Kalman Filter, Unscented Kalman Filter, Extended Kalman Filter and Related Filtering Algorithms with Implementation Code

This documentation presents a comprehensive collection of filtering algorithms including Kalman Filter (KF), Unscented Kalman Filter (UKF), and Extended Kalman Filter (EKF) programs developed in our laboratory. These implementations feature robust state estimation capabilities through recursive Bayesian filtering approaches, with the KF utilizing linear Gaussian systems, EKF employing first-order Taylor expansions for nonlinear systems, and UKF implementing the unscented transform for superior nonlinear estimation. The codebase includes essential functions for prediction and update steps, covariance management, and measurement integration. While these programs currently provide reliable performance for various applications, we can further explore their comparative advantages in different scenarios such as target tracking, navigation systems, and sensor fusion. Future development directions may include adaptive filtering techniques, computational optimization for real-time systems, and integration with machine learning approaches. The collection offers excellent foundation for advancing research in optimal estimation theory and practical implementation challenges.