Publisher : Institute of Control, Robotics and Systems
DOI : 10.5302/J.ICROS.2015.15.0060
Title & Authors
A Finite Impulse Response Fixed-lag Smoother for Discrete-time Nonlinear Systems Kwon, Bo-Kyu; Han, Sekyung; Han, Soohee;
In this paper, a finite impulse response(FIR) fixed-lag smoother is proposed for discrete-time nonlinear systems. If the actual state trajectory is sufficiently close to the nominal state trajectory, the nonlinear system model can be divided into two parts: The error-state model and the nominal model. The error state can be estimated by adapting the optimal time-varying FIR smoother to the error-state model, and the nominal state can be obtained directly from the nominal trajectory model. Moreover, in order to obtain more robust estimates, the linearization errors are considered as a linear function of the estimation errors. Since the proposed estimator has an FIR structure, the proposed smoother can be expected to have better estimation performance than the IIR-structured estimators in terms of robustness and fast convergence. Additionally the proposed method can give a more general solution than the optimal FIR filtering approach, since the optimal FIR smoother is reduced to the optimal FIR filter by setting the fixed-lag size as zero. To illustrate the performance of the proposed method, simulation results are presented by comparing the method with an optimal FIR filtering approach and linearized Kalman filter.
finite impulse response;nonlinear state estimation;linearized Kalman filter;fixed-lag FIR smoother;
B. D. O. Anderson and J. B. Moor, Optimal filtering, Dover, 2005.
F. L. Lewis, Optimal estimation, Wiley, 1986.
M. S. Grewal and A. P. Andrews, Kalman filtering: Theory and Practice, Prentice-Hall, 1993.
R. J. Fitzgerald, "Divergence of the Kalman filter," IEEE Transations on Automatic Control, vol. 16, pp. 736-747, 1971.
S. H. Han, B. K. Kwon, and W. H. Kwon, "Minimax FIR smoothers for deterministic continuous-time state space models," Automatica, vol. 45, no. 6, pp. 1561-1566, 2009.
B. K. Kwon, "An optimal FIR filter for discrete time-varying state space models," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 17, no. 12, pp. 1183-1187, 2011.
B. K. Kwon and S. Han, "An optimal fixed-lag FIR smoother for discrete time-varying state space models," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 20, no. 1, pp. 1-5, 2014.
S. Y. Cho and K. H. Kim, "FIR fixed-interval smoothing filter for discrete nonlinear system with modeling uncertainty and its application to dr/gps integrated navigation system," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 19, no. 5, pp. 481-487, 2013.
S. Han, B. K. Kwon, and S. Han, "An extened finite imoulse response filter for discrete-time nonlinear systems," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 21, no. 1, pp. 34-39, 2015.
H. S. Hong, J. G. Lee, and C. G. Park, "An extended Kalman filter robust to linearization error," Journal of Institute of Control, Robotics and Systems (in Korean), vol. 12, no. 2, pp. 92-100, 2006.