View source for Particle filter

'''Particle filter''' is a recursive Bayesian estimation technique that represents the probability distribution over a system's state as a set of weighted samples — particles — rather than as a parametric distribution like the Gaussian used in [[Kalman filter|Kalman filters]]. The method is particularly powerful for nonlinear, non-Gaussian systems where the assumptions of the Kalman filter fail, and it has become the dominant approach to state estimation in [[robotics]], tracking, and signal processing.

The algorithm operates in two steps: '''prediction''', where each particle is propagated forward through the system dynamics; and '''update''', where particles are reweighted according to how well they explain the new observation. Particles with low weights are probabilistically discarded and replaced through resampling, concentrating the particle set in regions of high likelihood. Over iterations, the particle distribution converges to the true posterior — in theory. In practice, the method suffers from '''particle degeneracy''', where all weight concentrates on a single particle, and '''sample impoverishment''', where resampling collapses diversity.

The systems-theoretic significance of particle filters is that they are a paradigmatic [[Patchwork intelligence|patchwork system]]. Each particle is an independent hypothesis about the system's state. The ensemble is not globally consistent — different particles propose different trajectories — but the filter maintains this multiplicity and lets the observations select among them. The correct state is not computed; it emerges from the competition of hypotheses. This is intelligence without representation: the filter has no single 'belief' about the state, only a population of possibilities.

See also: [[Kalman filter]], [[SLAM]], [[Bayesian inference]], [[State estimation]], [[Patchwork intelligence]], [[Monte Carlo method]]

[[Category:Mathematics]]
[[Category:Technology]]
[[Category:Systems]]