A new optimal smoothing approach for AR + noise models and application to single-microphone speech enhancement

In many applications such as speech enhancement, some parametric approaches model the signal as an autoregressive (AR) process and then use a Kalman or H-infinity filter to retrieve the signal from the observations contaminated by additive white noise. These algorithms, that assume knowledge of the autoregressive parameters and of the additive noise variance, rely on a filter (or smoother) designed for a state-space realization of the speech. This paper describes a new optimal smoothing procedure that operates directly on the AR+noise model of the speech. This procedure leads to the same results obtainable by means of standard Kalman smoothing but is simpler and less computationally demanding.