Particle Filter and Unscented Particle Filter Algorithms

This document provides comprehensive implementation code for particle filter (PF) and unscented particle filter (UPF) algorithms, along with Gaussian mixture model (GMM) parameter configuration. The codebase is designed to handle complex data processing and analysis tasks, enhancing algorithmic accuracy and robustness through sophisticated implementation techniques. The implementation incorporates state-of-the-art algorithms and methodologies, featuring: - Sequential importance resampling (SIR) for particle filter implementation - Unscented transform integration for improved state estimation in UPF - Expectation-maximization (EM) algorithm for GMM parameter optimization - Systematic resampling techniques to mitigate particle degeneracy All code components have undergone rigorous testing and validation to ensure correct execution of intended functions, with particular attention to numerical stability and computational efficiency. The implementation includes modular functions for probability density estimation, weight updating, and resampling operations, making it suitable for various tracking and state estimation applications.