Sequential Monte Carlo: a unified review

Sequential Monte Carlo methods—also known as particle filters—offer approximate solutions to filtering problems for nonlinear state-space systems. These filtering problems are notoriously difficult to solve in general due to a lack of closed-form expressions and challenging expectation integrals. The essential idea behind particle filters is to employ Monte Carlo integration techniques in order to ameliorate both of these challenges. This article presents an intuitive introduction to the main particle filter ideas and then unifies three commonly employed particle filtering algorithms. This unified approach relies on a nonstandard presentation of the particle filter, which has the advantage of highlighting precisely where the differences between these algorithms stem from. Some relevant extensions and successful application domains of the particle filter are also presented.