Rotated Unscented Kalman Filter for Two State Nonlinear Systems


In the several past years, Extended Kalman Filter (EKF) and Unscented Kalman Filter (UKF) have
became basic algorithm for state-variables and parameters estimation of discrete nonlinear systems.
The UKF has consistently outperformed for estimation. Sometimes least estimation error doesn't yield
with UKF for the most nonlinear systems. In this paper, we use a new approach for a two variable
state nonlinear systems which it is called Rotated UKF (R_UKF). R_UKF can be reduced estimation
error and reached for least error in state estimation.


[1] Simon Haykin, Kalman Filtering and
neural networks. Communications
Research Laboratory, McMaster
University, Hamilton, Ontario, Canada,
John Wiley & Sons, Inc. NewYork, ISBN
[2] S. J. Julier and J. K. Uhlmann, “A New
Extension of the Kalman Filter to
Nonlinear Systems,” in Proc. of Aero
Sense: The 11th Int. Symp. On
Aerospace/Defense Sensing, Simulation
and Controls., 1997.
[3] E.Wan, R. van derMerwe, and A. T.
Nelson, “Dual Estimation and the
Unscented Transformation,” in Neural
Information Processing Systems 12. 2000,
pp. 666–672, MIT Press.
[4] E. A. Wan and R. van der Merwe, “The
Unscented Kalman Filter for Nonlinear
Estimation,” in Proc. of IEEE Symposium
2000 (AS-SPCC), Lake Louise, Alberta,
Canada, Oct. 2000.
[5] S.Gannot, D. Burshtein, and E. Weinstein,
“Iterative and Sequential Kalman Filter-
Based Speech enhancement Algorithms,”
IEEE Trans. on Speech and Audio Proc.,
vol. 6, no. 4, pp. 373–385, Jul. 1998.
[6] J. L. Crassidis and J. L. Junkins," Optimal
Estimation of Dynamic Systems". Boca
Raton, Florida: CRC Press, to be
published 2004.
[7] S. J. Julier, “The Scaled Unscented
Transformation,” in Proceedings of the
American Control Conference, vol. 6,
pp. 4555–4559, 2002.