Inequality constrained parameter estimation using filtering approaches

• Development of inequality parameter constraints from steady state data.
• Implementation of parameter inequality constraints in recursive estimators and MHE.
• Two-stage approach to constrained parameter estimation.
• Initial unconstrained estimate followed by one-step constrained optimization.
• Improved estimation and control performance demonstrated on realistic processes.

Parameter estimation is usually approached by augmenting parameters to the states, leading to the simultaneous estimation of states and parameters. In practice, constraints on the values of the parameters can often be generated, and the incorporation of these constraints could improve the estimation performance. In this paper, we consider the inequality constrained parameter estimation problem. A new method of constructing inequality parameter constraints from routine operating data is introduced. Then, we introduce a framework for constraint implementation, based on first solving an unconstrained estimation problem and then a constrained problem, with recursive estimators such as the unscented Kalman filter (UKF) and the ensemble Kalman filter (EnKF); we also show that the same framework is applicable for moving horizon estimation (MHE). Then, we develop a method for constraint implementation for the UKF and the EnKF that yields faster convergence than the conventional projection method. Through simulations of two chemical processes, we show that the proposed method is able to provide fast recovery of state and parameter estimates from inaccurate initial guesses, leading to better estimation and control performance.