The Unscented Kalman Filter (UKF): A Novel Development in Estimation Theory
The Unscented Kalman Filter (UKF) represents a significant advancement in nonlinear estimation. The core concept involves generating strategically placed sampling points (Sigma points) around the current state estimate based on its covariance matrix. These points are then propagated through the nonlinear system model to capture the posterior mean and covariance more accurately than linearization methods. The UKF implementation typically involves three main steps: sigma point selection, nonlinear transformation, and statistics recovery.