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

This research focuses on the Extended Kalman Filter (EKF), Unscented Kalman Filter (UKF), and Modified Adaptive Unscented Kalman Filter (MAUKF), investigating the fundamental principles and distinctive characteristics of each algorithm. The EKF linearizes the Kalman Filter locally, featuring simple implementation with low computational complexity, suitable for weakly nonlinear Gaussian environments. The UKF approximates the posterior probability density of the state using a set of deterministic sample points (sigma points). The MAUKF introduces a fading factor to enhance the UKF's adaptability. Implementation considerations include Jacobian matrix calculations for EKF, sigma point propagation for UKF, and adaptive weight adjustments for MAUKF.