On some derivations of Gibson's approach for speech enhancement

This paper deals with a Kalman filter-based enhancement of a speech signal embedded in a colored noise, when using a single microphone system. Several approaches using Kalman filtering have been developed. More particularly, Gibson et al. (1991) reported an iterative method based on the so called "noise-free" state space model, which may imply the introduction of a coordinate transformation to perform Kalman filtering. The authors do not address the identification issue. We propose some derivations of this method through an identification step using subspace methods for identification, previously developed in the field of control by Van Overschee (1993). The methods proposed here are then compared with other Kalman based-approaches.