Performance evaluation of UKF-based nonlinear filtering

Authors:
K. Xiong;H. Y. Zhang;C. W. Chan
Affiliations:
School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100083, China;School of Automation Science and Electrical Engineering, Beihang University, Beijing, 100083, China;Department of Mechanical Engineering, The University of Hong Kong, Hong Kong, China
Venue:
Automatica (Journal of IFAC)
Year:
2006

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Abstract

The performance of the modified unscented Kalman filter (UKF) for nonlinear stochastic discrete-time system with linear measurement equation is investigated. It is proved that under certain conditions, the estimation error of the UKF remains bounded. Furthermore, it is shown that the design of noise covariance matrix plays an important role in improving the stability of the algorithm. Error behavior of the UKF is then derived in terms of mean square error (MSE), and the Cramer-Rao lower bound (CRLB) is introduced as a performance measure. The modified UKF is found to approach the CRLB if the difference between the real noise covariance matrix and the selected one is small enough. These results are verified by using Monte Carlo simulations on two example systems.