Abstract
Abstract Soft sensors are increasingly being used to estimate difficult to measure variables using using a mathematical model and other easily measured variables. Partial Least Squares and Principal Components Regression are two popular methods for developing the linear models used in soft sensors. However, the optimality of these methods has not been established. In this article, we develop a soft sensing technique by combining PCA with conecpts drawn from Data Reconciliation techniques. The solution we propose is a mathematically rigorous approach to the problem when the measurements are corrupted with homoscedastic or heteroscedastic errors.
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