A Comparison of Moving Horizon and Bayesian State Estimators with an Application to a pH Process

Abstract The moving horizon estimator (MHE) formulation utilizes a window of measurements to compute the estimates of the states in that particular window. This approach leads to smoothing of the state estimates included in the window, since future information is used to compute the same. However, the effect of smoothing, in the MHE algorithm, on the state estimates has not been studied in the literature. In this work the performance of the MHE is compared with recursive Bayesian state estimators (such as UKF, EnKF) to study the effect of the moving window of the past data on the quality of state estimates, via an application on a benchmark pH simulation case study. The simulations are carried out for two scenarios–the ideal case and the case with a parametric model-plant mismatch. The results obtained indicate that the use of MHE results in improved state estimates when compared to the recursive Bayesian state estimators, but does not help compensate for model-plant-mismatch.

[1]  Sirish L. Shah,et al.  Nonlinear Bayesian state estimation: A review of recent developments , 2012 .

[2]  L. Biegler,et al.  Constrained particle filter approach to approximate the arrival cost in Moving Horizon Estimation , 2011 .

[3]  Sirish L. Shah,et al.  Constrained Nonlinear State Estimation Using Ensemble Kalman Filters , 2010 .

[4]  S. Ungarala.  Computing arrival cost parameters in moving horizon estimation using sampling based filters , 2009 .

[5]  Juergen Hahn,et al.  Computation of arrival cost for moving horizon estimation via unscented Kalman filtering , 2009 .

[6]  Victor C. M. Leung,et al.  Unscented Rauch--Tung--Striebel Smoother , 2008, IEEE Transactions on Automatic Control.

[7]  Prem K. Goel,et al.  Bayesian estimation via sequential Monte Carlo sampling - Constrained dynamic systems , 2007, Autom..

[8]  P. Vachhani,et al.  Robust and reliable estimation via Unscented Recursive Nonlinear Dynamic Data Reconciliation , 2006 .

[9]  G. Evensen.  Data Assimilation: The Ensemble Kalman Filter , 2006 .

[10]  Raghunathan Rengaswamy,et al.  Recursive estimation in constrained nonlinear dynamical systems , 2005 .

[11]  Jeffrey K. Uhlmann,et al.  Unscented filtering and nonlinear estimation , 2004, Proceedings of the IEEE.

[12]  Paulo Afonso,et al.  Unscented Kalman Filtering of a Simulated pH System , 2004 .

[13]  C. V. Rao,et al.  Constrained process monitoring: Moving‐horizon approach , 2002 .

[14]  Jay H. Lee,et al.  Constrained linear state estimation - a moving horizon approach , 2001, Autom..

[15]  N. Gordon,et al.  Novel approach to nonlinear/non-Gaussian Bayesian state estimation , 1993 .

[16]  H. W. Sorenson,et al.  Kalman filtering : theory and application , 1985 .

[17]  Arthur Gelb,et al.  Applied Optimal Estimation , 1974 .

[18]  C. Striebel,et al.  On the maximum likelihood estimates for linear dynamic systems , 1965 .