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A great deal of attention has been paid to speech enhancement using a single microphone system. The various approaches, based on the Kalman filter, operate in two steps: (1) the noise variances and the parameters of the speech model are estimated, and (2) the speech signal is retrieved using standard Kalman filtering. This letter presents an alternative solution that does not require the explicit estimation of the noise and the driving process variances. This deals with a new formulation of the approach proposed within a control literature framework by Mehra (1970).