Implementation of EKF, IEKF, and UKF Algorithms in MATLAB

This article provides an in-depth exploration of three fundamental estimation algorithms: Extended Kalman Filter (EKF), Iterated Extended Kalman Filter (IEKF), and Unscented Kalman Filter (UKF). These algorithms are widely employed in state estimation problems for measuring system variables such as position, velocity, and acceleration. The implementations leverage MATLAB's powerful computational capabilities and user-friendly interface, enabling efficient execution and accurate results. We will examine each algorithm's implementation methodology, including their approaches to handling measurement noise, performing state predictions through time update steps, and executing measurement updates using Kalman gain calculations.

The EKF implementation linearizes nonlinear systems using Jacobian matrices for covariance propagation, while the IEKF enhances this through iterative linearization at each measurement update. The UKF employs a deterministic sampling approach using sigma points to capture mean and covariance statistics more accurately than linearization methods. Through detailed code explanations and practical examples demonstrating key MATLAB functions like "ekf," "iekf," and "ukf" implementations with proper noise covariance tuning, readers will gain comprehensive understanding of these algorithms and their practical application in projects involving nonlinear filtering and state estimation.