Particle Filter Resampling Methods

This document provides a comprehensive implementation of particle filter resampling methods, covering random resampling, multinomial resampling, systematic resampling, and residual resampling techniques. We conduct detailed analysis of each method's advantages and limitations, accompanied by relevant code implementations and practical application examples. Each resampling algorithm includes key function descriptions: random resampling employs basic probability-based selection, multinomial resampling uses cumulative distribution functions for particle selection, systematic resampling implements stratified sampling with fixed intervals, and residual resampling combines deterministic and stochastic approaches for efficient computation. Additionally, we present guidelines for selecting the most appropriate resampling method based on different dataset characteristics and discuss performance optimization strategies to enhance computational efficiency. We believe this documentation will prove valuable for researchers and practitioners working with particle filter resampling methodologies.