Suboptimal Nonlinear Moving Horizon Estimation

In this article, we propose a suboptimal moving horizon estimator for a general class of nonlinear systems. For the stability analysis, we transfer the feasibility-implies-stability/robustness paradigm from model predictive control to the context of moving horizon estimation in the following sense. Using a suitably defined, feasible candidate solution based on an auxiliary observer, robust stability of the proposed suboptimal estimator is inherited independently of the horizon length and even if no optimization is performed. Moreover, the proposed design allows for the choice between two cost functions different in structure: the former in the manner of a standard least squares approach, which is typically used in practice, and the latter following a time-discounted modification, resulting in better theoretical guarantees. We apply the proposed suboptimal estimator to a nonlinear chemical reactor process, verify the theoretical assumptions, and show that even a few iterations of the optimizer are sufficient to significantly improve the estimation results of the auxiliary observer. Furthermore, we illustrate the flexibility of the proposed design by employing different solvers and compare the performance with two state-of-the-art fast moving horizon estimation schemes from the literature.

Automated summary

In this article, a suboptimal moving horizon estimator for nonlinear systems is proposed. The feasibility-implies-stability/robustness paradigm is transferred from model predictive control to moving horizon estimation, ensuring robust stability of the estimator. The design allows for the choice between a standard least squares approach and a time-discounted modification for improved theoretical guarantees. The proposed estimator is applied to a nonlinear chemical reactor process, showing significant improvement in estimation results with just a few iterations of the optimizer. Different solvers are employed to illustrate the flexibility of the design, and performance is compared with state-of-the-art fast moving horizon estimation schemes.