ON FINDING THE MATRIX PROJECTION IN THE DATA RECONCILIATION SOLUTION

The focus of this note is to highlight two relatively simple approache s to determine the matrix projection first introduced by Crowe et al. (1983) to solve data reconciliation problems when unmeasured variables exist. The first method uses recursive matrix inversion by partition where the second uses a modified Cholesky factorization. The purpose o f the two algorithms is to identify dependent columns and rows in the topology matrix of the unmeasured variables where the matrix projectio n is then formulated. Although other methods are available to determin e the nullity of a matrix such as QR factorization and singular value decomposition, it is preferred to use this identification procedure al ong with Crowe's matrix projection formulation because of its numerica l efficiency, simplicity and interpretation. Two mass reconciliation e xamples are presented, one small and one large, to clarify and verify the techniques. (C) 1998 Elsevier Science Ltd. All rights reserved.