A Unified Family-optimal Solution to Covariance Intersection Problems with Semidefinite Programming
This work provides a systematic approach for improving distributed estimation in applications like cooperative localization, though it is incremental as it builds on and unifies prior covariance intersection methods.
The paper tackles the problem of fusing estimates with unknown cross-correlations by introducing a generalized covariance intersection framework called overlapping covariance intersection (OCI), which unifies existing methods and enables family-optimal solutions via semidefinite programming, recovering state-of-the-art results.
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.