A Unified Family-optimal Solution to Covariance Intersection Problems with Semidefinite Programming
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arXiv
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| Autori principali: | , , |
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| Natura: | Preprint |
| Pubblicazione: |
2026
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| _version_ | 1866915878130417664 |
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| author | Pedroso, Leonardo Heemels, W. P. M. H. Batista, Pedro |
| author_facet | Pedroso, Leonardo Heemels, W. P. M. H. Batista, Pedro |
| contents | Covariance intersection (CI) methods provide a principled approach to fusing estimates with unknown cross-correlations by minimizing a worst-case measure of uncertainty that is consistent with the available information. This paper introduces a generalized CI framework, called overlapping covariance intersection (OCI), which unifies several existing CI formulations within a single optimization-based framework. This unification enables the characterization of family-optimal solutions for multiple CI variants, including standard CI and split covariance intersection (SCI), as solutions to a semidefinite program, for which efficient off-the-shelf solvers are available. When specialized to the corresponding settings, the proposed family-optimal solutions recover the state-of-the-art family-optimal solutions previously reported for CI and SCI. The resulting formulation facilitates the systematic design and real-time implementation of CI-based fusion methods in large-scale distributed estimation problems, such as cooperative localization. |
| format | Preprint |
| id |
arxiv_https___arxiv_org_abs_2603_20402 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | A Unified Family-optimal Solution to Covariance Intersection Problems with Semidefinite Programming Pedroso, Leonardo Heemels, W. P. M. H. Batista, Pedro Systems and Control Signal Processing Covariance intersection (CI) methods provide a principled approach to fusing estimates with unknown cross-correlations by minimizing a worst-case measure of uncertainty that is consistent with the available information. This paper introduces a generalized CI framework, called overlapping covariance intersection (OCI), which unifies several existing CI formulations within a single optimization-based framework. This unification enables the characterization of family-optimal solutions for multiple CI variants, including standard CI and split covariance intersection (SCI), as solutions to a semidefinite program, for which efficient off-the-shelf solvers are available. When specialized to the corresponding settings, the proposed family-optimal solutions recover the state-of-the-art family-optimal solutions previously reported for CI and SCI. The resulting formulation facilitates the systematic design and real-time implementation of CI-based fusion methods in large-scale distributed estimation problems, such as cooperative localization. |
| title | A Unified Family-optimal Solution to Covariance Intersection Problems with Semidefinite Programming |
| topic | Systems and Control Signal Processing |
| url | https://arxiv.org/abs/2603.20402 |