Extended Kalman Filter Algorithm with MATLAB Implementation

This documentation presents an Extended Kalman Filter (EKF) algorithm implementation package, which includes first-order and second-order EKF prediction M-files. The Extended Kalman Filter is a widely-used state estimation algorithm designed for nonlinear systems. The algorithm operates by linearizing nonlinear systems through Taylor series expansion (first-order using Jacobian matrices, second-order incorporating Hessian matrices) and then applying standard Kalman filtering techniques for state estimation. Key implementation aspects include: state transition functions, measurement models, covariance propagation, and Kalman gain computation. In practical applications, EKF finds extensive use in control systems, navigation solutions, and signal processing domains. The provided MATLAB implementation demonstrates proper handling of nonlinear transformations through carefully designed state prediction and update functions. This algorithm package aims to facilitate better understanding and practical application of Extended Kalman Filter techniques, with clear code structure and commented mathematical formulations.