Robust Kalman Filtering Under Model Uncertainty: The Case of Degenerate Densities

• 成果类型: Article
• 署名作者: Yi, Shenglun; Zorzi, Mattia
• 署名单位: Beijing Institute of Technology; University of Padua
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2021.3106861
• 发表日期: 2022
• 页码: 3458-3471
• 关键词: Kalman filters; Symmetric matrices; STANDARDS; Filtering; uncertainty; Covariance matrices; CONVERGENCE; Contraction analysis; least favorable model; low-rank filtering; minimax problem; robust Kalman filtering

摘要

In this article, we consider a robust state-space filtering problem in the case that the transition probability density is unknown and possibly degenerate. The resulting robust filter has a Kalman-like structure and solves a minimax game: the nature selects the least favorable model in a prescribed ambiguity set, which also contains non-Gaussian probability densities, while the other player designs the optimum filter for the least favorable model. It turns out that the resulting robust filter is characterized by a Riccati-like iteration evolving on the cone of the positive-semidefinite matrices. Moreover, we study the convergence of such iteration in the case that the nominal model is with constant parameters on the basis of the contraction analysis in the same spirit of Bougerol. Finally, some numerical examples show that the proposed filter outperforms the standard Kalman filter.