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==History==
DVR has become more and more important due to industrial processes that are becoming more and more complex. DVR started in the early 1960s with applications aiming at closing [[mass balance|material balances]] in production processes where raw measurements were available for all [[variable (mathematics)|variables]].<ref>D.R. Kuehn, H. Davidson, ''Computer Control II. Mathematics of Control'', Chem. Eng. Process 57: 44–47, 1961.</ref> At the same time the problem of [[systematic error|gross error]] identification and elimination has been presented.<ref>V. Vaclavek, ''Studies on System Engineering I. On the Application of the Calculus of the Observations of Calculations of Chemical Engineering Balances'', Coll. Czech Chem. Commun. 34: 3653, 1968.</ref> In the late 1960s and 1970s unmeasured variables were taken into account in the data reconciliation process.,<ref>V. Vaclavek, M. Loucka, ''Selection of Measurements Necessary to Achieve Multicomponent Mass Balances in Chemical Plant'', Chem. Eng. Sci. 31: 1199–1205, 1976.</ref><ref name="Mah-Stanley-Downing-1976">[
,<ref name="Stanley-Mah-1977">G.M. Stanley and R.S.H. Mah, [http://gregstanleyandassociates.com/AIChEJ-1977-EstimationInProcessNetworks.pdf ''Estimation of Flows and Temperatures in Process Networks'', AIChE Journal 23: 642–650, 1977.]</ref><ref>P. Joris, B. Kalitventzeff, ''Process measurements analysis and validation'', Proc. CEF’87: Use Comput. Chem. Eng., Italy, 41–46, 1987.</ref> Quasi steady state dynamics for filtering and simultaneous parameter estimation over time were introduced in 1977 by Stanley and Mah.<ref name="Stanley-Mah-1977"/> Dynamic DVR was formulated as a nonlinear optimization problem by Liebman et al. in 1992.<ref>M.J. Liebman, T.F. Edgar, L.S. Lasdon, ''Efficient Data Reconciliation and Estimation for Dynamic Processes Using Nonlinear Programming Techniques'', Computers Chem. Eng. 16: 963–986, 1992.</ref>▼
▲<ref>P. Joris, B. Kalitventzeff, ''Process measurements analysis and validation'', Proc. CEF’87: Use Comput. Chem. Eng., Italy, 41–46, 1987.</ref> Quasi steady state dynamics for filtering and simultaneous parameter estimation over time were introduced in 1977 by Stanley and Mah.<ref name="Stanley-Mah-1977"/> Dynamic DVR was formulated as a nonlinear optimization problem by Liebman et al. in 1992.<ref>M.J. Liebman, T.F. Edgar, L.S. Lasdon, ''Efficient Data Reconciliation and Estimation for Dynamic Processes Using Nonlinear Programming Techniques'', Computers Chem. Eng. 16: 963–986, 1992.</ref>
==Data reconciliation==
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