Revisiting Split Covariance Intersection: Correlated Components and Optimality

• 成果类型: Article
• 署名作者: Cros, Colin; Amblard, Pierre-Olivier; Prieur, Christophe; Da Rocha, Jean-Francois
• 署名单位: Universite de Toulouse; Communaute Universite Grenoble Alpes; Institut National Polytechnique de Grenoble; Universite Grenoble Alpes (UGA); Centre National de la Recherche Scientifique (CNRS); Thales Group
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3530854
• 发表日期: 2025
• 页码: 4593-4607
• 关键词: VECTORS; estimation error; Covariance matrices; Upper bound; noise; Ellipsoids; cost function; Symmetric matrices; Simultaneous localization and mapping; reviews; Conservative fusion; linear estimation; split covariance intersection (SCI)

摘要

Linear fusion is a cornerstone of estimation theory. Implementing optimal linear fusion requires knowledge of the covariance of the vector of errors associated with all the estimators. In distributed or cooperative systems, the cross-covariance terms cannot be computed, and to avoid underestimating the estimation error, conservative fusions must be performed. A conservative fusion provides a fused estimator with a covariance bound that is guaranteed to be larger than the true, but computationally intractable, covariance of the error. Previous research by (Reinhardt et al., 2013, 2015) proved that if no additional assumption is made about the errors of the estimators, the minimal bound for fusing two estimators is given by a fusion called covariance intersection (CI). In distributed systems, the estimation errors contain independent and correlated terms induced by the measurement noises and the process noise. In this case, CI is no longer the optimal method. Split covariance intersection (SCI) has been developed to take advantage of the uncorrelated components. This article extends SCI to also take advantage of the correlated components. Then, it is proved that the new fusion provides the optimal conservative fusion bounds for two estimators, generalizing the optimality of CI to a wider class of fusion schemes. The benefits of this extension are demonstrated in simulations.