Particle Filter – Universal State Estimation Method Beyond Linear-Gaussian Restrictions

Abstract

State space representation of dynamical system is widely used in prediction and control, etc., and state estimation is a fundamental problem to be solved in this formulation. While analytical state estimations via Kalman filter, etc., are available for systems consisting of linear equations and Gaussian distributions, there is no analytical solution to the state estimation problem for nonlinear and/or non-Gaussian state space models in general case. As a breakthrough to this issue, in early 1990s, a particle filter called “Monte Carlo Filter” has been proposed in Japan as the first universal approximation method of state estimation for nonlinear and/or non-Gaussian models by utilizing many realizations in the state space to represent probability distribution of posterior state. Due to the universal property and allowed flexibility in modeling, now, particle filters have become standard methods in many fields, such as natural science, social science, engineering, and so on.