[WIP] Particle filter (sequential Monte Carlo method, SMC)

Particle filters, also known as sequential Monte Carlo methods form a family of online (incremental) estimation of hidden variables of dynamical, stochastic models through iteratively updating from a series of observed, possibly biased, noisy and unreliable variables.

They solve the filtering problem in a more general way than Kalman filters, which assume a more restrictive distribution of errors: Gaussian.

Particle filters are also in the group of Monte Carlo methods, with the notable property of being an online learning method, while many MC methods such as Markov Chain Monte Carlo (MCMC) are implemented as batch methods.

Particle filters are often used for Bayesian inference, signal processing, localization, financial model parameter estimation and machine learning in general.

Example: localization of a randomly moving robot on a known map

You are a robot with a map of the surroundings. You turn and move forward randomly, and continuously measure the distance to the closest object in front of you. You don't initially know where you are on the map. You want to figure out your location.

The cavern was generated with the donjon random dungeon generator.

To be continued with actual contents...