Unscented Kalman Filter

In control systems, filters serve as essential tools for noise removal and useful information extraction. The Kalman filter represents a widely-used filtering technique employed for estimating system states and tracking object motion. Among its variants, the Unscented Kalman Filter (UKF) constitutes a specialized Kalman filter designed primarily for nonlinear system tracking. Conventional Kalman filters fail to handle nonlinear relationships effectively in nonlinear systems, necessitating the implementation of UKF to address these scenarios and enhance filtering precision and reliability. The UKF algorithm operates through sigma point transformation, where a minimal set of carefully selected sample points (sigma points) propagate through the true nonlinear system model, preserving mean and covariance statistics more accurately than linearization approaches. Key implementation aspects include sigma point generation using scaling parameters, nonlinear transformation through system equations, and covariance update procedures that maintain numerical stability.