Many advanced approaches have been developed for on-line optimization and control of industrial processes. The realization of these approaches requires the information about the actual state of the processes. It is usually assumed that the state can be gained through measuring essential process variables. In many cases, however, it is not possible to measure all required variables, especially in on-line applications where a frequent update of measurements is necessary. A broad variety of methods have been proposed to address this problem, ranging from structural or non-structural observability analysis to various kinds of state observers such as the extended Kalman filter. The drawback of these methods lies in the fact that they either give only information about which variables should be additionally measured so as to be able to compute the unmeasured variables (with the method of structural observability analysis) or are only applicable to linear or linearized process models (with the method of state observers).

In this work, we propose an optimization-based approach to improve the identifiability of nonlinear large-scale systems. The basic idea is to utilize the available but not sufficient data of the measured variables to infer unmeasured variables based on a detailed nonlinear process model. The residual of the measured data to the computed values according to the model is to be minimized. Due to the nonlinearity of the model the sensitivity of the measured variables to the unmeasured variables strongly influences the estimation quality and a poor scaling may even lead to a wrong result. Therefore, the weighting matrix in the objective function plays a key role and has to be carefully chosen. We include the information of the sensitivity of the measured variables to the unmeasured variables in the estimation procedure. In addition, we apply a pre-scaling of the weighting matrix by using a sequential nonlinear optimization approach. Correction-terms of the weighting matrix will be computed based on the problem information matrix and the size of the inference regions will be minimized. The approach proposed not only can improve the identifiability but also gives information about which variables have the highest potential to increase the quality of the state estimation. To show the efficiency and applicability of the proposed approach, diverse case studies with different complexity will be presented to illustrate the analytical steps.