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Presented in this short document is a description of what is called Advanced Process Monitoring (APM) as described by Hedengren (2013). APM is the term given to the technique of estimating unmeasured but observable variables or "states" using statistical data reconciliation and regression (DRR) in an off-line or real-time environment and is also referred to as Moving Horizon Estimation (MHE) (Robertson et. al., 1996). Essentially, the model and data define a simultaneous nonlinear and dynamic DRR problem where the model is either engineering-based (first-principles, fundamental, mechanistic, causal, rigorous) or empirical-based (correlation, statistical data-based, observational, regressed) or some combination of both (hybrid).