The particle filter computes a numeric approximation of the posterior distribution of the state trajectory in nonlinear filtering problems. This is done by generating random state trajectories and assigning a weight to them according to how well they predict the observations. The weights are instrumental in a resampling step, where trajectories are either kept or thrown away. This exposition will focus on explaining the main principles and the main theory in an intuitive way, illustrated with figures from a simple scalar example. A real-time application is used to graphically show how the particle filter solves a nontrivial nonlinear filtering problem.
KeywordsNonlinear filtering Sequential Monte Carlo Estimation Kalman filter
- Forssell U, Hall P, Ahlqvist S, Gustafsson F (2002) Novel map-aided positioning system. In: Proceedings of FISITA, Helsinki, number F02-1131Google Scholar
- Gustafsson F (2010) Particle filter theory and practice with positioning applications. IEEE Trans Aerosp Electron Mag Part II Tutor 7:53–82Google Scholar
- Ristic B, Arulampalam S, Gordon N (2004) Beyond the Kalman filter: particle filters for tracking applications. Artech House, LondonGoogle Scholar