A measure of when and how much the UKF is better than the EKF

Sanat K. Biswas, Li Qiao, Andrew G. Dempster, A quantified approach of predicting suitability of using the Unscented Kalman Filter in a non-linear application, . Automatica, Volume 122, 2020, DOI: 10.1016/j.automatica.2020.109241.

A mathematical framework to predict the Unscented Kalman Filter (UKF) performance improvement relative to the Extended Kalman Filter (EKF) using a quantitative measure of non-linearity is presented. It is also shown that the range of performance improvement the UKF can attain, for a given minimum probability depends on the Non-linearity Indices of the corresponding system and measurement models. Three distinct non-linear estimation problems are examined to verify these relations. A launch vehicle trajectory estimation problem, a satellite orbit estimation problem and a re-entry vehicle position estimation problem are examined to verify these relations. Using these relations, a procedure is suggested to predict the estimation performance improvement offered by the UKF relative to the EKF for a given non-linear system and measurement without designing, implementing and tuning the two Kalman Filters.

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