Dynamic system multivariate calibration

In the first part of the paper, the optimal estimator for normally nonmeasured primary outputs from a linear, time invariant and stable dynamic system is developed. The optimal estimator is based on all available information in known inputs and measured secondary outputs. Assuming sufficient experimental data, the optimal estimator can be identified by standard system identification (SI) methods, utilizing an output error (OE) model. It is then shown that least squares estimation (LSE) and multivariate calibration by means of principal component regression (PCR) or partial least squares regression (PLSR) can be seen as special static cases of such a dynamic SI. Finally, it is shown that dynamic system PCR and PLSR solutions can be developed as special cases of the general estimator for dynamic systems.