Unscented Kalman Filter

In this article, we address a significant limitation of traditional Kalman filters - their inability to effectively track nonlinear systems. We present a solution implemented through the Unscented Kalman Filter (UKF), which employs a deterministic sampling technique known as the unscented transform. The UKF algorithm works by selecting sigma points around the mean, propagating these points through the nonlinear system, and then reconstructing a new Gaussian distribution from the transformed points. This approach differs fundamentally from traditional methods as it avoids linearization by directly approximating the probability distribution. Key implementation aspects include calculating sigma points using scaling parameters, propagating states through nonlinear functions, and updating covariance matrices. We discuss the advantages of UKF over Extended Kalman Filter (EKF), particularly its better performance for highly nonlinear systems and avoidance of Jacobian matrix calculations. While UKF requires more computational resources than EKF, it provides superior estimation accuracy. Potential future enhancements could involve adaptive parameter tuning and hybridization with particle filters for more complex scenarios.