Extended Kalman Filter

This article introduces the Extended Kalman Filter (EKF), a filtering technique designed for nonlinear systems. Unlike the traditional Kalman Filter, the EKF can handle nonlinear dynamics and in certain scenarios, provide more accurate estimations. The core concept of the EKF involves using linearized approximations to model nonlinear functions, enabling the filter to operate effectively within nonlinear environments. This implementation typically requires computing Jacobian matrices for the system's state transition and measurement models to linearize them around the current state estimate. We will comprehensively cover the fundamental principles, practical applications, and implementation methodologies of the EKF, including algorithmic steps such as prediction and update phases with linearization. Code-related aspects will discuss common functions like state prediction using nonlinear models, covariance propagation, and measurement updates with partial derivatives. This will equip readers with both theoretical understanding and practical implementation skills for applying this filter effectively.