Preferential Estimation via Tuning of the Kalman Filter

Abstract Estimation problems have been traditionally formulated so as to minimize the estimation error of the full state vector. However, in applications that involve the tracking of only a few unmeasured variables, it is sufficient to limit the attention along certain directions in state space. This way, it is hoped that better accuracy can be obtained along the desired directions, possibly at the cost of poorer estimates along the other directions. This problem, termed preferential estimation, is formally formulated in this paper as a least-squares minimization problem. Using calibration measurements of the preferred variables, the above mentioned problem is solved numerically via tuning of the Kalman filter. The approach is illustrated in simulation on the optimization of a penicillin fermentation process, where preferential estimation is used successfully to reduce the error in tracking a single unmeasured variable, the substrate concentration.

[1]  Francis J. Doyle,et al.  Nonlinear inferential control for process applications , 1997 .

[2]  Guanrong Chen,et al.  Introduction to random signals and applied Kalman filtering, 2nd edn. Robert Grover Brown and Patrick Y. C. Hwang, Wiley, New York, 1992. ISBN 0‐471‐52573‐1, 512 pp., $62.95. , 1992 .

[3]  T. Başar,et al.  A New Approach to Linear Filtering and Prediction Problems , 2001 .

[4]  Dominique Bonvin,et al.  Dynamic optimization of batch processes: I. Characterization of the nominal solution , 2003, Comput. Chem. Eng..

[5]  Christopher R. Houck,et al.  A Genetic Algorithm for Function Optimization: A Matlab Implementation , 2001 .

[6]  and Charles K. Taft Reswick,et al.  Introduction to Dynamic Systems , 1967 .

[7]  Mohinder S. Grewal,et al.  Kalman Filtering: Theory and Practice , 1993 .

[8]  R. E. Kalman,et al.  A New Approach to Linear Filtering and Prediction Problems , 2002 .

[9]  M. Soroush.  Nonlinear state-observer design with application to reactors , 1997 .

[10]  Thomas F. Edgar,et al.  An improved method for nonlinear model reduction using balancing of empirical gramians , 2002 .

[11]  Denis Dochain,et al.  State and parameter estimation in chemical and biochemical processes: a tutorial , 2003 .

[12]  Arthur E. Hoerl,et al.  Ridge Regression: Biased Estimation for Nonorthogonal Problems , 2000, Technometrics.

[13]  Sirish L. Shah,et al.  Modeling and control of multivariable processes: Dynamic PLS approach , 1997 .

[14]  Zoltan K. Nagy,et al.  Using genetic algorithm in robust nonlinear model predictive control , 2001 .

[15]  Guanrong Chen,et al.  Kalman Filtering with Real-time Applications , 1987 .