Two-Kalman filters approach for unbiased AR parameter estimation from noisy observations, application to speech enhancement

The AR model is used in many applications such as speech processing. However, when the observations are contaminated by additive noise, standard methods produce biased AR parameter estimates. To avoid a non linear approach to estimate the signal and the parameters at the same time, such as the EKF, a sequential method using two conditionally linked Kalman filters running in parallel is here presented. Following the instrumental variables concept, at each step in time, one of the filters uses the latest estimated AR parameters to estimate the signal, while the second one uses the estimated signal to estimate the AR parameters, to be used in the next step. This approach, already applied in hydrological applications, has the advantage of providing an unbiased estimation of the parameters and an estimation of the signal in the steady state. This method is then derived in the framework of speech enhancement.