Nonlinear State Estimation Using Hybrid Robust Cubature Kalman Filter
Subject Areas : Signal ProcessingBehrooz Safarinejadian 1 , Mohsen Taher 2
1 - Shiraz University of Technology
2 - Shiraz University of Technology
Keywords: Uncertainty, State Estimation, Cubature Kalman Filter (CKF), Robust CKF, Hybrid Robust CKF,
Abstract :
In this paper, a novel filter is provided that estimates the states of any nonlinear system, both in the presence and absence of uncertainty with high accuracy. It is well understood that a robust filter design is a compromise between the robustness and the estimation accuracy. In fact, a robust filter is designed to obtain an accurate and suitable performance in presence of modelling errors.So in the absence of any unknown or time-varying uncertainties, the robust filter does not provide the desired performance. The new method provided in this paper, which is named hybrid robust cubature Kalman filter (CKF), is constructed by combining a traditional CKF and a novel robust CKF. The novel robust CKF is designed by merging a traditional CKF with an uncertainty estimator so that it can provide the desired performance in the presence of uncertainty. Since the presence of uncertainty results in a large innovation value, the hybrid robust CKF adapts itself according to the value of the normalized innovation. The CKF and robust CKF filters are run in parallel and at any time, a suitable decision is taken to choose the estimated state of either the CKF or the robust CKF as the final state estimation. To validate the performance of the proposed filters, two examples are given that demonstrate their promising performance.
R. Grover and P. Y. C. Hwang, Introduction to random signals and applied Kalman filtering. Willey N. Y., 1992.
#[2] M. S. Grewal and A. P. Andrews, Kalman filtering: theory and practice using MATLAB. John Wiley & Sons, 2011.
#[3] I. Arasaratnam and S. Haykin, “Cubature Kalman filters,” IEEE Trans. On Autom. Control, vol. 54, no. 6, pp. 1254–1269, Jun. 2009.
#[4] I. Arasaratnam, “Cubature Kalman filtering: theory & applications,” Ph. D. Thesis, 2009.
#[5] B. Safarinejadian, M. A. Tajeddini, and A. Ramezani, “Predict time series using extended, unscented, and cubature Kalman filters based on feed-forward neural network algorithm,” 3rd International Conference on Control Instrumentation and Automation, (ICCIA), 2013, pp. 159–164.
#[6] M. Havlicek, K. J. Friston, J. Jan, M. Brazdil, and V. D. Calhoun, “Dynamic modeling of neuronal responses in fMRI using cubature Kalman filtering,” Neuroimage, vol. 56, no. 4, pp. 2109–2128, 2011.
#[7] D. Macagnano and G. T. F. de Abreu, “Multitarget tracking with the cubature Kalman probability hypothesis density filter,” Conference Record of the Forty Fourth Asilomar Conference on Signals, Systems and Computers (ASILOMAR), 2010, pp. 1455–1459.
#[8] K. P. B. Chandra, D.-W. Gu, and I. Postlethwaite, “Cubature Kalman filter based localization and mapping,” World Congress, 2011, pp. 2121–2125.
#[9] F. Yang, Z. Wang, and Y. Hung, “Robust Kalman filtering for discrete time-varying uncertain systems with multiplicative noises,” IEEE Trans. On Autom. Control, vol. 47, no. 7, pp. 1179-1183, 2002.
#[10] Z. Dong and Z. You, “Finite-horizon robust Kalman filtering for uncertain discrete time-varying systems with uncertain-covariance white noises,” IEEE Signal Process. Lett., vol. 13, no. 8, pp. 493–496, 2006.
#[11] U. Shaked and C. E. de Souza, “Robust minimum variance filtering,” IEEE Trans. On Signal Process., vol. 43, no. 11, pp. 2474–2483, 1995.
#[12] Y. Theodor and U. Shaked, “Robust discrete-time minimum-variance filtering,” IEEE Trans. On Signal Process., vol. 44, no. 2, pp. 181–189, 1996.
#[13] S. Habibi, “The smooth variable structure filter,” Proc. IEEE, vol. 95, no. 5, pp. 1026–1059, 2007.
#[14] S. Dey and J. B. Moore, “Risk-sensitive filtering and smoothing via reference probability methods,” IEEE Trans. On Autom. Control, vol. 42, no. 11, pp. 1587–1591, 1997.
#[15] H. Li and M. Fu, “A linear matrix inequality approach to robust H∞ filtering,” IEEE Trans. On Signal Process., vol. 45, no. 9, pp. 2338–2350, 1997.
#[16] R. S. Mangoubi, Robust estimation and failure detection: A concise treatment. Springer Science & Business Media, 2012.
#[17] L. Xie, Y. C. Soh, and C. E. de Souza, “Robust Kalman filtering for uncertain discrete-time systems,” IEEE Trans. On Autom. Control, vol. 39, no. 6, pp. 1310–1314, 1994.
#[18] S. J. Kwon, “Robust Kalman filtering with perturbation estimation process for uncertain systems,” IEE Proc.-Control Theory Appl., vol. 153, no. 5, pp. 600–606, 2006.
#[19] M. G. S. Bruno and A. Pavlov, “Improved sequential Monte Carlo filtering for ballistic target tracking,” IEEE Trans. On Aerosp. Electron. Syst., vol. 41, no. 3, pp. 1103–1108, 2005.
#[20] B. Teixeira, J. Chandrasekar, H. J. Palanthandalam-Madapusi, L. Torres, L. A. Aguirre, and D. S. Bernstein, “Gain-constrained Kalman filtering for linear and nonlinear systems,” IEEE Trans. On Signal Process., vol. 56, no. 9, pp. 4113–4123, 2008.
