Comparative Analysis of EKF, UKF, and PF Algorithms Using Simulation

In this paper, we conduct a comparative analysis of three prominent filtering algorithms—EKF, UKF, and PF—using simulation methodologies. The comparison framework will include implementing each algorithm with standardized state-space models and evaluating their performance through quantitative metrics like RMSE (Root Mean Square Error) and computational efficiency. We will discuss the intrinsic advantages and limitations of each algorithm: EKF's computational efficiency through linearization approximations, UKF's improved accuracy using sigma-point transformations for nonlinear systems, and PF's robustness in multi-modal distributions via sequential Monte Carlo sampling. The study will explore parameter optimization techniques, such as tuning process noise covariance matrices for EKF/UKF and resampling strategies for PF, to enhance tracking precision under varying noise conditions. Additionally, we will address practical implementation challenges, including numerical stability in EKF's Jacobian calculations, UKF's scaling parameter selection, and PF's particle degeneracy mitigation. By analyzing scenarios with different nonlinearities and noise distributions, this work provides insights into algorithm selection criteria for specific applications—such as robotic localization or sensor fusion—and proposes directions for hybrid approaches and adaptive filtering techniques in future research.