Hybrid Performance Bounds for Lie Group and Integer Parameters: Application to GNSS Attitude Estimation

• 成果类型: Article
• 署名作者: Labsir, Samy; Medina, Daniel; Vila-Valls, Jordi; Renaux, Alexandre; Chaumette, Eric
• 署名单位: Helmholtz Association; German Aerospace Centre (DLR); Communaute d'universites et etablissements de Toulouse (Comue); Institut Superieur de l'Aeronautique et de l'Espace (ISAE-SUPAERO); Universite de Toulouse (EPE); Institut Superieur de l'Aeronautique et de l'Espace (ISAE-SUPAERO); Universite Paris Saclay
• 刊物名称: IEEE TRANSACTIONS ON AUTOMATIC CONTROL
• ISSN/ISSBN: 0018-9286
• DOI: 10.1109/TAC.2025.3640486
• 发表日期: 2026
• 关键词: CRAMER-RAO BOUNDS

摘要

The estimation of a mixture of real-and integer-valued parameter vectors appears in different control and signal processing applications. In some particular cases, for instance when dealing with covariance or rotation matrices, the real parameter must be constrained by geometrical properties. This article considers the general estimation problem containing both Lie group and integer parameters, for which the corresponding performance bound is a important missing tool. Leveraging recent results on the Cramer-Rao bound (CRB) for a mixture of real/integer parameters and the CRB for matrix Lie groups, the aim is twofold: To derive new performance lower bounds (McAulay-Seidman bound and CRB) on the Lie group-integer space, and to obtain a closed-form CRB expression for multiantenna Global Navigation Satellite Systems attitude estimation, where observations depend on both an integer carrier phase ambiguity vector and a rotation matrix lying on the Lie group SO(3). The proposed bound is validated through numerical simulations in a realistic scenario to support the discussion.