Kalman filter and state-space approach to blind deconvolution

State-space model has been introduced as approach to blind deconvolution of dynamical systems. An efficient learning algorithm was developed for training the external parameters and the Kalman filter was also applied to compensate for the model bias and reduce the effect of noise for linear systems. In this paper 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.