Monte Carlo smoothing with application to audio signal enhancement

We describe methods for applying Monte Carlo filtering and smoothing for estimation of unobserved states in a nonlinear state-space model. By exploiting the statistical structure of the model, we develop a Rao–Blackwellized particle smoother. Due to the lengthy nature of real signals, we suggest processing the data in blocks, and a block-based smoother algorithm is developed for this purpose. All the algorithms suggested are tested with real speech and audio data, and the results are shown and compared with those generated using the generic particle smoother and the extended Kalman filter (EKF). It is found that the proposed Rao–Blackwellized particle smoother improves on the standard particle smoother and the extended Kalman smoother. In addition, the proposed Block-based smoother algorithm enhances the efficiency of the proposed Rao–Blackwellized smoother by significantly reducing the storage capacity required for the particle information.