Sequential Processing of Constraints

Consider in general the following set of m balance equations containing only measured variables  

As shown before, the general data reconciliation procedure for the overall system must solve the following constrained least squares problem  

because of the manner in which the balances arise, the total set of algebraic equations can be partitioned into two arbitrary subsystems. The first contains (m — a) equations and the second contains the remaining a equations, where a is an arbitrary number 1 a m. Note that the cases a = Ooi a = m correspond to the overall reconciliation problem. 

When the Lagrangian technique is used to solve the preceding problem, the least squares estimate of the measurement errors is given by 

for the covariance of the estimation error and the measurement estimates (see Appendix A) we have, respectively, 

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