Monte Carlo smoothing for non-linearly distorted signals

We develop methods for Monte Carlo filtering and smoothing for estimating an unobserved state given a non-linearly distorted signal. 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. In particular, we describe algorithms for de-quantisation and declipping in detail. Both algorithms are tested with real audio data which is either heavily quantised or clipped and the results are shown.

[1]  Simon J. Godsill,et al.  Monte Carlo filtering and smoothing with application to time-varying spectral estimation , 2000, 2000 IEEE International Conference on Acoustics, Speech, and Signal Processing. Proceedings (Cat. No.00CH37100).

[2]  B. Friedlander,et al.  Lattice filters for adaptive processing , 1982, Proceedings of the IEEE.

[3]  Simon J. Godsill,et al.  On sequential Monte Carlo sampling methods for Bayesian filtering , 2000, Stat. Comput..

[4]  Timothy J. Robinson,et al.  Sequential Monte Carlo Methods in Practice , 2003 .

[5]  Simon J. Godsill,et al.  MCMC methods for restoration of quantised time series , 1999, NSIP.