Cluster Computing

, Volume 20, Issue 4, pp 2919–2929 | Cite as

Robust and reliable estimation via recursive nonlinear dynamic data reconciliation based on cubature Kalman filter

  • Min Bian
  • Jianlin WangEmail author
  • Weimin Liu
  • Kepeng Qiu


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 



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).


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Copyright information

© Springer Science+Business Media New York 2017

Authors and Affiliations

  • Min Bian
    • 1
    • 2
  • Jianlin Wang
    • 1
    Email author
  • Weimin Liu
    • 1
  • Kepeng Qiu
    • 1
  1. 1.Beijing University of Chemical TechnologyBeijingPeople’s Republic of China
  2. 2.Beijing Institute of Graphic CommunicationBeijingPeople’s Republic of China

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