Comparison of Tracking Filter Performance: Extended Kalman Filter vs Unscented Kalman Filter

In this paper, we explore the tracking filter performance of Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF). Both filters serve as fundamental tools for estimating system states in various applications. The Extended Kalman Filter employs linearization techniques to handle nonlinear models by computing Jacobian matrices for state transitions and measurement functions. Conversely, the Unscented Kalman Filter utilizes the unscented transformation to propagate sigma points through the nonlinear system, providing more accurate covariance estimation without requiring derivative calculations.

From an implementation perspective, the EKF algorithm typically involves: 1. Prediction step using Taylor series expansion for linearization 2. Measurement update with computed Jacobians 3. Covariance propagation through linearized models The UKF implementation follows: 1. Sigma point selection around the current state estimate 2. Nonlinear propagation of sigma points through system dynamics 3. Weighted recombination for state and covariance updates Each filter presents distinct advantages and limitations: EKF offers computational efficiency for mildly nonlinear systems but may suffer from linearization errors, while UKF provides better accuracy for highly nonlinear problems at the cost of increased computational complexity. We will systematically compare their performance characteristics to assist in selecting the appropriate filter for specific application requirements.