Dynamic validation of on-line measurements: A probabilistic analysis

Dynamic systems, such as industrial production processes, are measured indirectly with fast on-line measurements. Occasionally, more direct and accurate measurements are made in laboratory to validate the on-line measurements. We discuss the optimal dynamic estimation of the parameters of characteristic curves under the assumption that their validity deteriorates through a stochastic process, describable through a stochastic differential equation. We provide the general formalism and an easy-to-implement algorithm for Gaussian distributions of measurement errors and random-walk deterioration of parameter validity. Furthermore, we analyze the dynamic estimation of the measurand given the earlier information about it deteriorates through (another) stochastic differential equation, and show the effect of uncertainty in the parameters of characteristic curve.