Dynamic system multivariate calibration by system identification methods

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