  Linear Systems , 1980 .

[3]  Shun-ichi Amari,et al.  Differential-geometrical methods in statistics , 1985 .

[4]  Christian Jutten,et al.  Blind separation of sources, part I: An adaptive algorithm based on neuromimetic architecture , 1991, Signal Process..

[5]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice , 1993 .

[6]  Fathi M. A. Salam,et al.  An adaptive network for blind separation of independent signals , 1993, 1993 IEEE International Symposium on Circuits and Systems.

[7]  Pierre Comon,et al.  Independent component analysis, A new concept? , 1994, Signal Process..

[8]  Terrence J. Sejnowski,et al.  An Information-Maximization Approach to Blind Separation and Blind Deconvolution , 1995, Neural Computation.

[9]  Yingbo Hua,et al.  Fast maximum likelihood for blind identification of multiple FIR channels , 1996, IEEE Trans. Signal Process..

[10]  Jean-François Cardoso,et al.  Equivariant adaptive source separation , 1996, IEEE Trans. Signal Process..

[11]  R. Ober.  Balanced Canonical Forms , 1996 .

[12]  Andrzej Cichocki,et al.  Robust neural networks with on-line learning for blind identification and blind separation of sources , 1996 .

[13]  Shun-ichi Amari,et al.  Blind source separation-semiparametric statistical approach , 1997, IEEE Trans. Signal Process..

[14]  Liqing Zhang,et al.  Two-stage Blind Deconvolution Using State-space Models , 1998, ICONIP.

[15]  Andrzej Cichocki,et al.  Blind deconvolution/equalization using state-space models , 1998, Neural Networks for Signal Processing VIII. Proceedings of the 1998 IEEE Signal Processing Society Workshop (Cat. No.98TH8378).

[16]  Shun-ichi Amari,et al.  Natural Gradient Works Efficiently in Learning , 1998, Neural Computation.

[17]  Liqing Zhang,et al.  Blind Separation of Filtered Sources Using State-Space Approach , 1998, NIPS.

[18]  Liqing Zhang,et al.  Blind separation and filtering using state space models , 1999, ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349).

[19]  Fathi M. A. Salam,et al.  The state space framework for blind dynamic signal extraction and recovery , 1999, ISCAS'99. Proceedings of the 1999 IEEE International Symposium on Circuits and Systems VLSI (Cat. No.99CH36349).