Since measurements of process variables are subject to measurements errors as well as process variability, data reconciliation is the procedure of optimally adjusting measured date so that the adjusted values obey the conservation laws and constraints. Thus, data reconciliation for dynamic systems is fundamental and important for control, fault detection, and system optimization. Attempts to successfully implement estimators are often hindered by serve process nonlinearities, complicated state constraints, and un-measurable perturbations. As a constrained minimization problem, the dynamic data reconciliation is dynamically carried out to product smoothed estimates with variances from the original data. Many algorithms are proposed to solve such state estimation such as the extended Kalman filter (EKF), the unscented Kalman filter, and the cubature Kalman filter (CKF). In this paper, we investigate the use of CKF algorithm in comparative with the EKF to solve the nonlinear dynamic data reconciliation problem. First we give a broad overview of the recursive nonlinear data dynamic reconciliation (RNDDR) scheme, then present an extension to the CKF algorithm, and finally address the issue of how to solve the constraints in the CKF approach. The CCRNDDR method is proposed by applying the RNDDR in the CKF algorithm to handle nonlinearity and algebraic constraints and bounds. As the sampling idea is incorporated into the RNDDR framework, more accurate estimates can obtained via the recursive nature of the estimation procedure. The performance of the CKF approach is compared with EKF and RNDDR on nonlinear process systems with constraints. The conclusion is that with an error optimization solution of the correction step, the reformulated CKF shows high performance on the selection of nonlinear constrained process systems. Simulation results show the CCRNDDR is an efficient, accurate and stable method for real-time state estimation for nonlinear dynamic processes.
Data reconciliation Nonlinear estimation Cubature Kalman filter Constrained optimization Nonlinear dynamic data reconciliation
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The authors would like to acknowledge the supports by Natural Science Foundation of Beijing (No. 4152041) and National Natural Science Foundation of China (No.61240047).
Vachhani, Pramod, Narasimhan, Shankar, Rengaswamy, Raghunathan: Robust and reliable estimation via unscented recursive nonlinear dynamic data reconciliation. J. Process Control 16, 1075–1086 (2006)CrossRefGoogle Scholar
Bai, Shuanghua, Thibault, Julies, McLean, David D.: Dynamic data reconciliation: alternative to Kalman filter. J. Process Control 16, 485–498 (2006)CrossRefGoogle Scholar
Kadu, S.C., Bhushan, M., Gudi, R., Roy, K.: Modified unscented recursive nonlinear dynamic data reconciliation for constrained state estimation. J. Process Control 20, 525–537 (2010)CrossRefGoogle Scholar
Mandela, R.K., Kuppuraj, V., Rengaswamy, R., Narasimhan, S.: Constrained unscented recursive estimator for nonlinear dynamic systems. J. Process Control 22, 718–728 (2012)CrossRefGoogle Scholar
WenlingLi, ShihaoSun, YingminJia, JunpingDu: Robust unscented Kalman filter with adaptation of process and measurement noise covariances. Digit. Signal Proc. 48, 93–103 (2016)CrossRefMathSciNetGoogle Scholar
Wang, Xiaoxu, Liang, Yan, Pan, Quan, Zhao, Chunhui, Yang, Feng: Design and implementation of Gaussian filter for nonlinear system with randomly delayed measurements and correlated noises. Appl. Math. Comput. 232, 1011–1024 (2014)MathSciNetGoogle Scholar
Julier, S.J., Uhlman, J.K.: Unscented filtering and nonlinear estimation. Proc. IEEE 92, 401–422 (2004)CrossRefGoogle Scholar
Chitralekha, S.B., Prakash, J., Raghavan, H.: A comparison of simultaneous state and parameter estimation for a continuous fermentor reactor. J. Process Control 20, 934–943 (2010)CrossRefGoogle Scholar
Arasaratnam, I., Haykin, S., Hurd, T.R.: Cubature Kalman filtering for continuous-discrete systems: theory and simulations. IEEE Trans Signal Process 58(10), 4977–4993 (2010)CrossRefMathSciNetGoogle Scholar
Gadsden, S.A., AI-Shabi, M., Arasaratnam, I., Habibi, S.R.: Combined cubature Kalman and smooth variable structure filtering: a robust nonlinear estimation strategy. Signal Process. 96, 290–299 (2014)CrossRefGoogle Scholar
Kolås, S., Foss, B., Schei, T.: Constrained nonlinear state estimation based on the UKF approach. Comput. Chem. Eng. 33, 1368–1401 (2009)CrossRefGoogle Scholar
Liqiang, Zhao, Wang Jianlin, Yu., Tao, Jian Huan, Tangjiang, Liu: Design of adaptive robust square-root cubature Kalman filter with noise statistic estimator. Appl. Math. Comput. 256, 352–367 (2015)CrossRefzbMATHMathSciNetGoogle Scholar
Vachhani, P., Narasimhan, S., Rengaswamy, R.: Robust and reliable Estimation via unscented recursive nonlinear dynamic data reconciliation. J. Process Control 16, 1075–1086 (2006)CrossRefGoogle Scholar
Vachhani, P., Rengaswamy, R., Gangwal, V., Narasimhan, S.: Recursive estimation in constrained nonlinear dynamical systems. AIChE J. 51, 946–959 (2005)CrossRefGoogle Scholar
Leong, P.H., Arulampalam, S., Lamahewa, T.A., Abhayapala, T.D.: A Gaussian-sum based cubature Kalman filter for bearings-only tracking. IEEE Trans. Aerosp. Elec. Syst 49(2), 1161–1176 (2013)CrossRefGoogle Scholar
Haseltine, E., Rawlings, J.: Critical evaluation of extended Kalman filtering and moving horizon estimation. Ind. Eng. Chem. Res. 8, 2451–2460 (2005)CrossRefGoogle Scholar