EKF, IEKF, and UKF Algorithms: Nonlinear Filtering Methods

EKF (Extended Kalman Filter), IEKF (Iterated Extended Kalman Filter), and UKF (Unscented Kalman Filter) are three commonly used nonlinear filtering algorithms widely applied in target tracking, navigation, and state estimation applications. EKF (Extended Kalman Filter) The EKF linearizes nonlinear functions through first-order Taylor series expansion, making it suitable for weakly nonlinear systems. In MATLAB implementation, you can use the built-in `ekf` function or manually code the state prediction and measurement update steps. The prediction step typically involves propagating the state estimate using the nonlinear system model, while the update step incorporates measurements through linearized matrices. However, the linearization approximation may introduce errors, causing performance degradation in strongly nonlinear systems. IEKF (Iterated Extended Kalman Filter) IEKF is an improved version of EKF that enhances filtering accuracy through multiple iterations of the measurement update step. Each iteration performs re-linearization around the current estimate, bringing the result closer to the true value. MATLAB implementation involves creating a loop structure around the measurement update step, where the innovation and Kalman gain are recalculated iteratively. This approach makes IEKF particularly suitable for systems with stronger nonlinearities. UKF (Unscented Kalman Filter) UKF employs the Unscented Transform to approximate nonlinear distributions, effectively avoiding linearization errors. Compared to EKF, UKF demonstrates more stable performance in strongly nonlinear systems. In MATLAB, UKF can be implemented using the `ukf` function or by manually coding the sigma point sampling and weighted calculation steps. The algorithm works by selecting sigma points that capture the mean and covariance of the state distribution, propagating them through the nonlinear system, and then reconstructing the posterior statistics. Each algorithm has distinct advantages and limitations: EKF requires less computational resources but offers limited accuracy; IEKF improves accuracy through iteration at the cost of increased computation; UKF excels in highly nonlinear systems but has higher computational complexity. When implementing these in MATLAB, the choice of filtering algorithm should be based on specific application requirements, considering the trade-off between nonlinearity strength, computational resources, and accuracy needs.