Particle Filter Made Simple: A Step-by-Step Beginner-friendly Guide

Abstract: The particle filter is a powerful framework for estimating hidden states in dynamic systems where uncertainty, noise, and nonlinearity dominate. This mini-book offers a clear and structured introduction to the core ideas behind particle filters-how they represent uncertainty through random samples, update beliefs using observations, and maintain robustness where linear or Gaussian assumptions fail. Starting from the limitations of the Kalman filter, the book develops the intuition that drives the particle filter: belief as a cloud of weighted hypotheses that evolve through prediction, measurement, and resampling. Step by step, it connects these ideas to their mathematical foundations, showing how probability distributions can be approximated by a finite set of particles and how Bayesian reasoning unfolds in sampled form. Illustrated examples, numerical walk-throughs, and Python code bring each concept to life, bridging the gap between theory and implementation. By the end, readers will not only understand the algorithmic flow of the particle filter but also develop an intuitive grasp of how randomness and structure together enable systems to infer, adapt, and make sense of noisy observations in real time.