Standard Particle Filter and Its Enhanced Variant: Auxiliary Particle Filter

This paper presents a comprehensive program featuring both standard particle filters and auxiliary particle filters, accompanied by significant research simulations. Particle filters are state estimation algorithms designed for nonlinear and non-Gaussian systems, widely applied across various fields including robotics, aerospace engineering, biomedical engineering, and financial engineering. The implementation typically involves sequential Monte Carlo methods where particles represent probability distributions, with key functions including particle initialization, weight updating, and resampling procedures. The auxiliary particle filter serves as an enhanced version of the standard particle filter, incorporating auxiliary variables to improve both performance and computational efficiency. This improvement is achieved through a sophisticated resampling technique that selects particles based on their prospective importance, implemented using predictive likelihood calculations before the actual measurement update. Our discussion will provide detailed algorithmic explanations covering: - Particle propagation using system dynamics models - Importance weight computation with measurement models - Systematic resampling implementations to mitigate degeneracy - Auxiliary variable integration for better proposal distributions The included simulations demonstrate practical applications through: - State estimation in nonlinear dynamical systems - Performance comparison between standard and auxiliary variants - Convergence analysis under different noise conditions - Computational efficiency measurements All implementations follow modular programming practices with clearly defined functions for filter initialization, prediction steps, update steps, and result visualization, ensuring reproducibility and ease of modification for research purposes.