Advantages and Disadvantages of Various Nonlinear Kalman Filters: UKF and EKF Variants

In this article, we provide a detailed comparison of the advantages and disadvantages of various nonlinear Kalman filters, particularly focusing on the Unscented Kalman Filter (UKF) and different variants of Extended Kalman Filters (EKF). Our analysis reveals that while EKF demonstrates excellent computational efficiency and can be implemented with relatively straightforward Jacobian matrix calculations using numerical differentiation methods, it encounters significant challenges when dealing with highly nonlinear systems due to linearization errors.

In contrast, UKF employs a sigma-point sampling approach that propagates carefully selected sample points through the true nonlinear system dynamics. This method, implemented through the unscented transformation, eliminates the need for Jacobian calculations and provides better adaptability and accuracy for systems with strong nonlinear characteristics. The core UKF algorithm typically uses 2n+1 sigma points (where n is the state dimension) and weights determined by scaling parameters.

Furthermore, we explore several enhanced UKF variants, including divergence-free UKF which incorporates statistical linear regression techniques to prevent filter divergence, and robust UKF that employs adaptive filtering mechanisms and outlier rejection algorithms to handle non-Gaussian noise conditions. Each variant offers distinct benefits and limitations in different application scenarios, such as target tracking, navigation systems, and financial modeling, where specific performance metrics like computational complexity, estimation accuracy, and robustness must be carefully balanced.