Comparative Analysis of Nonlinear Filtering Methods: KF, EKF, PF and Beyond

In this document, the author conducts a comprehensive comparison and analysis of several nonlinear filtering methods, including Kalman Filter (KF), Extended Kalman Filter (EKF), and Particle Filter (PF). Each method demonstrates distinct advantages and limitations across various domains and applications. The KF implementation typically involves state prediction and update steps using linear equations, while EKF extends this approach by linearizing nonlinear systems through Jacobian matrices. PF methods employ sequential Monte Carlo techniques using particle propagation and resampling algorithms. Analyzing the strengths, weaknesses, and applicable scope of these methods holds significant value for research and practice. Through detailed investigation of these filtering techniques, we can better understand their characteristics and applications, thereby providing stronger support and guidance for future research and practical implementations. Key implementation considerations include computational complexity, measurement update mechanisms, and handling of system nonlinearities.