On the Accuracy of the One-step UKF and the Two-step UKF

The most accurate version of the unscented Kalman filter (UKF) involves the construction of two ensembles. To reduce computational cost, however, UKF is often implemented without the second ensemble. This simplification comes at a price, however, since, for linear systems, the one-step variation of the two-step UKF does not specialize to the classical Kalman filter, with an associated loss of accuracy. This paper remedies this drawback by developing a modified one-step UKF that recovers the classical Kalman filter for linear systems. Numerical examples show that the modified one-step UKF also recovers the accuracy of the two-step UKF in nonlinear systems with linear outputs.