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http://dx.doi.org/10.5370/JEET.2015.10.3.1212

Kalman Randomized Joint UKF Algorithm for Dual Estimation of States and Parameters in a Nonlinear System  

Safarinejadian, Behrouz (Dept. of Control Engineering, Shiraz University of Technology)
Vafamand, Navid (Dept. of Control Engineering, Shiraz University of Technology)
Publication Information
Journal of Electrical Engineering and Technology / v.10, no.3, 2015 , pp. 1212-1220 More about this Journal
Abstract
This article presents a new nonlinear joint (state and parameter) estimation algorithm based on fusion of Kalman filter and randomized unscented Kalman filter (UKF), called Kalman randomized joint UKF (KR-JUKF). It is assumed that the measurement equation is linear. The KRJUKF is suitable for time varying and severe nonlinear dynamics and does not have any systematic error. Finally, joint-EKF, dual-EKF, joint-UKF and KR-JUKF are applied to a CSTR with cooling jacket, in which production of propylene glycol happens and performance of KR-JUKF is evaluated.
Keywords
Joint estimation; Kalman randomized joint UKF; Parameter estimation; CSTR;
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1 Hanif Tahersima, Mohammadjafar Saleh, Akram Mesgarisohani and Mohammadhossein Tahersima, “Design of stable model reference adaptive system via Lyapunov rule for control of chemical reactor,” 3rd Australian Control Conference (AUCC), Fremantle, WA, pp. 348-353, 2013.
2 Majdi Mansouri, Hazem Nounou and Mohamed Nounou, “State estimation of a chemical reactor process model - A comparative study,” 10th Int. Multi- Conf. Syst., Signals & Devices, pp. 1-6, 2013.
3 Rudolph E. Kalman, “A new approach to linear filtering and prediction problems,” Trans. ASME-J. Basic Eng., pp. 35-45, 1960.
4 Hazem N. Nouou and Mohamed N. Nounou, “Application of delay-dependent adaptive control to a continuous stirred tank reactor,” IEEE Symp. Comput. Intel. Cont. Auto. (CICA), Singapore, pp. 140-147, 2013.
5 Don Simon, “Optimal state estimation,” New Jersey: John Wiley & Sons, 2006.
6 J. Bellantoni, K. Dodge, “A square root formulation of the Kalman-Schmidt filter,” AIAA Journal, vol. 5, pp. 1309-1314, 1967.   DOI
7 Andrey Romanenko, Jose A. Castro, “The unscented filter as an alternative to the EKF for nonlinear state estimation: a simulation case study,” Comput. Chem. Eng., vol. 28, no. 3, pp. 347-355, 2004.   DOI   ScienceOn
8 Andrey Romanenko, Lino O. Santos and Paulo AFNA Afonso, “Unscented Kalman filtering of a simulated pH system,” Ind. Eng. Chem. Res., vol. 43, pp. 7531-7538, 2004.   DOI   ScienceOn
9 Rudolph Van der Merwe, Eric A. Wan and Simon Julier, “Sigma-point Kalman filters for nonlinear estimation and sensor-fusion-applications to integrated navigation,” AIAA, pp. 2004-5120, 2004.
10 Eric A. Wan and Rudolph Van der Merwe, “The unscented Kalman filter for nonlinear estimation,” Center for Spoken Language and Understanding, OGI School of Science and Engineering, 2006, URL: http://cslu.cse.ogi.edu/nsel/ukf/.
11 Eric A. Wan, Rudolph Van der Merwe and Alex T. Nelson, “Dual estimation and the unscented transformation,” Neural Inf. Proc. Syst., vol. 12, MIT Press, Massachusetts, USA, pp. 666-672, 2000.
12 Lawrence Nelson and Edwin Stear, “The simultaneous on-line estimation of parameters and states in linear systems,” IEEE Trans. Auto. Cont., pp. 438-442, 1967.
13 Stefano Mariani and Aldo Ghisi, “Unscented Kalman filtering for nonlinear structural dynamics,” Nonlinear Dyn., vol. 49, pp. 131-150, 2007.   DOI
14 Jindrich Dunik, Ondrej Straka and Miroslav Simandl, “The Development of a Randomised Unscented Kalman Filter,” 18th IFAC World Congress, pp. 8-13, Milano, Italy, 2011.
