Particle Filter Algorithm

Particle filters, also called sequential Monte Carlo methods, are a family of algorithms that estimate the changing internal state of a system from a series of noisy or incomplete observations, in cases where the system's behavior is too irregular for a Kalman filter's straightforward mathematics to handle well. The method represents its current belief about the system's state as a large collection of weighted sample points, called particles, updating each particle's weight as new observations arrive and periodically replacing low-weight particles with copies of higher-weight ones so the particle population keeps tracking the most likely states rather than collapsing onto a few poor guesses. Rough versions of the idea go back to a mid-1950s technique nicknamed the poor man's Monte Carlo, and the first serious applications to Bayesian estimation appeared in 1993 with Genshiro Kitagawa's Monte Carlo filter and Neil Gordon's bootstrap filter. Pierre Del Moral coined the term particle filters in 1996 by analogy with earlier mean-field particle methods from fluid mechanics, and Jun Liu and Rong Chen introduced the alternative name sequential Monte Carlo in 1998.