Hiukkasfilttereitä

Hiukkasfilttereitä, commonly known as particle filters, are a class of algorithms used for state estimation in systems where the underlying state is not directly observable or is subject to non-linear dynamics and non-Gaussian noise. They are particularly useful in situations where traditional Kalman filters are not applicable due to these complexities. The core idea behind particle filters is to approximate the probability distribution of the system's state using a set of random samples, called particles.

Each particle represents a possible state of the system, and it is assigned a weight that reflects how likely that state is given the available measurements. As new measurements become available, the particles are propagated forward in time according to the system's dynamics, and their weights are updated based on the likelihood of observing the new measurement from each particle's state. This process typically involves resampling, where particles with low weights are discarded and particles with high weights are duplicated, effectively concentrating the computational effort on the more probable states.

Particle filters have found applications in a wide range of fields, including robotics for localization and mapping, computer vision for object tracking, financial modeling, and aerospace engineering. Their flexibility in handling non-linear and non-Gaussian problems makes them a powerful tool for complex estimation tasks. The accuracy and performance of a particle filter are generally dependent on the number of particles used and the quality of the motion and measurement models.