Implementation of Unscented Kalman Filter Algorithm

This function implements the Unscented Kalman Filter (UKF) algorithm for state estimation and target tracking applications. The Kalman filter algorithm is a recursive filtering approach that generates optimal state estimates by combining past and current state information to predict future states. In target tracking applications, the Kalman filter algorithm is widely used to process sensor data for predicting target motion trajectories and positions. The UKF implementation particularly excels in handling nonlinear systems through sigma point transformation, which propagates carefully selected points through the nonlinear system to approximate the state distribution more accurately than traditional Extended Kalman Filters. The function typically includes key components such as sigma point generation, time update (prediction) step using nonlinear state transition functions, and measurement update step incorporating observation models. This implementation is particularly valuable in state estimation and target tracking scenarios where it provides improved accuracy for nonlinear systems while maintaining computational efficiency comparable to traditional Kalman filters.