Dual Kalman Filtering Methods for Nonlinear Prediction, Smoothing and Estimation

Prediction, estimation, and smoothing are fundamental to signal processing. To perform these interrelated tasks given noisy data, we form a time series model of the process that generates the data. Taking noise in the system explicitly into account, maximum-likelihood and Kalman frameworks are discussed which involve the dual process of estimating both the model parameters and the underlying state of the system. We review several established methods in the linear case, and propose several extensions utilizing dual Kalman filters (DKF) and forward-backward (FB) filters that are applicable to neural networks. Methods are compared on several simulations of noisy time series. We also include an example of nonlinear noise reduction in speech.

[1]  Lee A. Feldkamp,et al.  Neurocontrol of nonlinear dynamical systems with Kalman filter trained recurrent networks , 1994, IEEE Trans. Neural Networks.

[2]  E. Stear,et al.  The simultaneous on-line estimation of parameters and states in linear systems , 1976 .

[3]  Eric A. Wan,et al.  Neural speech enhancement using dual extended Kalman filtering , 1997, Proceedings of International Conference on Neural Networks (ICNN'97).

[4]  Les E. Atlas,et al.  Recurrent neural networks and robust time series prediction , 1994, IEEE Trans. Neural Networks.

[5]  S. Boll,et al.  Suppression of acoustic noise in speech using spectral subtraction , 1979 .

[6]  Hynek Hermansky,et al.  Speech enhancement based on temporal processing , 1995, 1995 International Conference on Acoustics, Speech, and Signal Processing.

[7]  Graham C. Goodwin,et al.  Adaptive filtering prediction and control , 1984 .