Recently I'm learning the unscented kalman filter (UKF). When designing the unscented kalman filter, it involves a non-linear function to generate the sigma points and then use the system non-linear function to transform those sigma points. However, I'm still confused about why we need to select sigma points to compute the estimate value and how the sigma points selecting function affects the efficiency of UKF.
Here is the pdf book I'm learning now:
In this book, it mentions the sigma function in Chapter 10.3