Pathfollowing approach for a sensitivity based moving horizon estimator

In moving horizon estimation (MHE), a computationally expensive nonlinear program (NLP) is solved at each sampling time to determine the current state of the system. To overcome the computational challenges, an advanced-step MHE (asMHE) framework has been proposed in the literature. asMHE consists of a computationally expensive offline part and a fast NLP sensitivity based online part. We propose a predictor-corrector pathfollowing method for the online part within asMHE. In this method, we solve a few quadratic programs sequentially in order to follow the optimal solution of the NLP for tracking a parameter change, which is the difference between a predicted measurement value and the real measurement value corresponding to the latest sample. This allows it to track the active set changes as they occur. To demonstrate the method, we performed simulations on a gas phase three component batch reaction model. We compare the solutions from the ideal-MHE and the pathfollowing based MHE. The results indicate that the pathfollowing based MHE is able to effectively trace the exact solution and the changes in active set in an efficient manner.