Moving Horizon Estimation
Estimating the state of a dynamical system, at each sampling instant, from available measurements is fundamental in many engineering domains such as signal processing, learning and control. One powerful approach that addresses the state estimation problem of constrained linear and nonlinear systems is moving horizon estimation (MHE). The key idea of MHE is to compute a state estimate, at each sampling time, by solving online a suitable optimization problem that incorporates a fixed and limited number of the most recent measurements. As soon as a new measurement becomes available, the considered horizon of measurements is thus shifted forward in time, in a receding horizon fashion.
MHE can be computationally intensive since it involves the online solution of an optimization problem each time a new measurement becomes available. By contrast, desirable theoretical properties of MHE schemes, such as nominal stability and robustness of the estimation error in the presence of disturbances, are usually established based on the exact solution of the constrained optimization problem. Thus, there is a need for an efficient and real-time capable implementation of MHE algorithms with theoretical guarantees, where only a limited number of optimization algorithm iterations are executed at each sampling time.
The goal of our research is to develop theoretically sound and numerically efficient MHE approaches for a broad variety of system classes and performance criteria. This can be achieved within the novel framework of proximity moving horizon estimation (pMHE). It is based on the general conceptual idea of employing a stabilizing analytical a priori solution and combining it with an online optimization in order to obtain an improved performance without jeopardizing the stability properties. For example, using the well-known Extended Kalman Filter (EKF) as a prior estimate, the pMHE idea significantly improves the quality of the EKF estimates. We devote our attention to the theoretical analysis of MHE as well as to the practical challenge of computational efficiency. More specifically, we develop anytime proximity-based MHE algorithms, where stability of the resulting estimation error is guaranteed for any arbitrary number of optimization algorithm iterations.
Related Publications
| Title | Authors and Contributors |
|---|---|
| Anytime Proximity Moving Horizon Estimation: Stability and Regret (2021) Preprint | Gharbi, Meriem Gharesifard, Bahman Ebenbauer, Christian Johannes |
| Proximity Moving Horizon Estimation for Discrete-Time Nonlinear Systems In: IEEE control systems letters, 5 (2020), 6, 2090-2095 Journal Article [DOI: 10.1109/LCSYS.2020.3046377] | Gharbi, Meriem (Corresponding author) Bayer, Fabia Ebenbauer, Christian Johannes |
| Proximity moving horizon estimation for linear time-varying systems and a Bayesian filtering view In: 2019 IEEE 58th Conference on Decision and Control (CDC) / general chair: Carlos Canudas de Wit (CNRS GIPSA-Lab, France) (2019), 3208-3213 Contribution to a book, Contribution to a conference proceedings [DOI: 10.1109/CDC40024.2019.9029264] | Gharbi, Meriem (Corresponding author) Ebenbauer, Christian Johannes |