Unscented Kalman filtering for additive noise case: augmented versus nonaugmented

This paper concerns the unscented Kalman filtering (UKF) for the nonlinear dynamic systems with additive process and measurement noises. It is widely accepted for such a case that the system state needs not to be augmented with noise vectors and the resultant nonaugmented UKF yields similar, if not the same, results to the augmented UKF. In this letter, we find that under the condition of n+κ=const, the basic difference between them is that the augmented UKF draws a sigma set only once within a filtering recursion, while the nonaugmented UKF has to redraw a new set of sigma points to incorporate the effect of additive process noise. This difference generally favors the augmented UKF in that the odd-order moment information is partly captured by the nonlinearly transformed sigma points and propagated throughout the recursion. The simulation results agree well with the analyses.