Selection of Tuning Parameters of the Unscented Kalman Filter using Analytical Truth Statistics

Nonlinear state estimation is an important aspect of aerospace sensing and navigation. Due to the inherent nonlinearity of flight mechanics, nonlinear filtering techniques such as Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) are commonly implemented in aerospace applications. One of the issues surrounding the UKF is how to select the various scaling parameters in the filter. While some works discuss these parameters, research is limited in terms of guidance on how to properly select these parameters. This work utilizes truth statistics for nonlinear transformations to investigate the effect of the UKF scaling parameters on mean and covariance estimation for various common nonlinear functions.