Particle Filtering: the First 25 Years and beyond

This paper presents a survey of the ideas behind the particle filtering, or sequential Monte Carlo, method, from at least 1930 up to the present day. The particle filter, which is now 25 years old, has been an immensely successful and widely used suite of methods for filtering and smoothing in state space models, and it is still under research today. The key ideas that led to the development in 1993 of the original particle filter, the bootstrap filter, were Monte Carlo integration, Importance Sampling, Bayesian updating, Probabilistic State Space models, and Sampling-Importance-Resampling. We survey these methods within their historical context and then provide a general framework for description of most current variants on the particle filtering methodology, based upon updating the joint smoothing distribution of the states. This framework aids in the understanding of the various elements of a particle filter, including resampling. prediction and weighting. We further summarise recent developments and look to the future of the methodology.