Particle Filtering and Sequential Monte Carlo Explained

We explain Particle Filtering, also known as Sequential Monte Carlo, as a method for tracking hidden states in systems with noisy measurements where traditional filters struggle due to non-linear or non-Gaussian characteristics. The core idea involves using a "swarm" of particles representing possible states, which are weighted based on how well they match observations and then resampled to focus computational effort on more likely states. Operating within a Hidden Markov Model framework, this technique iteratively predicts, updates weights based on observations, and resamples particles to approximate the posterior distribution of the hidden state over time. While basic Sequential Importance Sampling suffers from weight degeneracy, resampling helps alleviate this issue, making Sequential Importance Resampling (or the Bootstrap Filter) a common implementation.