Extended Kalman Filter: The Standard Nonlinear Kalman Filter

In this article, we explore the applications of the Extended Kalman Filter (EKF), a widely adopted nonlinear Kalman filter designed for systems with nonlinear mathematical models. The EKF infers system states by combining prior knowledge with observational data, providing accurate state estimation through linearization techniques around the current mean and covariance. Key implementation aspects include Jacobian matrix calculations for system linearization and recursive prediction-update cycles. Our accompanying toolbox features multiple EKF implementations addressing diverse application requirements, incorporating variations like the Iterated EKF and Second-Order EKF for enhanced accuracy. Each implementation includes MATLAB/Simulink code examples demonstrating state transition functions, measurement models, and covariance propagation. We aim to help readers deepen their understanding of EKF principles and algorithms while facilitating practical implementation in real-world engineering applications.