Unscented Kalman Filter Using Augmented State in the Presence of Additive Noise

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Unscented Kalman filter (UKF) using augmented state for the nonlinear dynamic systems in the presence of additive process and measurement noises is addressed. There are two alternative versions of UKF in which the system state may be augmented or not be augmented by the process and measurement noises. It was reported that the augmented UKF has better performance for dynamic systems than the nonaugmented UKF. However, the research results apply only to the dynamic system with weak noises, not to mention how the performance of these two UKFs compared in the presence of strong noises. Under the condition of n+k=const, the basic difference in one filtering recursion between them is that the covariance of state vector in augmented UKF incorporates the process noises. This difference generally makes the gain in augmented UKF bigger than the counterpart in nonaugmented UKF. We cast augmented KF and nonaugmented UKF into a discrete-time dynamic system equation. Then we find that the nonaugmented UKF yields better performance than the augmented UKF in the case of strong noises, which contradicts with the results obtained in the presence of weak noises.