Investigation on the commonality and consistency among data fusion algorithms with unknown cross-covariances and an improved algorithm

• Published in: Advances in space research Vol. 67; no. 7; pp. 2044 - 2057
• Main Authors: Liu, Baoyu, Zhan, Xingqun, Gao, Yang
• Format: Journal Article
• Language: English
• Published: Elsevier B.V 01.04.2021
• Subjects: Consistency; Convex combination; Covariance intersection; Ellipsoidal intersection; GNSS; Largest ellipsoid; Convex combination; Largest ellipsoid; Ellipsoidal intersection; GNSS; Consistency; Covariance intersection
• ISSN: 0273-1177; 1879-1948
• DOI: 10.1016/j.asr.2021.01.006

•Strong commonality in principle exists among CI, CC, LE and EI fusion algorithms.•Consistency of CC, LE and EI algorithms are very dependent on correlation levels.•Separately fuse each dimension of the state can improve the consistency performance.•Fusion algorithm for different applications can be selected according to correlation. The cross-covariances among local sensor estimates are usually unknown or can’t be accurately known in multi-sensor systems. The Covariance Intersection (CI), Convex Combination (CC), Largest Ellipsoid (LE) and Ellipsoidal Intersection (EI) algorithms have been developed for the estimate fusion with unknown cross-covariances. In this contribution, we reveal a strong commonality in principle among CI, CC, LE and EI algorithms after a transformation into a new Euclidean space, although each algorithm is designed based on different criteria. We also assess the consistencies of CC, LE and EI algorithms under different conditions which have been found significantly dependent on the correlation level among local estimates. All the CI, CC, LE and EI algorithms have the capability to enhance consistency or accuracy but at a cost of accuracy or consistency. Based on the commonality and consistency features among different algorithms, an improved algorithm is presented which can significantly improve the consistency performance at a very little expense of accuracy. The theoretical analysis and the fusion algorithm selection strategy are testified through simulated examples and the fusion of GPS and GLONASS horizontal position solutions.