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.

提出了一种数学框架，可使用非线性量化方法来预测相对于扩展卡尔曼滤波器（EKF）的无味卡尔曼滤波器（UKF）性能的提高。还表明，对于给定的最小概率，UKF可以实现的性能改进范围取决于相应系统和测量模型的非线性指标。研究了三个不同的非线性估计问题，以验证这些关系。研究了运载火箭的轨迹估计问题，卫星轨道的估计问题和重返飞行器的位置估计问题，以验证这些关系。利用这些关系，