A 2012 paper includes simulation results which suggest that some published variants of the UKF fail to be as accurate as the Second Order Extended Kalman Filter (SOEKF), also known as the augmented Kalman filter.Gustafsson, F.; Hendeby, G.; , "Some Relations Between Extended and Unscented Kalman Filters," Signal Processing, IEEE Transactions on , vol.60, no.2, pp.545-555, Feb. 2012 The SOEKF predates the UKF by approximately 35 years with the moment dynamics first described by Bass et al.R. Bass, V. Norum, and L. Schwartz, “Optimal multichannel nonlinear filtering(optimal multichannel nonlinear filtering problem of minimum variance estimation of state of n- dimensional nonlinear system subject to stochastic disturbance),” J. Mathematical Analysis and Applications,vol. 16, pp. 152–164, 1966 The difficulty in implementing any Kalman-type filters for nonlinear state transitions stems from the numerical stability issues required for precision, however the UKF does not escape this difficulty in that it uses linearization as well, namely linear regression. The stability issues for the UKF generally stem from the numerical approximation to the square root of the covariance matrix, whereas the stability issues for both the EKF and the SOEKF stem from possible issues in the Taylor Series approximation along the trajectory.
