Hiukkasfiltterit

Hiukkasfiltterit, also known as particle filters, are a class of Bayesian filtering algorithms used to estimate the state of a dynamic system. They are particularly useful when dealing with non-linear systems and non-Gaussian noise, where traditional Kalman filters struggle. The core idea behind particle filtering is to represent the probability distribution of the system's state using a set of discrete samples, called particles.

Each particle represents a possible state of the system, and these particles are propagated forward in time according to the system's dynamics. When new measurements become available, the particles are re-weighted based on how well they explain the observed data. Particles that are more consistent with the measurements are given higher weights, and those that are less consistent are given lower weights. This re-weighting process effectively approximates the posterior probability distribution of the system's state.

A crucial step in particle filtering is resampling. After re-weighting, there can be a concentration of probability mass on a few particles, while many others have very low weights. Resampling involves drawing new particles from the current set, with the probability of drawing a particle being proportional to its weight. This process helps to avoid the "degeneracy" problem where most particles have negligible weights, and it ensures that the particle set remains diverse and representative of the posterior distribution.

Particle filters have found applications in various fields, including robotics for localization and mapping, computer vision for object tracking, and finance for time series analysis. Their ability to handle complex, non-linear scenarios makes them a powerful tool for state estimation.