An Excellent Introduction to Particle Filter with Practical Code Examples

Particle filter is a probabilistic inference technique based on Monte Carlo methods, commonly used for state estimation in nonlinear, non-Gaussian systems. This introductory program starts from fundamental concepts and employs intuitive implementation approaches to help beginners grasp its core principles. The core idea of particle filtering involves approximating probability distributions using a set of random samples (particles). Each particle represents a possible system state, with weights reflecting their credibility. The algorithm primarily consists of three stages: prediction, update, and resampling. In the prediction phase, particles are propagated according to the system model. The update phase adjusts particle weights using observation data. The resampling phase eliminates low-weight particles while preserving high-weight particles to prevent degeneracy issues. This program is particularly suitable for learning key concepts including: approximating continuous distributions with discrete particles, implementation of importance sampling principles, and weight normalization techniques. Through visual outputs, users can observe how particle clusters gradually converge toward the true state trajectory, providing valuable insights into the filter's dynamic characteristics. For readers seeking deeper understanding, suggested extensions include: comparing different noise models, observing accuracy changes by adjusting particle quantities, or replacing simple linear models with more complex motion models. These practical exercises enhance understanding of particle filter robustness and limitations. Key implementation considerations include: proper initialization of particle distributions, efficient weight calculation using likelihood functions, and systematic resampling methods like multinomial or stratified sampling to maintain particle diversity while computational efficiency.