Unscented Kalman Filter Implementation

In this application, we will implement the Unscented Kalman Filter (UKF) functionality. This implementation enables more accurate state estimation and prediction when dealing with nonlinear systems. The UKF utilizes sigma point transformation to approximate nonlinear functions, avoiding the need for linearization required in traditional Kalman Filters. The implementation typically involves key functions for: - Sigma point generation using the unscented transform - Time update (prediction step) through nonlinear system dynamics - Measurement update (correction step) incorporating actual observations We will conduct comprehensive comparisons with traditional Kalman Filter methods, analyzing the advantages and disadvantages of both approaches. The comparison will focus on: - Handling of nonlinear system dynamics - Estimation accuracy and computational efficiency - Robustness in various operating conditions Through this comparative analysis, we can better understand the superiority of the Unscented Kalman Filter and why it proves more reliable and precise than traditional Kalman Filter methods when processing nonlinear systems. The implementation will include performance metrics evaluation and real-time adaptation capabilities.