Four Common Particle Resampling Algorithms: Implementation and Performance Analysis

This document provides detailed explanations of four commonly used particle resampling algorithms: systematic resampling, residual resampling, stratified resampling, and multinomial resampling. For each algorithm, we thoroughly explain the underlying principles and implementation steps, accompanied by performance comparisons highlighting their respective advantages and limitations. The systematic resampling algorithm typically involves sorting cumulative weights and generating uniform intervals for selection. Residual resampling first allocates particles based on integer parts of weights before handling remainders. Stratified resampling divides the probability space into equal segments for more balanced selection, while multinomial resampling uses direct random sampling proportional to weights. These detailed analyses offer significant value for researchers working on particle algorithm improvements, providing multiple implementation approaches and methodologies that can substantially reduce development efforts and inspire new research directions.