Correntropy estimator for data reconciliation

Constructing a reliable model for process monitoring, control and optimization requires accurate data satisfying balance equations of absolute validity, such as mass and energy balances. Under normal circumstances, process data are inaccurate since they are affected by random errors and possibly gross errors. A robust estimator for data reconciliation is needed to reduce the effect of gross errors and to yield less biased estimates, but most of the estimators are not robust enough to deal with gross errors. A novel robust estimator using correntropy, an information theoretic alternative to the traditional mean square error criterion, is proposed. As correntropy measures both the uncertainty and dispersion, it can be used as an optimality criterion in the estimation problems. By properly adjusting its kernel width, the effectiveness of this correntropy estimator can be tuned. The optimal kernel width value is chosen by minimizing Aikake information criterion. The results of two case studies demonstrate the advantages of using the correntropy estimator. The effectiveness of the proposed estimator is compared to several conventional methods, especially the quasi-weight least squares estimator, which does not have much computation load.