MATLAB Code Implementation of Kalman Filtering Algorithms

In this article, we primarily discuss filtering algorithms including Kalman filter, Extended Kalman Filter (EKF), and Unscented Kalman Filter (UKF). The implementation covers core algorithms such as state prediction using linear dynamic models for standard Kalman filter, Taylor series linearization for EKF to handle nonlinear systems, and sigma point transformation for UKF to better capture nonlinear characteristics without linearization. We also introduce an Interacting Multiple Model (IMM) implementation based on a hybrid EKF-UKF approach, which enables better handling of system uncertainties through model probability weighting and mode-switching logic. Additionally, we discuss supporting Rauch-Tung-Striebel (RTS) fixed-interval smoothing and two-filter smoothing tools that employ forward-backward filtering techniques to improve estimation accuracy by reducing lag effects. The framework provides modular MATLAB functions for each component, allowing flexible configuration of process noise covariance (Q) and measurement noise covariance (R) matrices. Overall, we present a robust and user-friendly framework that facilitates effective data processing and analysis through well-structured MATLAB classes and standardized interface functions.