MATLAB Implementation of Unscented Kalman Filter (UKF) Simulation with Algorithm Analysis

The Unscented Kalman Filter (UKF) is an estimation method designed for nonlinear systems that eliminates linearization errors inherent in traditional Extended Kalman Filter (EKF) approaches through unscented transformation. This MATLAB simulation example demonstrates UKF implementation for target tracking applications, highlighting key implementation aspects and performance advantages. The simulation architecture consists of three core components: First, the UKF algorithm module implements sigma point sampling, unscented transformation, and state update procedures. The symmetrical distribution of sigma points around the mean enables more accurate capture of nonlinear distributions. Second, motion-observation model definitions include simplified nonlinear motion equations for 1D demonstrations and common turning maneuver scenarios for 2D simulations. Third, the performance comparison framework runs EKF and UKF in parallel under identical initial conditions, using Mean Square Error (MSE) metrics for quantitative evaluation. Simulation results from two typical scenarios reveal: Under strong nonlinear conditions (such as sharp turning phases), UKF reduces position estimation errors by 30%-50% compared to EKF. This improvement stems from EKF's Jacobian matrix linearization introducing systematic bias, while UKF preserves complete nonlinear characteristics through sigma point propagation. Particularly during state mutations, UKF provides more accurate covariance matrix updates, resulting in superior tracking robustness for sudden maneuvers. The simulation program's value lies not only in verifying UKF's theoretical advantages but also in its modular design facilitating adaptation to other nonlinear systems. Code annotations specifically emphasize practical parameter tuning experiences, such as how sigma point spread coefficients impact numerical stability, offering direct guidance for engineering applications. Key implementation details include MATLAB functions for sigma point generation using chol() for Cholesky decomposition, nonlinear state transition functions handling coordinate transformations, and Monte Carlo simulation loops for statistical performance analysis.