The unscented Kalman filter (UKF) is based on the “unscented transformation” (UT). First proposed by Julier et al.  the UT allows for the estimation of the mean and the covariance of an arbitrary analytical transformation y = f() of a random Gaussian vector with a mean value and a covariance matrix .
If L denotes the size of the vector , the method put forth by Julier et al. runs in three steps:
1) 2L+1 particles or σ-points  are generated as follows:
where (M)i is the iith row or column of matrix M and λ = α2(L + κ)– L is a scaling factor. Element α is a parameter which allows us to control the dispersion of the σ-points around the mean . κ is a secondary scaling factor.
2) The σ-points are transformed using function f:
3) The mean and ...