Geometric estimation of nonlinear process systems

An estimation approach to jointly design the estimation model, data assimilation structure, and algorithm in the light of particular estimation objectives is developed within a constructive framework. On the basis of the detectability property which underlies the Lie derivative-based geometric estimator (GE) in conjunction with singular perturbation and robust stability tools, the GE is redesigned to remove its Lie derivation applicability obstacle. Then, the equivalence between the GE and the extended Kalman filter (EKF) is established, and the GE is endowed with uncertainty assessment capability. The resulting GE has: (i) a simple construction in terms of model Jacobians, (ii) a nonlocal convergence criterion coupled with easy to apply tuning guidelines, and (iii) the model and its detectability structure as key design degrees of freedom. The proposed methodology is illustrated and tested with an experimental binary distillation column.