EKF UKF PF Algorithm Comparison with Particle Filter MATLAB Simulation

In this article, we conduct a comprehensive comparison of three filtering algorithms: EKF, UKF, and PF. These algorithms represent commonly used filtering methods, with their primary differences lying in how they handle nonlinear systems, each possessing distinct advantages and limitations. First, we examine the Extended Kalman Filter (EKF) algorithm. As an extension of the standard Kalman filter, EKF is designed for state estimation in nonlinear systems. Although EKF offers simplicity and ease of understanding, it demonstrates higher sensitivity to noise and strong nonlinearities. In MATLAB implementation, EKF typically requires linearization using Jacobian matrices through the jacobian() function or manual derivative calculations. Next, we introduce the Unscented Kalman Filter (UKF) algorithm. UKF represents a nonlinear filtering approach based on unscented transformation. By employing sigma points to capture the mean and covariance through nonlinear functions, UKF achieves higher accuracy than EKF without requiring derivative calculations. The MATLAB implementation utilizes the unscentedKalmanFilter object with carefully tuned alpha, beta, and kappa parameters. Finally, we analyze the Particle Filter (PF) algorithm. PF is a Monte Carlo-based filtering method suitable for nonlinear system state estimation. Its main advantage lies in handling arbitrary nonlinear systems, but it suffers from high computational complexity and requires substantial particle samples for accurate state estimation. The MATLAB implementation typically involves systematic resampling using residual resampling algorithms and importance weight calculation through pdf() functions. To facilitate better understanding of these filtering algorithms, we have developed comprehensive MATLAB simulation programs. These simulations feature configurable system models, noise parameters, and performance metrics calculation (RMSE, consistency tests) to visually demonstrate each algorithm's strengths and weaknesses through comparative plots and statistical analysis.