arXiv subjects

Angelo Alessandri

Publications and source records attributed to Angelo Alessandri.

3 recordsLinked to original sources

arXiv2025

Robust Moving-horizon Estimation for Nonlinear Systems: From Perfect to Imperfect Optimization

Robust stability of moving-horizon estimators is investigated for nonlinear discrete-time systems that are detectable in the sense of incremental input/output-to-state stability and are affected by disturbances. The estimate of a moving-horizon estimator stems from the on-line solution of a least-squares minimization problem at each time instant. The resulting stability guarantees depend on the optimization tolerance in solving such minimization problems. Specifically, two main contributions are established: (i) the robust stability of the estimation error, while supposing to solve exactly the on-line minimization problem; (ii) the practical robust stability of the estimation error with state estimates obtained by an imperfect minimization. Finally, the construction of such robust moving-horizon estimators and the performances resulting from the design based on the theoretical findings are showcased with two numerical examples.

eess.SY↗

arXiv2022

Robust Bayesian Inference for Moving Horizon Estimation

The accuracy of moving horizon estimation (MHE) suffers significantly in the presence of measurement outliers. Existing methods address this issue by treating measurements leading to large MHE cost function values as outliers, which are subsequently discarded. This strategy, achieved through solving combinatorial optimization problems, is confined to linear systems to guarantee computational tractability and stability. Contrasting these heuristic solutions, our work reexamines MHE from a Bayesian perspective, unveils the fundamental issue of its lack of robustness: MHE's sensitivity to outliers results from its reliance on the Kullback-Leibler (KL) divergence, where both outliers and inliers are equally considered. To tackle this problem, we propose a robust Bayesian inference framework for MHE, integrating a robust divergence measure to reduce the impact of outliers. In particular, the proposed approach prioritizes the fitting of uncontaminated data and lowers the weight of contaminated ones, instead of directly discarding all potentially contaminated measurements, which may lead to undesirable removal of uncontaminated data. A tuning parameter is incorporated into the framework to adjust the robustness degree to outliers. Notably, the classical MHE can be interpreted as a special case of the proposed approach as the parameter converges to zero. In addition, our method involves only minor modification to the classical MHE stage cost, thus avoiding the high computational complexity associated with previous outlier-robust methods and inherently suitable for nonlinear systems. Most importantly, our method provides robustness and stability guarantees, which are often missing in other outlier-robust Bayes filters. The effectiveness of the proposed method is demonstrated on simulations subject to outliers following different distributions, as well as on physical experiment data.

eess.SY↗

arXiv2020

Parameter Estimation of Fire Propagation Models Using Level Set Methods

The availability of wildland fire propagation models with parameters estimated in an accurate way starting from measurements of fire fronts is crucial to predict the evolution of fire and allocate resources for firefighting. Thus, we propose an approach to estimate the parameters of a wildland fire propagation model combining an empirical fire spread rate and level set methods to describe the evolution of the fire front over time and space. After validating the model, the estimation of parameters in the spread rate is performed by using fire front shapes measured at different time instants as well as wind velocity and direction, landscape elevation, and vegetation distribution. Parameter estimation is performed by solving an optimization problem, where the objective function to be minimized is the symmetric difference between predicted and measured fronts. Numerical results obtained by the application of the proposed method are reported in two simulated scenarios and in an application case study using real data of the 2002 Troy fire in Southern California, thus showing the effectiveness of the proposed approach.

math.NA↗