MATLAB Implementation of Unscented Kalman Filter (UKF) with Code Examples

The Unscented Kalman Filter (UKF) is a filtering algorithm suitable for nonlinear systems. Compared to the traditional Extended Kalman Filter (EKF), it avoids complex Jacobian matrix calculations through Unscented Transformation (UT). In target tracking applications, UKF effectively handles nonlinear motion models and measurement models, providing more accurate state estimation. First, it's essential to define the state vector and observation vector in target tracking. A typical state vector may include target position, velocity, and acceleration, while the observation vector might only contain position information. The core of UKF lies in approximating the state distribution through a carefully selected set of Sigma points, which capture both the mean and covariance of the state distribution. Implementing UKF in MATLAB primarily involves several key steps: initializing state and covariance matrices, generating Sigma points, performing state prediction, calculating predicted mean and covariance, and updating state estimates through observations. Each step requires attention to matrix dimension matching and maintaining covariance symmetry. Key MATLAB functions for implementation include chol (Cholesky decomposition) for Sigma point generation and mtimes (matrix multiplication) for covariance propagation. For target tracking applications, UKF can adapt to various nonlinear motion models such as turning models or acceleration change models. Compared to linear Kalman filters, UKF performs better in strongly nonlinear scenarios, making it a powerful tool for achieving precise target tracking. The algorithm's strength lies in its deterministic sampling approach, which typically uses 2n+1 Sigma points (where n is the state dimension) to propagate the system's statistics through nonlinear transformations without requiring derivative calculations.