15 Henry Cox, “On the estimation of state variables and parameters for noisy dynamic systems,” IEEE Trans. Auto. Cont., vol. 9, pp. 5-12, 1964.   DOI
16 Jacek Czeczot, “Balance-based adaptive control methodology and its application to the non-isothermal CSTR,” Chem. Eng. Proc., pp. 359-371, 2006.
17 S. C. Stubberud and M. Owen, “Artificial neural network feedback loop with on-line training,” Proc. IEEE. Int. Symp. Intell. Cont. Dearborn, August, pp. 514-519, 1996.
18 Eric A. Wan and Alex T. Nelson, “Dual Kalman filtering methods for nonlinear prediction, estimation, and smoothing,” Adv. in Neural Inf. Proc. Syst. Vol. 9, Cambridge, MA: MIT Press, 1997.
19 Stefano Mariani and Alberto Corigliano, “Impact induced composite delamination: state a parameter identification via joint and dual extended Kalman filters,” Comput. Methods Appl. Mech. Eng., vol. 194, pp. 5242-5272, 2005.   DOI   ScienceOn
20 William L. Luyben, “Chemical reactor design and control,” New Jersey: John Wiley & Sons, 2007.
21 Richard E. Kopp and Richard J. Orford, “Linear regression applied to system identification for adaptive control systems,” AIAA Journal, vol. 1, no. 10, pp. 2300-2306, 1963.   DOI
22 Vinary A. Bavdekar, R. Bhushan Gopaluni and Sirish L. Shah, “Evaluation of Adaptive Extended Kalman Filter Algorithms for State Estimation in Presence of Model-Plant Mismatch”, 10th IFAC Int. Symp. Dyn. Cont. Proc. Syst., Mumbai, India, 2013.
23 Eric A. Wan and Alex T. Nelson, “Dual extended Kalman filter methods,” Kalman filtering and neural networks, pp. 123-173, 2001.
24 Hossein Khodadadi and Hooshang Jazayeri-Rad, “Applying a dual extended Kalman filter for the nonlinear state and parameter estimations of a continuous stirred tank reactor,” Comput. Chem. Eng., vol. 35, no. 11, pp. 2426- 2436, 2011.   DOI   ScienceOn
25 Li Meng, Liu Li, and S.M. Veres, “Aerodynamic Parameter Estimation of an Unmanned Aerial Vehicle Based on Extended Kalman Filter and Its Higher Order Approach,” Adv. Comput. Cont. (ICACC), 2nd Int. Conf., Vol. 5, pp. 526-531, March 2010, Shenyang, China.
26 Alan Genz and John Monahan, “A Stochastic Algorithm for High Dimensional Integrals over Unbounded Regions with Gaussian Weight,” J. Comput. Appl. Math, vol. 112, no. 1, pp. 71-81, 1999.   DOI   ScienceOn
27 M.F. Samadi, S.M. Alavi, and M. Saif, “Online state and parameter estimation of the Li-ion battery in a Bayesian framework,” American Control Conference (ACC), pp. 4693-4698, June 2013, Washington, DC.
28 Nader Meskin, Hazem Nounou, Mohamed Nounou, and A. Datta, “Parameter Estimation of Biological Phenomena: An Unscented Kalman Filter Approach,” IEEE/ACM Trans. Comput. Biol. Bioinforma., Vol. 10, No. 2, 2013.
29 Ji-Hoon Seung, Deok-Jin Lee and Kil-To Chong, “Parameter Estimation Method for Coupled Tank System using Dual Extended Kalman Filter,” 13th Int. Conf. Cont., Auto. Syst., pp. 1223-1228, Gwangju, Korea, October, 2013.
30 Ondrej Straka, Jindrich Dunik, and Mioslav Simandl, “Randomized unscented Kalman filter in target tracking,” 15th Int. Conf. Inf. Fusion (FUSION), pp. 503-510, Singapore, July 2012.