The estimation of Line Spectral Frequencies trajectories based on Unscented Kalman Filtering

In recent studies the unscented Kalman filter (UKF) was applied to some nonlinear systems. Several speech processing problems like the estimation of the formant trajectories, the state and parameter Kalman estimation for speech enhancement and the estimation of line spectral frequency (LSF) trajectories. In this paper we apply the UKF to the estimation of LSF trajectories, in the case of synthetic and real noisy speech. The expectation maximization (EM) approach is used to iteratively estimate the LSF parameters. Furthermore, the square-root implementation of the UKF is used as it provides numeric stability and guarantees positive semi-definiteness of the state covariance.