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.