Comparison of Four Gaussian Filter Algorithms: EKF, UKF, QKF, and CKF

This article provides a comprehensive comparison of four Gaussian filter algorithms: Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), Quadrature Kalman Filter (QKF), and Cubature Kalman Filter (CKF). These algorithms serve as essential tools for state estimation in nonlinear systems and are widely applied across various engineering domains. We conduct detailed analysis of each algorithm's strengths and limitations while evaluating their performance characteristics and application suitability. Additionally, we examine implementation methodologies, including key mathematical models and underlying assumptions. For implementation reference, EKF typically requires Jacobian matrix calculations through numerical differentiation, UKF employs sigma point transformation via the unscented transform, QKF utilizes numerical integration points based on Gaussian quadrature rules, and CKF implements spherical-radial cubature rules for numerical integration. Through systematic comparison, we aim to provide readers with deeper understanding and practical insights for selecting the most appropriate filtering algorithm in real-world applications.