Monte Carlo methods for signal processing: Recent advances

In many areas of signal processing, the trend of addressing problems with increased complexity continues. This is best reflected by the forms of the models used for describing phenomena of interest. Typically, in these models the number of unknowns that have to be estimated is large and the assumptions about noise distributions are often non-tractable for analytical derivations. One major reason that allows researchers to resolve such difficult problems and delve into uncharted territories is the advancement of methods based on Monte Carlo simulations including Markov chain Monte Carlo sampling and particle filtering. In this paper, the objective is to provide a brief review of the basics of these methods and then elaborate on the most recent advances in the field.