The number of unscented transformations and the effect of noise estimates in an unscented kalman filtering problem

The unscented transformation is known as a technique to firstly generate a set of 2n + 1 sigma points and their weights, and secondly to propagate each sigma point value through a nonlinear function, where n denotes the dimension of the random state variable. Note however that there are two cases in a discrete-time filtering problem: one is the case where such a transformation is applied two times to the nonlinear model function and the nonlinear measurement function separately by using different mean and covariance, whereas the other is the case where such a transformation is basically applied to the nonlinear model function and the same sigma point values are only propagated to the nonlinear measurement function. So, we here examine the performance difference between them in a particular estimation problem. In addition, it is sometimes to encounter the case where for an unscented Kalman filter, the original state is augmented with other system and measurement noises simultaneously as if the original state and measurement noises are included in nonlinear functions, even though they are actually to be additive to each model function. Therefore, we further check how much the performance improvement or degradation is, compared to the case where there is no inconsistency in the model assumptions.