Li, L; Yang, M; (2021) Joint Localization Based on Split Covariance Intersection on the Lie Group. IEEE Transactions on Robotics , 37 (5) pp. 1508-1524. 10.1109/TRO.2021.3063455.

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Abstract

This paper presents a pose fusion method that accounts for the possible correlations among measurements. The proposed method can handle data fusion problems whose uncertainty has both independent part and dependent part. Different from the existing methods, the uncertainties of the various states or measurements are modeled on the Lie algebra and projected to the manifold through the exponential map, which is more precise than that modeled in the vector space. The dealing of the correlation is based on the theory of covariance intersection, where the independent and dependent parts are split to yield a more consistent result. In this paper, we provide a novel method for correlated pose fusion algorithm on the manifold. Theoretical derivation and analysis are detailed first, and then the experimental results are presented to support the proposed theory. The main contributions are threefold: (1) We provide a theoretical foundation for the split covariance intersection filter performed on the manifold, where the uncertainty is associated on the Lie algebra. (2) The proposed method gives an explicit fusion formalism on SE(3) and SE(2), which covers the most use cases in the field of robotics. (3) We present a localization framework that can work both for single robot and multi-robots systems, where not only the fusion with possible correlation is derived on the manifold, the state evolution and relative pose computation are also performed on the manifold. Experimental results validate its advantage over state-of-the-art methods.

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