Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Modified Adaptive Unscented Kalman Filter (MAUKF) Algorithms

In this paper, we conduct an in-depth study of the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Modified Adaptive Unscented Kalman Filter (MAUKF), examining their fundamental principles, distinctive features, and practical advantages and limitations. Our research reveals that the EKF operates through local linearization of the Kalman Filter, characterized by algorithmic simplicity and low computational requirements, making it suitable for weakly nonlinear Gaussian environments. Implementation typically involves calculating Jacobian matrices for linear approximation. The UKF employs a set of deterministically selected sigma points to approximate the posterior probability density of the state, demonstrating superior performance in handling nonlinear systems without requiring derivative calculations. The sigma points are propagated through the nonlinear system model to capture the mean and covariance accurately. Finally, we propose the MAUKF by incorporating a fading factor into the UKF framework, which enhances the filter's adaptability and tracking performance in practical applications. This modification involves adjusting the covariance matrices through adaptive weighting factors to improve estimation accuracy in dynamic environments.