Joint Localization Based on Split Covariance Intersection on the Lie Group

This article presents a pose fusion method that accounts for the possible correlations among measurements. The proposed can handle data problems whose uncertainty has both independent and dependent parts. Different from existing methods, uncertainties of various states or measurements are modeled on Lie algebra projected to manifold through exponential map, which is more precise than in vector space. correlation based theory covariance intersection, where parts split yield consistent result. In this article, we provide novel correlated algorithm manifold. Theoretical derivation analysis detailed first, then, experimental results presented support theory. main contributions threefold: First, theoretical foundation intersection filter performed manifold, associated with algebra. Second, gives an explicit formalism $ \text{SE}(3)$ \text{SE}(2)$ , covers most use cases field robotics. Third, present localization framework work single-robot multirobot systems, not only derived but also state evolution relative computation validate advantage approach over state-of-the-art methods.